Profit, Loss and Discount

C.P. of 10 articles = ₹ 40

C.P. of 1 article = ₹ $\frac{40}{10}$ = ₹ 4

S.P. of 1 article = ₹ 5

(∵ S.P. is greater than C.P., means article is sold at a profit.)

Profit = S.P. - C.P.

= ₹ 5 - ₹ 4 = ₹ 1

$\text{Profit}$% $= \frac{\text{Profit}}{\text{C.P.}} \times 100$ %

$= \frac{1}{4} \times 100$ %

$= \frac{100}{4}$ %

$= 25$ %

Hence, option 2 is the correct option.

Lets take the C.P. of table to be ₹ $100$.

S.P. of table = ₹ $80%$ of cost price.

$$\begin{aligned}\text{S.P.}= ₹\Big(\frac{80}{100} \times 100\Big) \\[1em] = ₹\Big(\frac{80}{\cancel{100}} \times \cancel{100}\Big) \\[1em] = ₹ 80\end{aligned}$$

(∵ C.P. is greater than S.P., means table is sold at a loss.)

Loss = C.P. - S.P.

= ₹ 100 - ₹ 80 = ₹ 20

$\text{Loss}$% $= \frac{\text{Loss}}{\text{C.P.}} \times 100$%

$= \frac{20}{100} \times 100$%

$= \frac{20}{\cancel{100}} \times \cancel{100}$%

$= 20$%

Hence, option 1 is the correct option.

Given:

C.P. = ₹ 150

Loss = ₹ 50

Loss = C.P. - S.P.

Putting the values, we get

₹ 50 = ₹ 150 - S.P.

S.P. = ₹ 150 - ₹ 50

= ₹ 100

Hence, option 2 is the correct option.

Given:

C.P. = ₹ 150

Loss % = 50%

$\text{Loss}$ % $= \frac{\text{Loss}}{\text{C.P.}} \times \text{100}$

Putting the values, we get

$$\begin{aligned}\Rightarrow\text{50} = \frac{\text{Loss}}{150} \times 100\\[1em] \Rightarrow\text{Loss} = \frac{50 \times 150}{100} \\[1em] = \frac{7500}{100} \\[1em] = 75\end{aligned}$$

As we know:

$$\begin{aligned}\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow 75 = 150 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 150 - 75\\[1em] \Rightarrow \text{S.P.} = 75\end{aligned}$$

Hence, option 4 is the correct option.

Given:

S.P. = ₹ 250

Profit % = 25%

Let C.P. = $₹x$.

$\text{Profit }$% $= \frac{\text{Profit}}{\text{C.P.}} \times \text{100}$

Putting the values, we get

$$\begin{aligned}\Rightarrow 25 = \frac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \frac{25 \times x}{100}\\[1em] = \frac{x}{4}\end{aligned}$$

As we know:

$$\begin{aligned}\text{Profit} = \text{S.P. - C.P.}\\[1em] \Rightarrow \frac{x}{4} = 250 - x\\[1em] \Rightarrow 250 = \frac{x}{4} + x\\[1em] \Rightarrow 250 = \frac{x}{4} + \frac{4x}{4}\\[1em] \Rightarrow 250 = \frac{(x + 4x)}{4} \\[1em] \Rightarrow 250 = \frac{5x}{4}\\[1em] \Rightarrow x = \frac{4 \times 250}{5}\\[1em] \Rightarrow x = \frac{1000}{5}\\[1em] \Rightarrow x = 200\end{aligned}$$

Hence, option 3 is the correct option.

Given:

C.P. = ₹ 400

Overheads = ₹ 100

Hence, total C.P. = C.P. + overheads

= ₹ 400 + ₹ 100 = ₹ 500

Loss % = 10%

$\text{Loss }$% $= \frac{\text{Loss}}{\text{C.P.}} \times \text{100}$

Putting the values, we get

$$\begin{aligned}\Rightarrow10 = \frac{\text{Loss}}{500} \times 100\\[1em] \Rightarrow\text{Loss} = \frac{10 \times 500}{100} \\[1em] = \frac{5000}{100} \\[1em] = 50\end{aligned}$$

As we know:

$$\begin{aligned}\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow 50 = 500 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 500 - 50\\[1em] = 450\end{aligned}$$

Hence, option 3 is the correct option.

C.P. of 4 oranges = ₹ 8

C.P. of 1 orange = ₹ $\frac{8}{4}$ = ₹ 2

S.P. of 3 oranges = ₹ 9

S.P. of 1 orange = ₹ $\frac{9}{3}$ = ₹ 3

(∵ S.P. is greater than C.P., means oranges are sold at a profit.)

Profit = S.P. - C.P.

= ₹ 3 - ₹ 2 = ₹ 1

$\text{Profit }$% $= \frac{\text{Profit}}{\text{C.P.}} \times 100$ %

$= \frac{1}{2} \times 100$ %

$= \frac{100}{2}$ %

$= 50$ %

Hence, the profit percent = $50%$.

(i) C.P. of 15 articles = ₹ 112.50

C.P. of 1 article = ₹ $\frac{112.50}{15}$ = ₹ 7.5

S.P. of 12 articles = ₹ 108

S.P. of 1 article = ₹ $\frac{108}{12}$ = ₹ 9

(∵ S.P. is greater than C.P., means article is sold at a profit.)

Profit = S.P. - C.P.

= ₹ 9 - ₹ 7.5 = ₹ 1.5

$\text{Profit }$% $= \frac{\text{Profit}}{\text{C.P.}} \times 100$ %

$= \frac{1.5}{7.5} \times 100$ %

$= \frac{150}{7.5}$ %

$= \frac{1500}{75}$ %

$= 20$ %

Hence, the profit percent = $20%$.

(ii) Profit on 1 article = ₹ 1.5

Lets suppose $x$ articles are sold to make the profit of ₹ 75.

Profit on $x$ articles = ₹ 75

No. of articles x Profit on 1 article = Total Profit

$$\begin{aligned}⇒ x \times 1.5 = 75\\[1em] ⇒ x = \frac{75}{1.5}\\[1em] ⇒ x = \frac{750}{15}\\[1em] ⇒ x = 50\end{aligned}$$

Hence, 50 articles need to be sold to make a profit of ₹ 75.

C.P. of bicycle = ₹ 162

Amount spent on its repair = ₹ 18

Final C.P. = ₹ 162 + ₹ 18 = ₹ 180

S.P. of bicycle = ₹ 207

(∵ S.P. is greater than C.P., means bicycle is sold at a gain.)

Gain = S.P. - C.P.

= ₹ 207 - ₹ 180

= ₹ 27

$\text{Gain }$% $= \frac{\text{Gain}}{\text{C.P.}} \times 100$%

$= \frac{27}{180} \times 100$%

$= \frac{2700}{180}$%

$= 15$%

Hence, bicycle is sold at a gain of 15%.

Given:

C.P. of an article = ₹ 4,800

Cost spent on transportation, etc. = ₹ 1,200

Total C.P. = ₹ 4,800 + ₹ 1,200

= ₹ 6,000

S.P. of the article = ₹ 5,820

(∵ C.P. is greater than S.P., means article is sold at loss.)

Loss = C.P. - S.P.

= ₹ 6,000 - ₹ 5,820

= ₹ 180

$\text{Loss }$% $= \frac{\text{Loss}}{\text{C.P.}} \times 100$%

$= \frac{180}{6000} \times 100$%

$= \frac{18,000}{6000}$%

$= 3$%

Hence, article is sold at a loss of 3%.

(i) Given:

S.P. of T.V. = ₹ 3,600

Gain = one-sixth of its selling price

$$\begin{aligned}\text{Gain}= ₹\Big(\frac{1}{6} \times 3,600\Big) \\[1em] = ₹ \frac{3,600}{6}\\[1em] = ₹ 600\end{aligned}$$

Gain = ₹600

(ii) As we know that,

Gain = S.P. - C.P.

Putting the values, we get

₹ 600 = ₹ 3,600 - C.P.

C.P. = ₹ 3,600 - ₹ 600

= ₹ 3,000

The cost price of the T.V. = ₹ 3,000.

(iii)

$\text{Gain }$% $= \frac{\text{Gain}}{\text{C.P.}} \times 100$%

$= \frac{600}{3000} \times 100$%

$= \frac{1}{5} \times 100$%

$= \frac{100}{5}$%

$= 20$%

Hence, T.V. is sold at a gain of 20%.

(i) Given:

S.P. of a certain number of goods = ₹ 5,500

Loss = one-tenth of its selling price

$$\begin{aligned}= ₹ \frac{1}{10} \times 5,500\\[1em] = ₹ \frac{5,500}{10}\\[1em] = ₹ 550\end{aligned}$$

Loss = ₹ 550

(ii) As we know that,

Loss = C.P. - S.P.

Putting the values, we get

₹ 550 = C.P. - ₹ 5,500

C.P. = ₹ 5,500 + ₹ 550

= ₹ 6,050

The cost price of the goods = ₹ 6,050.

(iii)

$\text{Loss }$% $= \frac{\text{Loss}}{\text{C.P.}} \times 100$%

$= \frac{550}{6050} \times 100$%

$= \frac{55,000}{6050}$%

$= \frac{100}{11}$%

$= 9\frac{1}{11}$%

Hence, T.V. is sold at a loss of $9\frac{1}{11}%$.

Given:

The S.P. of a sofa set = $\frac{4}{5}$ times of its C.P.

Let the cost price of sofa set is ₹$100$.

S.P. = ₹$\frac{4}{5} \times 100$

= ₹$\frac{400}{5}$

= ₹80

(∵ C.P. is greater than S.P., means sofa is sold at a loss.)

Loss = C.P. - S.P.

= ₹100 - ₹80

= ₹20

$\text{Loss}$% $= \frac{\text{Loss}}{\text{C.P.}} \times 100$%

$= \frac{20}{100} \times 100$%

$= \frac{20}{\cancel{100}} \times \cancel{100}$%

$= 20$%

Hence, Sofa is sold at a loss of 20%.

Given:

The C.P. of an article = $\frac{4}{5}$ times of its S.P.

Let the S.P. be ₹ $100$.

$$\begin{aligned}\text{C.P.} = ₹ \frac{4}{5} \times 100\\[1em] = ₹ \frac{400}{5}\\[1em] = ₹ 80\end{aligned}$$

(∵ S.P. is greater than C.P., means article is sold at gain.)

Gain = S.P. - C.P.

= ₹ 100 - ₹ 80

= ₹ 20

$\text{Gain}$% $= \frac{\text{Gain}}{\text{C.P.}} \times 100$%

$= \frac{20}{80} \times 100$%

$= \frac{1}{4} \times 100$%

$= \frac{100}{4}$%

$= 25$%

Hence, Gain% = 25%

Given:

The C.P. of an article = 90% of its S.P.

Let the S.P. be ₹ 100.

$$\begin{aligned}\text{C.P.} = ₹ \frac{90}{100} \times 100\\[1em] = ₹ \frac{90}{\cancel{100}}\times\cancel{100}\\[1em] = ₹ 90\end{aligned}$$

(∵ S.P. is greater than C.P., means article is sold at profit.)

Profit = S.P. - C.P.

= ₹ 100 - ₹ 90

= ₹ 10

$\text{Profit}$% $= \frac{\text{Profit}}{\text{C.P.}} \times 100$%

$= \frac{10}{90} \times 100$%

$= \frac{1}{9} \times 100$%

$= \frac{100}{9}$%

$= 11\frac{1}{9}$%

Hence, Profit% = $11\frac{1}{9}$%

Given:

The C.P. of an article = 30% less than its S.P.

Let the S.P. be ₹ 100.

$$\begin{aligned}\text{C.P.} = \text{S.P.} - \frac{30}{100} \times \text{S.P.}\\[1em] \text{C.P.} = ₹100 - \frac{30}{100} \times 100\\[1em] = ₹ 100 - \frac{30}{\cancel{100}}\times\cancel{100}\\[1em] = ₹ 100 - 30\\[1em] = ₹ 70\end{aligned}$$

(∵ S.P. is greater than C.P., means article is sold at profit.)

Profit = S.P. - C.P.

= ₹ 100 - ₹ 70

= ₹ 30

$\text{Profit}$ % $= \frac{\text{Profit}}{\text{C.P.}} \times 100$%

$= \frac{30}{70} \times 100$%

$= \frac{3,000}{70}$%

$= \frac{300}{7}$%

$= 42\frac{6}{7}$%

Hence, Profit% = $42\frac{6}{7}$%

C.P. of 1 egg = 80 paisa

C.P. of 300 eggs = 300 x $\frac{80}{100}$

= 300 x $\frac{4}{5}$

= $\frac{1,200}{5}$

= ₹ 240

S.P. of 1 egg = ₹ 1

Total number of eggs = 300

Broken eggs = 30

Remaining eggs = 300 - 30 = 270

S.P. of 270 egg = 270 x ₹ 1 = ₹ 270

(∵ S.P. is greater than C.P.,means eggs are sold at gain.)

Gain = S.P. - C.P.

= ₹ 270 - ₹ 240

= ₹ 30

$\text{Gain}$% $= \frac{\text{Gain}}{\text{C.P.}} \times 100$%

$= \frac{30}{240} \times 100$%

$= \frac{1}{8} \times 100$%

$= \frac{100}{8}$%

$= 12.5$%

Hence, Gain% = 12.5%

Given:

S.P. = ₹ 900

Gain % = 20%

Let C.P. = $₹x$.

$\text{Profit }$% $= \frac{\text{Profit}}{\text{C.P.}} \times \text{100}$

Putting the values, we get

$$\begin{aligned}\Rightarrow 20 = \frac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \frac{20 \times x}{100}\\[1em] = \frac{x}{5}\end{aligned}$$

As we know:

$$\begin{aligned}\text{Profit} = \text{S.P. - C.P.}\\[1em] \Rightarrow \frac{x}{5} = 900 - x\\[1em] \Rightarrow 900 = \frac{x}{5} + x\\[1em] \Rightarrow 900 = \frac{x}{5} + \frac{5x}{5}\\[1em] \Rightarrow 900 = \frac{(x + 5x)}{5} \\[1em] \Rightarrow 900 = \frac{6x}{5}\\[1em] \Rightarrow x = \frac{5 \times 900}{6}\\[1em] \Rightarrow x = \frac{4500}{6}\\[1em] \Rightarrow x = 750\end{aligned}$$

Gain = $\frac{x}{5}$

Gain = $\frac{750}{5}$ = 150

Hence, C.P. = ₹ 750 and gain = ₹ 150.

Given:

S.P. = ₹ 704

Loss % = 12%

Let C.P. = $₹x$.

$\text{Loss }$% $= \frac{\text{Loss}}{\text{C.P.}} \times \text{100}$

Putting the values, we get

$$\begin{aligned}\Rightarrow 12 = \frac{\text{Loss}}{x} \times 100\\[1em] \Rightarrow \text{Loss} = \frac{12 \times x}{100}\\[1em] = \frac{3x}{25}\end{aligned}$$

As we know:

$$\begin{aligned}\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow \frac{3x}{25} = x - 704\\[1em] \Rightarrow 704 = x - \frac{3x}{25}\\[1em] \Rightarrow 704 = \frac{25x}{25} - \frac{3x}{25}\\[1em] \Rightarrow 704 = \frac{(25x - 3x)}{25} \\[1em] \Rightarrow 704 = \frac{22x}{25}\\[1em] \Rightarrow x = \frac{25 \times 704}{22}\\[1em] \Rightarrow x = \frac{17,600}{22}\\[1em] \Rightarrow x = ₹ 800\end{aligned}$$

Loss = $\frac{3x}{25}$

Gain = $\frac{3 \times 800}{25}$

Gain = $\frac{2400}{25}$ = $96$

Hence, C.P. = ₹ 800 and loss = ₹ 96.

(i) Given:

C.P. = ₹ 352

Overheads = ₹ 28

Hence, total C.P. = C.P. + overheads

= ₹ 352 + ₹ 28 = ₹ 380

Profit % = 20%

$\text{Profit }$% $= \frac{\text{Profit}}{\text{C.P.}} \times \text{100}$

Putting the values, we get

$$\begin{aligned}\Rightarrow20 = \frac{\text{Profit}}{380} \times 100\\[1em] \Rightarrow\text{Profit} = \frac{20 \times 380}{100} \\[1em] = \frac{7600}{100} \\[1em] = 76\end{aligned}$$

As we know:

$$\begin{aligned}\text{Profit} = \text{S.P. - C.P.}\\[1em] \Rightarrow 76 = \text{S.P.} - 380\\[1em] = 380 + 76\\[1em] = 456\end{aligned}$$

Hence, S.P. = ₹ 456.

(ii) Given:

C.P. = ₹ 576

Overheads = ₹ 44

Hence, total C.P. = C.P. + overheads

= ₹ 576 + ₹ 44 = ₹ 620

Loss % = 16%

Let the C.P. be ₹ $x$.

$\text{Loss }$% $= \frac{\text{Loss}}{\text{C.P.}} \times \text{100}$

Putting the values, we get

$$\begin{aligned}\Rightarrow16 = \frac{\text{Loss}}{620} \times 100\\[1em] \Rightarrow\text{Loss} = \frac{16 \times 620}{100} \\[1em] = \frac{9,920}{100} \\[1em] = 99.2\end{aligned}$$

As we know:

$$\begin{aligned}\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow 99.2 = 620 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 620 - 99.2\\[1em] = 520.80\end{aligned}$$

Hence, S.P. = ₹ 520.80.

Given:

S.P. of bicycle = ₹ 637

Loss % = 9%

Let C.P. = $₹x$.

$\text{Loss }$% $= \frac{\text{Loss}}{\text{C.P.}} \times \text{100}$

Putting the values, we get

$$\begin{aligned}\Rightarrow 9 = \frac{\text{Loss}}{x} \times 100\\[1em] \Rightarrow \text{Loss} = \frac{9 \times x}{100}\\[1em] = \frac{9x}{100}\end{aligned}$$

As we know:

$$\begin{aligned}\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow \frac{9x}{100} = x - 637\\[1em] \Rightarrow 637 = x - \frac{9x}{100}\\[1em] \Rightarrow 637 = \frac{100x}{100} - \frac{9x}{100}\\[1em] \Rightarrow 637 = \frac{(100x - 9x)}{100} \\[1em] \Rightarrow 637 = \frac{91x}{100}\\[1em] \Rightarrow x = \frac{100 \times 637}{91}\\[1em] \Rightarrow x = \frac{63,700}{91}\\[1em] \Rightarrow x = 700\end{aligned}$$

Hence, C.P. = ₹ 700

Profit % = 5 %

$\text{Profit}$% $= \frac{\text{Profit}}{\text{C.P.}} \times 100$

Putting the values, we get

$$\begin{aligned}\Rightarrow 5 = \frac{\text{Profit}}{700} \times 100\\[1em] \Rightarrow \text{Profit} = \frac{5 \times 700}{100}\\[1em] = \frac{3500}{100}\\[1em] = 35\end{aligned}$$

And,

$\text{Profit} = \text{S.P. - C.P.}$

Putting all the values, we get

$$\begin{aligned}\Rightarrow 35 = \text{S.P.} - 700\\[1em] \Rightarrow \text{S.P.} = 35 + 700\\[1em] = 735\end{aligned}$$

John should sell his bicycle for ₹ 735 to make a profit of 5%.

Given:

S.P. of radio set = ₹ 605

Gain % = 10 %

Let C.P. = $₹x$.

$\text{Profit }$% $= \frac{\text{Profit}}{\text{C.P.}} \times \text{100}$

Putting the values, we get

$$\begin{aligned}\Rightarrow 10 = \frac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \frac{10 \times x}{100}\\[1em] = \frac{10x}{100}\\[1em] = \frac{x}{10}\end{aligned}$$

As we know:

$$\begin{aligned}\text{Profit} = \text{S.P. - C.P.}\\[1em] \Rightarrow \frac{x}{10} = 605 - x\\[1em] \Rightarrow 605 = \frac{x}{10} + x\\[1em] \Rightarrow 605 = \frac{10x}{10} + \frac{x}{10}\\[1em] \Rightarrow 605 = \frac{(10x + x)}{10} \\[1em] \Rightarrow 605 = \frac{11x}{10}\\[1em] \Rightarrow x = \frac{10 \times 605}{11}\\[1em] \Rightarrow x = \frac{6,050}{11}\\[1em] \Rightarrow x = 550\end{aligned}$$

Hence, C.P. = ₹ 550

Profit % = 16 %

$\text{Profit }$% $= \frac{\text{Profit}}{\text{C.P.}} \times 100$

Putting the values, we get

$$\begin{aligned}\Rightarrow 16 = \frac{\text{Profit}}{550} \times 100\\[1em] \Rightarrow \text{Profit} = \frac{16 \times 550}{100}\\[1em] = \frac{8800}{100}\\[1em] = 88\end{aligned}$$

And,

$\text{Profit} = \text{S.P. - C.P.}$

Putting all the values, we get

$$\begin{aligned}\Rightarrow 88 = \text{S.P.} - 550\\[1em] \Rightarrow \text{S.P.} = 88 + 550\\[1em] = 638\end{aligned}$$

The man should sell the other radio for ₹ 638 in order to make a profit of 16%.

Given:

S.P. of sofa set = ₹ 2,500

Loss % = 20 %

Let C.P. = $₹x$.

$\text{Loss }$% $= \frac{\text{Loss}}{\text{C.P.}} \times \text{100}$

Putting the values, we get

$$\begin{aligned}\Rightarrow 20 = \frac{\text{Loss}}{x} \times 100\\[1em] \Rightarrow \text{Loss} = \frac{20 \times x}{100}\\[1em] = \frac{x}{5}\end{aligned}$$

As we know:

$$\begin{aligned}\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow \frac{x}{5} = x - 2,500\\[1em] \Rightarrow 2,500 = x - \frac{x}{5}\\[1em] \Rightarrow 2,500 = \frac{5x}{5} - \frac{x}{5}\\[1em] \Rightarrow 2,500 = \frac{(5x - x)}{5} \\[1em] \Rightarrow 2,500 = \frac{4x}{5}\\[1em] \Rightarrow x = \frac{2,500 \times 5}{4}\\[1em] \Rightarrow x = \frac{12,500}{4}\\[1em] \Rightarrow x = 3,125\end{aligned}$$

When C.P. = ₹ 3,125

New S.P. = ₹ 3,150

(∵ When S.P. is greater than C.P., means sofa set will be sold at a profit.)

Profit = S.P. - C.P.

= ₹ 3,150 - ₹ 3,125

= ₹ 25

$\text{Profit }$% $= \frac{\text{Profit}}{\text{C.P.}} \times 100$%

$= \frac{25}{3125} \times 100$%

$= \frac{1}{125} \times 100$%

$= \frac{100}{125}$%

$= 0.8$%

If the man sells the same sofa set for ₹ 3,150, profit % = 0.8%.

C.P. of 10 pens = ₹ 80

C.P. of 1 pen = ₹ $\frac{80}{10}$ = ₹ 8

Profit = 25%

$\text{Profit}$% $= \frac{\text{Profit}}{\text{C.P.}} \times 100$

$$\begin{aligned}\Rightarrow 25 = \frac{\text{Profit}}{8} \times 100\\[1em] \Rightarrow \text{Profit} = \frac{25 \times 8}{100}\\[1em] = \frac{200}{100}\\[1em] = 2\end{aligned}$$

As we know,

$\text{Profit} = \text{S.P. - C.P.}$

Putting the values, we get

$$\begin{aligned}\Rightarrow 2 = \text{S.P.} - 8\\[1em] \Rightarrow \text{S.P.} = 2 + 8\\[1em] \Rightarrow \text{S.P.} = 10\\[1em]\end{aligned}$$

Hence,option 2 is the correct option.

C.P. of 20 articles = S.P. of 25 articles

Let the C.P. of 20 articles be ₹ 100.

The C.P. of 1 article = ₹ $\frac{100}{20}$ = ₹ 5

The S.P. of 25 articles = The C.P. of 20 articles = ₹ 100

The S.P. of 1 article = ₹ $\frac{100}{25}$ = ₹ 4

(∵ C.P. is greater than S.P., means articles are sold at a loss.)

Loss = C.P. - S.P.

= ₹ (5 - 4) = ₹ 1

$\text{Loss }$% $= \frac{\text{Loss}}{\text{C.P.}} \times 100$%

$= \frac{1}{5} \times 100$%

$= \frac{100}{5}$%

$= 20$%

Hence,option 3 is the correct option.

Given:

M.P. of an article = ₹ 500

S.P. of article = ₹ 400

Discount = M.P. - S.P.

= ₹ 500 - ₹ 400

= ₹ 100

$\text{Discount}$% $= \frac{\text{Discount}}{\text{M.P.}}\times 100$%

$= \frac{100}{500}\times 100$%

$= \frac{1}{5}\times 100$%

$= \frac{100}{5}$%

$= 20$%

Hence,option 2 is the correct option.

Given:

M.P. = ₹ 800

Discount % = 20%

$\text{Discount}$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

Putting the values, we get

$$\begin{aligned}\Rightarrow\ 20 = \frac{\text{Discount}}{800} \times 100\\[1em] \Rightarrow\ \text{Discount} = \frac{20 \times 800}{100}\\[1em] = \frac{16000}{100}\\[1em] = 160\end{aligned}$$

And we know,

$\text{Discount} = \text{M.P. - S.P}$

Putting the values,we get

$$\begin{aligned}160 = 800 - \text{S.P}\\[1em] \Rightarrow \text{S.P.} = 800 - 160\\[1em] \Rightarrow \text{S.P.} = 640\end{aligned}$$

Hence, option 3 is the correct option.

Let the C.P. of 1 article be ₹ 100.

So, the C.P. of 2 article = ₹ 100 x 2 = ₹ 200

Similarly, the C.P. of 10 article = ₹ 100 x 10 = ₹ 1000

Gain = Cost price of 2 articles = ₹ 200

As we know,

$\text{Profit}$% $= \frac{\text{Profit}}{\text{C.P.}} \times 100$%

$= \frac{200}{1000} \times 100$%

$= \frac{1}{5} \times 100$%

$= \frac{100}{5}$%

$= 20$%

Hence,option 2 is the correct option.

(i) Given:

S.P. of 4 oranges = ₹ 3

S.P. of 1 orange = ₹ $\frac{3}{4}$

Gain = 50%

Let C.P. = $₹x$.

$\text{Profit }$% $= \frac{\text{Profit}}{\text{C.P.}} \times \text{100}$

Putting the values, we get

$$\begin{aligned}\Rightarrow 50 = \frac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \frac{50 \times x}{100}\\[1em] = \frac{x}{2}\end{aligned}$$

As we know:

$$\begin{aligned}\text{Profit} = \text{S.P. - C.P.}\\[1em] \Rightarrow \frac{x}{2} = \frac{3}{4} - x\\[1em] \Rightarrow \frac{3}{4} = \frac{x}{2} + x\\[1em] \Rightarrow \frac{3}{4} = \frac{x}{2} + \frac{2x}{2}\\[1em] \Rightarrow \frac{3}{4} = \frac{(x + 2x)}{2} \\[1em] \Rightarrow \frac{3}{4} = \frac{3x}{2}\\[1em] \Rightarrow x = \frac{3 \times 2}{4 \times 3}\\[1em] \Rightarrow x = \frac{6}{12}\\[1em] \Rightarrow x = \frac{1}{2}\end{aligned}$$

C.P. of 1 orange = ₹ $\frac{1}{2}$

C.P. of 4 oranges = ₹ $4\times\frac{1}{2}$

= ₹ $\frac{4}{2}$

= ₹ 2

Hence, C.P. of 4 oranges = ₹ 2.

(ii) C.P. of 1 orange = ₹ $\frac{1}{2}$ = ₹ 0.5

(iii) S.P. of 1 orange = ₹ $\frac{3}{4}$ = ₹ 0.75

(iv) Profit = S.P. - C.P.

= ₹ 0.75 - ₹ 0.50

= ₹ 0.25

Hence, Profit = ₹ 0.25.

(v) Gain on 1 orange = ₹ 0.25

Let number of oranges needed to gain ₹ 24 be $x$

Gain on $x$ orange = ₹ 0.25 x $x$ = ₹ 24

⇒ $x = \frac{24}{0.25}$

⇒ $x = \frac{2400}{25}$

⇒ $x = 96$

Hence, 96 oranges need to be bought and sold in order to gain ₹ 24.

Given:

S.P. of 12 articles = ₹ 80

S.P. of 1 article = ₹ $\frac{80}{12}$ = ₹ $\frac{20}{3}$

Gain = $33\frac{1}{3}%$ = $\frac{100}{3}%$

Let C.P. of 1 article = $₹x$.

$\text{Profit }$% $= \frac{\text{Profit}}{\text{C.P.}} \times \text{100}$

Putting the values, we get

$$\begin{aligned}\Rightarrow \frac{100}{3} = \frac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \frac{100 \times x}{3 \times 100}\\[1em] = \frac{\cancel{100} \times x}{3 \times \cancel{100}}\\[1em] = \frac{x}{3}\end{aligned}$$

As we know:

$$\begin{aligned}\text{Profit} = \text{S.P. - C.P.}\\[1em] \Rightarrow \frac{x}{3} = \frac{20}{3} - x\\[1em] \Rightarrow \frac{20}{3} = \frac{x}{3} + x\\[1em] \Rightarrow \frac{20}{3} = \frac{x}{3} + \frac{3x}{3}\\[1em] \Rightarrow \frac{20}{3} = \frac{(x + 3x)}{3} \\[1em] \Rightarrow \frac{20}{3} = \frac{4x}{3}\\[1em] \Rightarrow x = \frac{20 \times 3}{4 \times 3}\\[1em] \Rightarrow x = \frac{60}{12}\\[1em] \Rightarrow x = 5\end{aligned}$$

C.P. of 1 article = ₹ 5

Let number of articles bought by the man for ₹ 90 be $y$

C.P. of $y$ articles = ₹ 5 x $y$ = ₹ 90

⇒ $y = \frac{90}{5}$

⇒ $y = 18$

Hence, 18 articles are bought by the man for ₹ 90.

Let the C.P. of 1 article be ₹ 100.

The C.P. of 12 articles = ₹ 100 x 12 = ₹ 1200

The S.P. of 15 articles = the C.P. of 12 articles

The S.P. of 15 articles = ₹ 1200

The S.P. of 1 article = ₹ $\frac{1200}{15}$ = ₹ 80

(∵ C.P. is greater than S.P., means article is sold at a loss.)

Loss = C.P. - S.P.

= ₹ 100 - ₹ 80

= ₹ 20

$\text{Loss }$% $= \frac{\text{Loss}}{\text{C.P.}} \times 100$%

$= \frac{20}{100} \times 100$%

$= \frac{20}{\cancel{100}} \times \cancel{100}$%

$= 20$%

Hence, loss % = 20%.

(i) Given:

C.P. of whole rice = ₹ 4,500

Profit desired on the whole = 12 %

$\text{Profit}$% $= \frac{\text{Profit}}{\text{C.P}}\times 100$

Putting the values, we get

$$\begin{aligned}12 = \frac{\text{Profit}}{4,500} \times 100\\[1em] \Rightarrow \text{Profit} = \frac{12 \times 4,500}{100}\\[1em] = \frac{54,000}{100}\\[1em] = 540\end{aligned}$$

As we know,

$\text{Profit} = \text{S.P. - C.P.}$

Putting the values, we get

$$\begin{aligned}540 = \text{S.P.} - 4,500\\[1em] \Rightarrow \text{S.P.} = 540 + 4,500\\[1em] = 5,040\end{aligned}$$

C.P. of $\frac{1}{3}$rice = ₹ $\frac{1}{3} \times 4,500$

= ₹ $\frac{4,500}{3}$

= ₹ $1,500$

Gain on it = 10%

$\text{Profit}$% $= \frac{\text{Profit}}{\text{C.P}}\times 100$

Putting the values, we get

$$\begin{aligned}10 = \frac{\text{Profit}}{1,500} \times 100\\[1em] \Rightarrow \text{Profit} = \frac{10 \times 1,500}{100}\\[1em] = \frac{15,000}{100}\\[1em] = 150\end{aligned}$$

As we know,

$\text{Profit} = \text{S.P. - C.P.}$

Putting the values, we get

$$\begin{aligned}150 = \text{S.P.} - 1,500\\[1em] \Rightarrow \text{S.P.} = 150 + 1,500\\[1em] = 1,650\end{aligned}$$

The S.P. of the rest of the rice = ₹ 5,040 - ₹ 1,650 = ₹ 3,390

The selling price of the rest of the rice = ₹ 3,390.

(ii) C.P. of the rest of the rice = ₹ 4,500 - ₹ 1,500 = ₹ 3,000

Profit on the rest of the rice = Remaining S.P. - Remaining C.P.

= ₹ 3,390 - ₹ 3,000

= ₹ 390

$\text{Profit}$% $= \frac{Profit}{C.P.}\times 100$%

$= \frac{390}{3000}\times 100$%

$= \frac{13}{100}\times 100$%

$= \frac{1300}{100}$%

$= 13$%

The profit percentage of rest of the rice = 13%.

Given:

C.P. of notebooks = ₹ 600

Gain desired on the whole = 10 %

$\text{Profit}$% $= \frac{\text{profit}}{\text{C.P}}\times 100$%

Putting the values, we get

$$\begin{aligned}10 = \frac{\text{Profit}}{600} \times 100\\[1em] \Rightarrow \text{Profit} = \frac{10 \times 600}{100}\\[1em] = \frac{6000}{100}\\[1em] = 60\end{aligned}$$

As we know,

$\text{Profit} = \text{S.P. - C.P.}$

Putting the values, we get

$$\begin{aligned}60 = \text{S.P.} - 600\\[1em] \Rightarrow \text{S.P.} = 60 + 600\\[1em] = 660\end{aligned}$$

C.P. of $\frac{1}{4}$number of notebooks = ₹ $\frac{1}{4} \times 600$

= ₹ $\frac{600}{4}$

= ₹ $150$

Loss of $\frac{1}{4}$number of notebooks = 5%

$\text{Loss}$% $= \frac{\text{Loss}}{\text{C.P}}\times 100$

Putting the values, we get

$$\begin{aligned}5 = \frac{\text{Loss}}{150} \times 100\\[1em] \Rightarrow \text{Loss} = \frac{5 \times 150}{100}\\[1em] = \frac{750}{100}\\[1em] = 7.5\end{aligned}$$

As we know,

$\text{Loss} = \text{C.P. - S.P.}$

Putting the values, we get

$$\begin{aligned}7.5 = 150 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 150 - 7.5\\[1em] = 142.5\end{aligned}$$

The S.P. of rest of notebooks = ₹ 660 - ₹ 142.5 = ₹ 517.5

The selling price of the rest of the notebooks = ₹ 517.50.

Let C.P. of the watch be ₹ $x$.

Profit % = 5 %

$\text{Profit}$% $= \frac{\text{Profit}}{\text{C.P}}\times 100$

Putting the values, we get

$$\begin{aligned}5 = \frac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \frac{5 \times x}{100}\\[1em] = \frac{x}{20}\end{aligned}$$

As we know,

$\text{Profit} = \text{S.P. - C.P.}$

Putting the values, we get

$$\begin{aligned}\frac{x}{20} = \text{S.P.} - x\\[1em] \Rightarrow \text{S.P.} = \frac{x}{20} + x\\[1em] = \frac{x}{20} + \frac{20x}{20}\\[1em] = \frac{(x + 20x)}{20}\\[1em] = \frac{21x}{20}\end{aligned}$$

Given,

If S.P. was 24 more gain would have been 11%

New S.P. = $\frac{21x}{20} + 24$

New Profit = New S.P. - C.P.

$$\begin{aligned}= \frac{21x}{20} + 24 - x \\[1em] = \frac{21x + 480 - 20x}{20} \\[1em] = \frac{x + 480}{20}\end{aligned}$$

New Profit % = 11 %

$\text{Profit}$% $$\begin{aligned}= \frac{\text{Profit}}{\text{C.P}}\times 100 \\[1em]\end{aligned}$$

$$\begin{aligned}\Rightarrow 11 = \frac{\frac{x + 480}{20}}{x} \times 100 \\[1em] \Rightarrow 11 = \frac{x + 480}{20x} \times 100 \\[1em] \Rightarrow 11 = \frac{x + 480}{x} \times 5 \\[1em] \Rightarrow 11x = 5x + 2400 \\[1em] \Rightarrow 11x - 5x = 2400 \\[1em] \Rightarrow 6x = 2400 \\[1em] \Rightarrow x = \frac{2400}{6} \\[1em] \Rightarrow x = 400\end{aligned}$$

Hence, cost price of watch = ₹ 400.

Given:

M.P. of the watch = ₹ 1,400

Discount = 9%

$\text{Discount}$% $$\begin{aligned}= \frac{\text{Discount}}{\text{M.P.}}\times 100\\[1em]\end{aligned}$$

$$\begin{aligned}\Rightarrow 9 = \frac{\text{Discount}}{1400}\times 100\\[1em] \Rightarrow \text{Discount} = \frac{9 \times 1,400}{100}\\[1em] = \frac{12,600}{100}\\[1em] = ₹ 126\\[1em]\end{aligned}$$

As we know,

$$\begin{aligned}\text{Discount} = \text{M.P. - S.P}\\[1em] \Rightarrow 126 = 1,400 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 1,400 - 126\\[1em] = ₹ 1,274\\[1em]\end{aligned}$$

Hence, discount = ₹ 126 and S.P. = ₹ 1,274

Given:

S.P. of an article = ₹ 248.50

Discount = 10%

Let the M.P. of the article be ₹ $x$.

As we know,

$\text{Discount }$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 10 = \frac{\text{Discount}}{x} \times 100\\[1em] \Rightarrow \text{Discount} = \frac{10 \times x}{100}\\[1em] = \frac{10x}{100}\\[1em] = \frac{x}{10}\end{aligned}$$

And

$$\begin{aligned}\text{Discount = M.P. - S.P}\\[1em] \Rightarrow\frac{x}{10} = x - 248.50\\[1em] \Rightarrow 248.50 = x - \frac{x}{10}\\[1em] \Rightarrow 248.50 = \frac{10x}{10} - \frac{x}{10}\\[1em] \Rightarrow 248.50 = \frac{(10x - x)}{10} \\[1em] \Rightarrow 248.50 = \frac{9x}{10} \\[1em] \Rightarrow x = \frac{10 \times 248.50}{9} \\[1em] \Rightarrow x = \frac{2485}{9} \\[1em] \Rightarrow x = ₹ 276.11 \\[1em]\end{aligned}$$

Hence, the list price = ₹ 276.11

(i) Given:

C.P. of an article = ₹ 450.

M.P. of the article = 20% above the C.P.

= C.P. + 20% of C.P.

= ₹ $450 + \frac{20}{100} \times 450$

= ₹ $450 + \frac{1}{5} \times 450$

= ₹ $450 + \frac{450}{5}$

= ₹ $450 + 90$

= ₹ $540$

Hence, M.P. of the article = ₹ $540$.

(ii) M.P. of the article = ₹ $540$

Discount = 10 %

As we know,

$\text{Discount }$% $$\begin{aligned}= \frac{\text{Discount}}{\text{M.P.}} \times 100\\[1em]\end{aligned}$$

$$\begin{aligned}\Rightarrow 10 = \frac{\text{Discount}}{540} \times 100\\[1em] \Rightarrow \text{Discount} = \frac{10 \times 540}{100}\\[1em] = \frac{5400}{100}\\[1em] = 54\end{aligned}$$

And

$$\begin{aligned}\text{Discount = M.P. - S.P}\\[1em] \Rightarrow 54 = 540 - \text{S.P}\\[1em] \Rightarrow \text{S.P} = 540 - 54\\[1em] \Rightarrow \text{S.P} = ₹ 486\end{aligned}$$

Hence, S.P. of the article = ₹ 486.

(iii) When M.P. of the article = ₹ 540

S.P. of the article = ₹ 496.80

As we know ,

$$\begin{aligned}\text{Discount = M.P. - S.P.}\\[1em] \text{Discount} = 540 - 496.80\\[1em] \text{Discount} = ₹ 43.2\end{aligned}$$

And,

$\text{Discount}$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$\Rightarrow\text{Discount}$% $= \frac{43.2}{540} \times 100$

$= \frac{4320}{540}$%

$= 8$%

If S.P. of the article is ₹ 496.80, then the percentage discount is 8%.

(i) Given:

M.P. of an article = ₹ 800

Discount of the article = 15%

$\text{Discount}$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 15 = \frac{\text{Discount}}{800} \times 100\\[1em] \Rightarrow \text{Discount} = \frac{15 \times 800}{100}\\[1em] = \frac{12000}{100}\\[1em] = 120\end{aligned}$$

And,

$$\begin{aligned}\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow 120 = 800 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 800 - 120\\[1em] \Rightarrow \text{S.P.} = 680\end{aligned}$$ Hence, S.P. of the article = ₹ 680.

(ii) S.P. of the article = ₹ 680

Profit = $13\frac{1}{3}%$ = $\frac{40}{3}%$

Let the C.P. be ₹ $x$.

As we know,

$\text{Profit}$% $= \frac{\text{Profit}}{\text{C.P.}} \times 100$

$$\begin{aligned}\Rightarrow \frac{40}{3} = \frac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \frac{40 \times x}{3 \times 100}\\[1em] = \frac{40x}{300}\\[1em] = \frac{2x}{15}\\[1em]\end{aligned}$$

And,

$$\begin{aligned}\text{Profit = S.P. - C.P.}\\[1em] \Rightarrow \frac{2x}{15} = 680 - x\\[1em] \Rightarrow \frac{2x}{15} + x = 680\\[1em] \Rightarrow \frac{2x}{15} + \frac{15x}{15} = 680\\[1em] \Rightarrow \frac{(2x + 15x)}{15} = 680\\[1em] \Rightarrow \frac{17x}{15} = 680\\[1em] \Rightarrow x = \frac{680 \times 15}{17}\\[1em] \Rightarrow x = \frac{10,200}{17}\\[1em] \Rightarrow x = 600\\[1em]\end{aligned}$$

Hence, C.P. of the article = ₹ 600.

(i) Given:

M.P. of an article = ₹ 2,250

Discount % = 12 %

$\text{Discount}$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 12 = \frac{\text{Discount}}{2250} \times 100\\[1em] \Rightarrow \text{Discount} = \frac{12 \times 2250}{100}\\[1em] = \frac{27,000}{100}\\[1em] = 270\end{aligned}$$

$$\begin{aligned}\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow 270 = 2,250 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 2,250 - 270\\[1em] \Rightarrow \text{S.P.} = 1,980\end{aligned}$$

The S.P. of the article = ₹ 1,980.

(ii) S.P. of the article = ₹ 1,980

Profit of the article = 10%

Let the C.P. of the article be ₹ $x$.

$\text{Profit}$% $$\begin{aligned}= \frac{\text{Profit}}{\text{C.P.}}\times 100\\[1em]\end{aligned}$$

$$\begin{aligned}\Rightarrow 10 = \frac{\text{Profit}}{x}\times 100\\[1em] \Rightarrow \text{Profit} = \frac{10 \times x}{100}\\[1em] = \frac{10x}{100}\\[1em] = \frac{x}{10}\end{aligned}$$

and,

$$\begin{aligned}\text{Profit = S.P. - C.P.}\\[1em] \Rightarrow \frac{x}{10} = 1980 - x\\[1em] \Rightarrow \frac{x}{10} + x = 1980 \\[1em] \Rightarrow \frac{x}{10} + \frac{10x}{10} = 1980 \\[1em] \Rightarrow \frac{(x + 10x)}{10} = 1980 \\[1em] \Rightarrow \frac{11x}{10} = 1980 \\[1em] \Rightarrow x = \frac{1980 \times 10}{11} \\[1em] \Rightarrow x = \frac{19800}{11} \\[1em] \Rightarrow x = 1800\end{aligned}$$

The cost price of the article = ₹ 1,800

(i) Given:

Discount on the article = 20%

S.P. of the article = ₹ 1,440

Let the M.P. of the article be ₹$x$.

As we know,

$\text{Discount}$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 20 = \frac{\text{Discount}}{x} \times 100\\[1em] \Rightarrow \text{Discount} = \frac{20 \times x}{100}\\[1em] \Rightarrow \text{Discount} = \frac{20x}{100}\\[1em] \Rightarrow \text{Discount} = \frac{x}{5}\\[1em]\end{aligned}$$

And,

$$\begin{aligned}\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow \frac{x}{5} = x - 1440\\[1em] \Rightarrow 1440 = x - \frac{x}{5}\\[1em] \Rightarrow 1440 = \frac{5x}{5} - \frac{x}{5}\\[1em] \Rightarrow 1440 = \frac{(5x - x)}{5} \\[1em] \Rightarrow 1440 = \frac{4x}{5} \\[1em] \Rightarrow x = \frac{5 \times 1,440}{4} \\[1em] \Rightarrow x = \frac{7,200}{4} \\[1em] \Rightarrow x = 1,800\end{aligned}$$

Hence, M.P. of the article = ₹ 1,800

(ii) S.P. of the article = ₹ 1,440

Gain% of the article = 25%

Let the C.P. be ₹ $y$.

$\text{Gain }$% $= \frac{\text{Gain}}{\text{C.P.}}\times 100$

$$\begin{aligned}\Rightarrow 25 = \frac{\text{Gain}}{y}\times 100\\[1em] \Rightarrow \text{Gain} = \frac{25 \times y}{100}\\[1em] \Rightarrow \text{Gain} = \frac{25y}{100}\\[1em] \Rightarrow \text{Gain} = \frac{y}{4}\end{aligned}$$

And,

$$\begin{aligned}\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow \frac{y}{4} = 1,440 - y\\[1em] \Rightarrow \frac{y}{4} + y = 1,440 \\[1em] \Rightarrow \frac{y}{4} + \frac{4y}{4} = 1,440 \\[1em] \Rightarrow \frac{(y + 4y)}{4} = 1,440 \\[1em] \Rightarrow \frac{5y}{4} = 1,440 \\[1em] \Rightarrow y = \frac{1,440 \times 4}{5} \\[1em] \Rightarrow y = \frac{5,760}{5} \\[1em] \Rightarrow y = 1,152\end{aligned}$$

Hence, C.P. of the article = ₹ 1,152

Given:

M.P. of the goods = 30% above the C.P.

Let the C.P. be ₹ $100$.

M.P. = C.P. + 30% of C.P.

= $100 + \frac{30}{100} \times 100$

= $100 + \frac{30}{\cancel{100}} \times \cancel{100}$

= $100 + 30$

= $130$

So, M.P. of the goods = ₹ $130$

Discount % = 10%

$\text{Discount}$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 10 = \frac{\text{Discount}}{130} \times 100 \\[1em] \Rightarrow \text{Discount} = \frac{10 \times 130}{100}\\[1em] = \frac{1300}{100}\\[1em] = 13\end{aligned}$$

Now,

$$\begin{aligned}\text{Discount = M.P. - S.P.} \\[1em] \Rightarrow 13 = 130 - \text{S.P.} \\[1em] \Rightarrow \text{S.P.} = 130 - 13 \\[1em] = 117\end{aligned}$$

Hence, S.P. of the goods = ₹ $117$

C.P. of the goods = ₹ 100

($\because$ S.P. is greater than C.P., means goods are sold at a gain.)

$$\begin{aligned}\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow \text{Gain} = 117 - 100 \\[1em] \Rightarrow \text{Gain} = 17\end{aligned}$$

And

$\text{Gain}$% $= \frac{\text{Gain}}{\text{C.P.}} \times 100$%

$\Rightarrow\text{Gain}$% $= \frac{17}{100} \times 100$%

$= \frac{17}{\cancel{100}} \times \cancel{100}$%

$= 17$%

Hence, Gain percent = 17%

Given:

C.P. of a dress = ₹ 400

Profit of the dress = 20%

$\text{Profit}$% $= \frac{\text{Profit}}{\text{C.P.}} \times 100$

$$\begin{aligned}\Rightarrow 20 = \frac{\text{Profit}}{400} \times 100\\[1em] \Rightarrow \text{Profit} = \frac{20 \times 400}{100}\\[1em] = \frac{8000}{100}\\[1em] = 80\\[1em]\end{aligned}$$

And,

$$\begin{aligned}\text{Profit = S.P. - C.P.}\\[1em] \Rightarrow 80 = \text{S.P.} - 400\\[1em] \Rightarrow \text{S.P.} = 80 + 400\\[1em] = 480\end{aligned}$$

S.P. of the dress = ₹ 480

Discount on the dress = 20%

Let the M.P. of the dress = ₹ $x$.

$$\begin{aligned}\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow \text{Discount} = x - 480\end{aligned}$$

And,

$\text{Discount}$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 20 = \frac{(x - 480)}{x} \times 100\\[1em] \Rightarrow 20 \times x = (x - 480) \times 100\\[1em] \Rightarrow 20x = 100x - 48000\\[1em] \Rightarrow 48000 = 100x - 20x \\[1em] \Rightarrow 48000 = 80x \\[1em] \Rightarrow x = \frac{48000}{80} \\[1em] \Rightarrow x = 600\end{aligned}$$

Hence, M.P. of the dress = ₹ 600.

Given:

S.P. of the pen = ₹ 13.20

Discount % = 12%

Let the M.P. of the pen = ₹ $x$.

$$\begin{aligned}\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow \text{Discount} = x - 13.20\end{aligned}$$

And,

$\text{Discount}$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 12 = \frac{(x - 13.20)}{x} \times 100\\[1em] \Rightarrow 12 \times x = (x - 13.20) \times 100\\[1em] \Rightarrow 12x = 100x - 1320\\[1em] \Rightarrow 1320 = 100x - 12x \\[1em] \Rightarrow 1320 = 88x \\[1em] \Rightarrow x = \frac{1320}{88} \\[1em] \Rightarrow x = 15\end{aligned}$$

Now, M.P. of the pen = ₹ 15

Discount% = 5 %

$\text{Discount}$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 5 = \frac{\text{Discount}}{15}\times 100\\[1em] \Rightarrow \text{Discount} = \frac{5 \times 15}{100}\\[1em] = \frac{75}{100}\\[1em] = 0.75\end{aligned}$$

And,

$$\begin{aligned}\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow 0.75 = 15 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 15 - 0.75\\[1em] \Rightarrow \text{S.P.} = 14.25\end{aligned}$$

Hence, M.P. of pen = ₹ 15 and new S.P. = ₹ 14.25

Given:

M.P. of the article = 25% above the C.P.

The C.P. of the article = ₹ 2,400.

M.P. = C.P. + 25% of C.P.

= $2,400 + \frac{25}{100} \times 2,400$

= $2,400 + \frac{1}{4} \times 2,400$

= $2,400 + \frac{2,400}{4}$

= $2,400 + 600$

= $3,000$

So, M.P. of the goods = ₹ $3,000$

Discount % = 15%

$\text{Discount}$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 15 = \frac{\text{Discount}}{3000} \times 100 \\[1em] \Rightarrow \text{Discount} = \frac{15 \times 3,000}{100}\\[1em] = \frac{45,000}{100}\\[1em] = 450\end{aligned}$$

Now,

$$\begin{aligned}\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow 450 = 3,000 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 3,000 - 450\\[1em] = 2,550\end{aligned}$$

Hence, S.P. of the goods = ₹ $2,550$

C.P. of the goods = ₹ $2,400$

($\because$ S.P. is greater than C.P., means goods are sold at a gain.)

$$\begin{aligned}\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow \text{Gain} = 2,550 - 2,400 \\[1em] \Rightarrow \text{Gain} = 150\end{aligned}$$

And

$\text{Gain}$% $= \frac{\text{Gain}}{\text{C.P.}} \times 100$%

$\Rightarrow\text{Gain}$% $= \frac{150}{2400} \times 100$%

$= \frac{15000}{2400}$%

$= 6.25$%

Hence, Gain = ₹ 150 and Gain percent = 6.25%

Given:

C.P. of 1 article = ₹ 450

C.P. of 30 articles = ₹ 450 x 30 = ₹ 13,500

Profit desired on the whole = 10%

$\text{Profit}$% $= \frac{\text{Profit}}{\text{C.P}}\times 100$

Putting the values, we get

$$\begin{aligned}10 = \frac{\text{Profit}}{13500} \times 100\\[1em] \Rightarrow \text{Profit} = \frac{10 \times 13500}{100}\\[1em] = \frac{135000}{100}\\[1em] = 1350\end{aligned}$$

As we know,

$\text{Profit} = \text{S.P. - C.P.}$

Putting the values, we get

$$\begin{aligned}1350 = \text{S.P.} - 13500\\[1em] \Rightarrow \text{S.P.} = 13500 + 1350\\[1em] = 14850\end{aligned}$$

C.P. of $\frac{1}{3}$articles = ₹ $\Big(\frac{1}{3} \times 13500\Big)$

= ₹ $\frac{13500}{3}$

= ₹ $4500$

Loss on it = 6%

$\text{Loss}$% $= \frac{\text{Loss}}{\text{C.P}}\times 100$

Putting the values, we get

$$\begin{aligned}6 = \frac{\text{Loss}}{4500} \times 100\\[1em] \Rightarrow \text{Loss} = \frac{6 \times 4500}{100}\\[1em] = \frac{27000}{100}\\[1em] = 270\end{aligned}$$

As we know,

$\text{Loss} = \text{C.P. - S.P.}$

Putting the values, we get

$$\begin{aligned}270 = 4500 - \text{S.P}\\[1em] \Rightarrow \text{S.P.} = 4500 - 270\\[1em] = 4230\end{aligned}$$

The S.P. of the rest of the articles = ₹ 14850 - ₹ 4230 = ₹ 10620

Total articles = 30

Two - third of articles = $\frac{2}{3} \times 30$ = 20

The S.P. of each of the 20 articles = ₹ $\frac{10620}{20}$ = ₹ 531

The selling price of each of the article = ₹ 531.

(i) Let M.P. be ₹ $100$.

1st discount % = 80%

$\text{Discount }$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 80 = \frac{\text{Discount}}{100} \times 100\\[1em] \Rightarrow 80 = \frac{\text{Discount}}{\cancel{100}} \times \cancel{100}\\[1em] \Rightarrow \text{Discount} = 80\end{aligned}$$

And,

$$\begin{aligned}\text{S.P. = M.P. - Discount}\\[1em] \Rightarrow \text{S.P.} = 100 - 80\\[1em] \Rightarrow \text{S.P.} = 20\end{aligned}$$

New M.P. = ₹ 20

2nd Discount % = 80%

$\text{Discount}$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 80 = \frac{\text{Discount}}{20} \times 100\\[1em] \Rightarrow \text{Discount} = \frac{80 \times 20}{100}\\[1em] \Rightarrow \text{Discount} = \frac{1600}{100}\\[1em] \Rightarrow \text{Discount} = 16\end{aligned}$$

And,

$$\begin{aligned}\text{S.P. = M.P. - Discount}\\[1em] \Rightarrow \text{S.P.} = 20 - 16\\[1em] \Rightarrow \text{S.P.} = 4\end{aligned}$$

Single equivalent discount = Initial M.P. - Final S.P.

= 100 - 4

= 96

$\text{Discount}$ % $= \frac{\text{Single Discount}}{\text{Initial M.P.}} \times 100$%

$\Rightarrow \text{Discount}$% $= \frac{96}{100} \times 100$%

$\Rightarrow \text{Discount}$% $= \frac{96}{\cancel{100}} \times \cancel{100}$%

$\Rightarrow \text{Discount}$% $= 96$%

Hence, single equivalent discount = 96%.

(ii) Let M.P. be ₹ $100$.

1st discount % = 60%

$\text{Discount }$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 60 = \frac{\text{Discount}}{100} \times 100\\[1em] \Rightarrow 60 = \frac{\text{Discount}}{\cancel{100}} \times \cancel{100}\\[1em] \Rightarrow \text{Discount} = 60\end{aligned}$$

And,

$$\begin{aligned}\text{S.P. = M.P. - Discount}\\[1em] \Rightarrow \text{S.P.} = 100 - 60\\[1em] \Rightarrow \text{S.P.} = 40\end{aligned}$$

New M.P. = ₹ 40

2nd Discount % = 60%

$\text{Discount }$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 60 = \frac{\text{Discount}}{40} \times 100\\[1em] \Rightarrow \text{Discount} = \frac{60 \times 40}{100}\\[1em] \Rightarrow \text{Discount} = \frac{2400}{100}\\[1em] \Rightarrow \text{Discount} = 24\end{aligned}$$

And,

$$\begin{aligned}\text{S.P. = M.P. - Discount}\\[1em] \Rightarrow \text{S.P.} = 40 - 24\\[1em] \Rightarrow \text{S.P.} = 16\end{aligned}$$

Single equivalent discount = Initial M.P. - Final S.P.

= 100 - 16

= 84

$\text{Discount}$% $= \frac{\text{Single Discount}}{\text{Initial M.P.}} \times 100$%

$\Rightarrow \text{Discount}$% $= \frac{84}{100} \times 100$%

$\Rightarrow \text{Discount}$% $= \frac{84}{\cancel{100}} \times \cancel{100}$%

$\Rightarrow \text{Discount}$ % $= 84$%

Hence, single equivalent discount = 84%.

(iii) Let M.P. be ₹ $100$.

1st discount % = 60%

$\text{Discount }$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 60 = \frac{\text{Discount}}{100} \times 100\\[1em] \Rightarrow 60 = \frac{\text{Discount}}{\cancel{100}} \times \cancel{100}\\[1em] \Rightarrow \text{Discount} = 60\end{aligned}$$

And,

$$\begin{aligned}\text{S.P. = M.P. - Discount}\\[1em] \Rightarrow \text{S.P.} = 100 - 60\\[1em] \Rightarrow \text{S.P.} = 40\end{aligned}$$

New M.P. = ₹ 40

2nd Discount % = 80%

$\text{Discount }$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 80 = \frac{\text{Discount}}{40} \times 100\\[1em] \Rightarrow \text{Discount} = \frac{80 \times 40}{100}\\[1em] \Rightarrow \text{Discount} = \frac{3200}{100}\\[1em] \Rightarrow \text{Discount} = 32\end{aligned}$$

And,

$$\begin{aligned}\text{S.P. = M.P. - Discount}\\[1em] \Rightarrow \text{S.P.} = 40 - 32\\[1em] \Rightarrow \text{S.P.} = 8\end{aligned}$$

Single equivalent discount = Initial M.P. - Final S.P.

= 100 - 8

= 92

$\text{Discount}$% $= \frac{\text{Single Discount}}{\text{Initial M.P.}} \times 100$%

$\Rightarrow \text{Discount}$% $= \frac{92}{100} \times 100$%

$\Rightarrow \text{Discount}$% $= \frac{92}{\cancel{100}} \times \cancel{100}$%

$\Rightarrow \text{Discount}$% $= 92$%

Hence, single equivalent discount = 92%.

Selling price of the article = ₹ 600

and, Tax = 10% of ₹ 600

= $\frac{10}{100} \times ₹ 600$

= $\frac{1}{10} \times ₹ 600$

= $₹ \frac{600}{10}$

= $₹ 60$

Total amount to be paid by Rohit = ₹ 600 + ₹ 60

= ₹ 660

Hence, option 2 is the correct option.

Selling price of an article = ₹ 1,000

and, Tax = 10% of ₹ 1,000

= $\frac{10}{100} \times ₹ 1,000$

= $\frac{1}{10} \times ₹ 1,000$

= $₹ \frac{1,000}{10}$

= $₹ 100$

Total amount to be paid = ₹ 1,000 + ₹ 100

= ₹ 1,100

When the selling price of the article = ₹ 1,000

and, Tax = 15% of ₹ 1,000

= $\frac{15}{100} \times ₹ 1,000$

= $\frac{3}{20} \times ₹ 1,000$

= $₹ \frac{3,000}{20}$

= $₹ 150$

Total amount to be paid = ₹ 1,000 + ₹ 150

= ₹ 1,150

The increase in tax = ₹ 1,150 - ₹ 1,100

= ₹ 50

Hence, option 3 is the correct option.

The selling price of an article = ₹ 440

and, Tax = 10% of marked price

Let the marked price be ₹ $x$.

x + {10% of x} = 440

$$\begin{aligned}\Rightarrow x + \frac{10}{100} \times x = ₹ 440\\[1em] \Rightarrow x + \frac{1}{10} \times x = ₹ 440\\[1em] \Rightarrow \frac{10x}{10} + \frac{x}{10} = ₹ 440\\[1em] \Rightarrow \frac{(10x + x)}{10} = ₹ 440\\[1em] \Rightarrow \frac{11x}{10} = ₹ 440\\[1em] \Rightarrow x = ₹ \frac{440 \times 10}{11}\\[1em] \Rightarrow x = ₹ \frac{4400}{11}\\[1em] \Rightarrow x = ₹ 400\\[1em]\end{aligned}$$

Hence, option 2 is the correct option.

Cost of some goods/services = ₹ 800

and, GST = 12% of ₹ 800

= $\frac{12}{100} \times ₹ 800$

= $\frac{6}{50} \times ₹ 800$

= $₹ \frac{4,800}{50}$

= $₹ 96$

Total amount of bill = ₹ 800 + ₹ 96

= ₹ 896

Hence, option 1 is the correct option.

Cost of some goods/services = ₹ 1,500

and, GST = 8% of ₹ 1,500

= $\frac{8}{100} \times ₹ 1,500$

= $\frac{2}{25} \times ₹ 1,500$

= $₹ \frac{3,000}{25}$

= $₹ 120$

Total amount of bill = ₹ 1,500 + ₹ 120

= ₹ 1,620

Hence, option 3 is the correct option.

Given:

Sale price = ₹ 3,840

Tax paid = ₹ 345.60

Let rate of tax = $x%$

$$\begin{aligned}\Rightarrow\frac{x}{100} \times ₹ 3,840 = ₹ 345.60\\[1em] \Rightarrow x = \frac{345.60 \times 100}{3840}%\\[1em] \Rightarrow x = \frac{34560}{3840}%\\[1em] \Rightarrow x = 9%\end{aligned}$$

Hence, the rate of tax = $9%$.

Given:

Selling price of the washing machine = ₹ 13,530

and, Tax = 10% of marked price

Let the marked price be ₹ $x$.

$x + 10$ % $\text{ of } x$ = $₹ 13,530$

$$\begin{aligned}\Rightarrow x + \frac{10}{100} \times x = ₹ 13,530\\[1em] \Rightarrow x + \frac{1}{10} \times x = ₹ 13,530\\[1em] \Rightarrow \frac{10x}{10} + \frac{x}{10} = ₹ 13,530\\[1em] \Rightarrow \frac{(10x + x)}{10} = ₹ 13,530\\[1em] \Rightarrow \frac{11x}{10} = ₹ 13,530\\[1em] \Rightarrow x = ₹ \frac{13,530 \times 10}{11}\\[1em] \Rightarrow x = ₹ \frac{1,35,300}{11}\\[1em] \Rightarrow x = ₹ 12,300\\[1em]\end{aligned}$$

Hence, the cost of washing machine is ₹ 12,300.

Given:

Sale price of biscuits = ₹ 158

and, Tax = 6% of ₹ 158

= $\frac{6}{100} \times ₹ 158$

= $\frac{3}{50} \times ₹ 158$

= $₹ \frac{474}{50}$

= $₹ 9.48$

Total amount to be paid by Sarita for biscuits = ₹ 158 + ₹ 9.48

= ₹ 167.48

Sale price of the cosmetic goods = ₹ 354

and, Tax = 9% of ₹ 354

= $\frac{9}{100} \times ₹ 354$

= $\frac{3,186}{100}$

= $₹ 31.86$

Total amount to be paid by Sartia for cosmetic goods = ₹ 354 + ₹ 31.86

= ₹ 385.86

Total amount paid by Sartia = ₹ 167.48 + ₹ 385.86

= ₹ 553.34

Given:

The selling price of a T.V. = ₹ 13,407

and, Tax = 9% of marked price

Let the marked price be ₹ $x$.

$x + 9$ % $\text{of } x = ₹ 13,407$

$$\begin{aligned}\Rightarrow x + \frac{9}{100} \times x = ₹ 13,407\\[1em] \Rightarrow \frac{100x}{100} + \frac{9x}{100} = ₹ 13,407\\[1em] \Rightarrow \frac{(100x + 9x)}{100} = ₹ 13,407\\[1em] \Rightarrow \frac{109x}{100} = ₹ 13,407\\[1em] \Rightarrow x = ₹ \frac{13,407 \times 100}{109}\\[1em] \Rightarrow x = ₹ \frac{13,40,700}{109}\\[1em] \Rightarrow x = ₹ 12,300\\[1em]\end{aligned}$$

Marked price of the T.V. = ₹ 12,300

Increased Tax = 13% of marked price

$$\begin{aligned}\Rightarrow\frac{13}{100} \times ₹ 12,300 \\[1em] \Rightarrow₹ \frac{1,59,900}{100} \\[1em] \Rightarrow ₹ 1,599\end{aligned}$$

Total amount paid = ₹ 12,300 + ₹ 1,599

= ₹ 13,899

Difference of selling price = ₹ 13,899 - ₹ 13,407

= ₹ 492

Hence, the cost of the T.V. is ₹ 12,300 and the customer has to pay ₹ 492 more for the T.V. when tax is increased by 13%.

Given:

The selling price of an article = ₹ 8,250

and, Tax = 10% of marked price

Let the marked price be ₹ $x$.

$x + 10$ % $\text{of } x = ₹ 8,250$

$$\begin{aligned}\Rightarrow x + \frac{10}{100} \times x = ₹ 8,250\\[1em] \Rightarrow x + \frac{1}{10} \times x = ₹ 8,250\\[1em] \Rightarrow \frac{10x}{10} + \frac{x}{10} = ₹ 8,250\\[1em] \Rightarrow \frac{(10x + x)}{10} = ₹ 8,250\\[1em] \Rightarrow \frac{11x}{10} = ₹ 8,250\\[1em] \Rightarrow x = ₹ \frac{8,250 \times 10}{11}\\[1em] \Rightarrow x = ₹ \frac{82,500}{11}\\[1em] \Rightarrow x = ₹ 7,500\\[1em]\end{aligned}$$

(i) Marked price of the article = ₹ 7,500

And, Tax = 15% of marked price

$$\begin{aligned}\Rightarrow\frac{15}{100} \times ₹ 7,500 \\[1em] \Rightarrow₹ \frac{1,12,500}{100} \\[1em] \Rightarrow ₹ 1,125\end{aligned}$$

Total amount paid = ₹ 7,500 + ₹ 1,125

= ₹ 8,625

Difference in selling price = ₹ 8,625 - ₹ 8,250

= ₹ 375

Hence, the customer has to pay ₹ 375 more for the article when tax is increased by 15%.

(ii) Marked price of the article = ₹ 7,500

And, Tax = 6% of marked price

$$\begin{aligned}\Rightarrow\frac{6}{100} \times ₹ 7,500 \\[1em] \Rightarrow₹ \frac{45,000}{100} \\[1em] \Rightarrow ₹ 450\end{aligned}$$

Total amount paid = ₹ 7,500 + ₹ 450

= ₹ 7,950

Difference in selling price = ₹ 8,250 - ₹ 7,950

= ₹ 300

Hence, the customer has to pay ₹ 300 less for the article when tax was decreased by 6%.

(iii) Marked price of the article = ₹ 7,500

Tax is increased by 2% means (10% + 2%) = 12%

Increased Tax = 12% of marked price

$$\begin{aligned}\Rightarrow\frac{12}{100} \times ₹ 7,500 \\[1em] \Rightarrow₹ \frac{90,000}{100} \\[1em] \Rightarrow ₹ 900\end{aligned}$$

Total amount paid = ₹ 7,500 + ₹ 900

= ₹ 8,400

Difference in selling price = ₹ 8,400 - ₹ 8,250

= ₹ 150

Hence, the customer has to pay ₹ 150 more for the article when tax is increased to 2%.

(iv) Marked price of the article = ₹ 7,500

Tax is decreased by 3% means (10% - 3%) = 7%.

Decreased Tax = 7% of marked price

$$\begin{aligned}\Rightarrow\frac{7}{100} \times ₹ 7,500 \\[1em] \Rightarrow₹ \frac{52,500}{100} \\[1em] \Rightarrow ₹ 525\end{aligned}$$

Total amount paid = ₹ 7,500 + ₹ 525

= ₹ 8,025

Difference in selling price = ₹ 8,250 - ₹ 8,025

= ₹ 225

Hence, the customer has to pay ₹ 225 less for the article when tax is decreased to 3%.

(i) Given:

Sale price of bicycle = ₹ 1,664

List price of bicycle = ₹ 1,600

Let rate of tax = $x%$

Tax on the sale = $x%$ of ₹ 1,600

$$\begin{aligned}\Rightarrow\frac{x}{100} \times ₹ 1,600\\[1em] \Rightarrow\frac{1,600x}{100}\\[1em] \Rightarrow 16x\\[1em]\end{aligned}$$

The amount to be paid = Sale price of bicycle

$\Rightarrow 1,600 + x$ % $\text{of } 1,600 = 1,664$

$$\begin{aligned}\Rightarrow 1,600 + 16x = 1,664\\[1em] \Rightarrow 16x = 1,664 - 1,600\\[1em] \Rightarrow 16x = 64\\[1em] \Rightarrow x = \frac{64}{16}\\[1em]\end{aligned}$$

$\Rightarrow x = 4$%

Hence the rate of Tax = $4%$

(ii) Given:

List price of bicycle = ₹ 1,600

Tax is increased by 6%, means (4% + 6%) = 10% of marked price.

Increased Tax = 10% of ₹ 1,600

$$\begin{aligned}\Rightarrow\frac{10}{100} \times 1,600\\[1em] \Rightarrow\frac{16,000}{100}\\[1em] \Rightarrow 160\end{aligned}$$

Total amount to be paid = ₹ 1,600 + ₹ 160

= ₹ 1,760

Hence, the price a customer will pay for the bicycle = ₹ 1,760.

Given:

List price of goods = ₹ 25,000

The rate of GST = 5% of list price

$$\begin{aligned}\Rightarrow₹ \frac{5}{100} \times 25,000\\[1em] \Rightarrow₹ \frac{1}{20} \times 25,000\\[1em] \Rightarrow₹ \frac{25,000}{20}\\[1em] \Rightarrow₹ 1,250\end{aligned}$$

Total amount to be paid = ₹ 25,000 + ₹ 1,250

= ₹ 26,250

John will pay ₹ 26,250 for all goods.

Given:

Cost of transaction = ₹ 30,000

Discount = 30% of cost of transaction

$\Rightarrow30$ % $\text{of } ₹ 30,000$

$$\begin{aligned}\Rightarrow \frac{30}{100} \times ₹ 30,000\\[1em] \Rightarrow 3 \times ₹ 3,000\\[1em] \Rightarrow ₹ 9,000\end{aligned}$$

Taxable cost of goods = ₹ 30,000 - ₹ 9,000 = ₹ 21,000

IGST = 28% of ₹ 21,000.

$$\begin{aligned}\Rightarrow \frac{28}{100} \times ₹ 21,000\\[1em] \Rightarrow \frac{7}{25} \times ₹ 21,000\\[1em] \Rightarrow ₹ \frac{147,000}{25}\\[1em] \Rightarrow ₹ 5,880\end{aligned}$$

Amount of bill = ₹ 21,000 + ₹ 5,880

= ₹ 26,880

Hence, amount of bill = ₹ 26,880.

(i) Given:

Cost of service = ₹ 5,000

Discount = 20% of cost of service

$\Rightarrow20$ % $\text{of } ₹ 5,000$

$$\begin{aligned}\Rightarrow \frac{20}{100} \times ₹ 5,000\\[1em] \Rightarrow \frac{1}{5} \times ₹ 5,000\\[1em] \Rightarrow ₹ \frac{5,000}{5}\\[1em] \Rightarrow ₹ 1,000\end{aligned}$$

Taxable cost of service = ₹ 5,000 - ₹ 1,000 = ₹ 4,000

IGST = 12% of ₹ 4,000.

$$\begin{aligned}\Rightarrow \frac{12}{100} \times ₹ 4,000\\[1em] \Rightarrow \frac{3}{25} \times ₹ 4,000\\[1em] \Rightarrow ₹ \frac{12,000}{25}\\[1em] \Rightarrow ₹ 480\end{aligned}$$

Amount of bill = ₹ 4,000 + ₹ 480 = ₹ 4,480

(ii) Given:

Cost of service = ₹ 12,500

Discount = 40% of cost of service

$\Rightarrow40$ % $\text{of } ₹ 12,500$

$$\begin{aligned}\Rightarrow \frac{40}{100} \times ₹ 12,500\\[1em] \Rightarrow \frac{10}{25} \times ₹ 12,500\\[1em] \Rightarrow ₹ \frac{125,000}{25}\\[1em] \Rightarrow ₹ 5,000\end{aligned}$$

Taxable cost of service = ₹ 12,500 - ₹ 5,000

= ₹ 7,500

IGST = 18% of ₹ 7,500.

$$\begin{aligned}\Rightarrow \frac{18}{100} \times ₹ 7,500\\[1em] \Rightarrow \frac{9}{50} \times ₹ 7,500\\[1em] \Rightarrow ₹ \frac{67,500}{50}\\[1em] \Rightarrow ₹ 1,350\end{aligned}$$

Amount of bill = ₹ 7,500 + ₹ 1,350 = ₹ 8,850

Total amount of bill for both the services = ₹ 4,480 + ₹ 8,850

= ₹ 13,330

Hence, total amount of bill = ₹ 13,330.

Selling price of 1 article = ₹ 450

Selling price of 20 articles = ₹ 450 x 20

= ₹ 9,000

Discount = 20% of ₹ 9,000

$$\begin{aligned}\Rightarrow\frac{20}{100} \times ₹ 9,000\\[1em] \Rightarrow\frac{1}{5} \times ₹ 9,000\\[1em] \Rightarrow ₹ \frac{9,000}{5}\\[1em] \Rightarrow ₹ 1,800\end{aligned}$$

Taxable cost of articles = ₹ 9,000 - ₹ 1,800

= ₹ 7,200

IGST = 28% of ₹ 7,200.

$$\begin{aligned}\Rightarrow \frac{28}{100} \times ₹ 7,200\\[1em] \Rightarrow \frac{7}{25} \times ₹ 7,200\\[1em] \Rightarrow ₹ \frac{50,400}{25}\\[1em] \Rightarrow ₹ 2,016\end{aligned}$$

Amount of bill = ₹ 7,200 + ₹ 2,016

= ₹ 9,216

Hence, amount of bill = ₹ 9,216.

Selling price of 1 article = ₹ 800

Selling price of 40 articles = ₹ 800 x 40

= ₹ 3,200

Discount = 30% of ₹ 32,000

$$\begin{aligned}\Rightarrow\frac{30}{100} \times ₹ 32,000\\[1em] \Rightarrow\frac{3}{10} \times ₹ 32,000\\[1em] \Rightarrow ₹ \frac{96,000}{10}\\[1em] \Rightarrow ₹ 9,600\end{aligned}$$

Taxable cost of articles = ₹ 32,000 - ₹ 9,600

= ₹ 22,400

GST = 12% of ₹ 22,400.

$$\begin{aligned}\Rightarrow \frac{12}{100} \times ₹ 22,400\\[1em] \Rightarrow \frac{3}{25} \times ₹ 22,400\\[1em] \Rightarrow ₹ \frac{67,200}{25}\\[1em] \Rightarrow ₹ 2,688\end{aligned}$$

Amount of bill = ₹ 22,400 + ₹ 2,688

= ₹ 25,088

Selling price of 1 article = ₹ 1,000

Selling price of 75 articles = ₹ 1,000 x 75

= ₹ 75,000

Discount = 20% of ₹ 75,000

$$\begin{aligned}\Rightarrow\frac{20}{100} \times ₹ 75,000\\[1em] \Rightarrow\frac{1}{5} \times ₹ 75,000\\[1em] \Rightarrow ₹ \frac{75,000}{5}\\[1em] \Rightarrow ₹ 15,000\end{aligned}$$

Taxable cost of article = ₹ 75,000 - ₹ 15,000

= ₹ 60,000

GST = 12% of ₹ 60,000.

$$\begin{aligned}\Rightarrow \frac{12}{100} \times ₹ 60,000\\[1em] \Rightarrow \frac{3}{25} \times ₹ 60,000\\[1em] \Rightarrow ₹ \frac{1,80,000}{25}\\[1em] \Rightarrow ₹ 7,200\end{aligned}$$

Amount of bill = ₹ 60,000 + ₹ 7,200

= ₹ 67,200

Total amount the dealer at Mumbai will pay to dealer in Bihar = ₹ 25,088 + ₹ 67,200

= ₹ 92,288

Hence, amount of bill = ₹ 92,288.

Given:

S.P. = ₹ 18

Loss % = 10%

Let C.P. = $₹x$.

$\text{Loss}$% $= \frac{\text{Loss}}{\text{C.P.}} \times \text{100}$

Putting the values, we get

$$\begin{aligned}\Rightarrow 10 = \frac{\text{Loss}}{x} \times 100\\[1em] \Rightarrow \text{Loss} = \frac{10 \times x}{100}\\[1em] = \frac{x}{10}\end{aligned}$$

As we know:

$$\begin{aligned}\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow \frac{x}{10} = x - 18\\[1em] \Rightarrow 18 = x - \frac{x}{10} \\[1em] \Rightarrow 18 = \frac{10x}{10} - \frac{x}{10}\\[1em] \Rightarrow 18 = \frac{(10x - x)}{10} \\[1em] \Rightarrow 18 = \frac{9x}{10}\\[1em] \Rightarrow x = \frac{18 \times 10}{9}\\[1em] \Rightarrow x = \frac{180}{9}\\[1em] \Rightarrow x = 20\end{aligned}$$

When C.P. = ₹ 20

Profit % = 15 %

$\text {Profit}$% $= \frac{\text{Profit}}{\text{C.P.}}\times 100$

$$\begin{aligned}\Rightarrow\text {15} = \frac{\text{Profit}}{20}\times 100\\[1em] \Rightarrow\text{Profit} = \frac{15 \times 20}{100}\\[1em] \Rightarrow\text{Profit} = \frac{300}{100}\\[1em] \Rightarrow\text{Profit} = 3\end{aligned}$$

And,

$$\begin{aligned}\text{Profit = S.P. - C.P.}\\[1em] \Rightarrow 3 =\text{S.P.} - 20\\[1em] \Rightarrow \text{S.P.} = ₹ 20 + 3\\[1em] \Rightarrow \text{S.P.} = ₹ 23\end{aligned}$$

Hence, option 4 is the correct option.

C.P. of 20 articles = S.P. of 16 articles

Let the C.P. of 20 articles be ₹ 100.

The C.P. of 1 article = ₹ $\frac{100}{20}$ = ₹ 5

The S.P. of 16 articles = The C.P. of 20 articles = ₹ 100

The S.P. of 1 article = ₹ $\frac{100}{16}$ = ₹ 6.25

(∵ S.P. is greater than C.P., means articles are sold at a profit.)

Profit = S.P. - C.P.

= ₹ (6.25 - 5) = ₹ 1.25

$\text{Profit }$% $= \frac{\text{Profit}}{\text{C.P.}} \times 100$%

$= \frac{1.25}{5} \times 100$%

$= \frac{125}{5}$%

$= 25$%

Hence,option 1 is the correct option.

Let the marked price of goods be ₹ $100$.

Discount = 20% of marked price

= $\frac{20}{100} \times 100$

= $\frac{20}{\cancel{100}} \times \cancel{100}$

= $20$

Selling price of goods = Marked price - Discount

= ₹ $100 - 20$

= ₹ $80$

Selling price without discount = marked price of the goods = ₹ $100$

Difference in the selling price = ₹ $100 - 80$

(∵ Difference is positive means selling price has increased.)

Increase in price = $\frac{\text{Difference in S.P.}}{\text{Initial M.P.}} \times 100%$

= $\frac{20}{100}\times100%$

= $\frac{20}{\cancel{100}}\times\cancel{100}%$

= $20% \text{ increase}$

Hence,option 3 is the correct option.

Marked price of the article = ₹ 400

and, Tax = 10% of ₹ 400

= $\frac{10}{100} \times ₹ 400$

= $\frac{1}{10} \times ₹ 400$

= $₹ \frac{400}{10}$

= $₹ 40$

Total amount to be paid = ₹ 400 + ₹ 40

= ₹ 440

When Marked price of the article = ₹ 400

and, Tax = 15% of ₹ 400

= $\frac{15}{100} \times ₹ 400$

= $\frac{3}{20} \times ₹ 400$

= $₹ \frac{1200}{20}$

= $₹ 60$

Total amount to be paid = ₹ 400 + ₹ 60

= ₹ 460

Difference in the total amount to be paid = ₹ 460 - ₹ 440

= ₹ 20

Hence, option 4 is the correct option.

Let the cost of services be ₹ $200$

and, GST = 18% of ₹ 200

= $\frac{18}{100} \times ₹ 200$

= $\frac{9}{50} \times ₹ 200$

= $₹ \frac{1800}{50}$

= $₹ 36$

Total amount of bill = ₹ (200 + 36) = ₹ 236

Hence, option 3 is the correct option.

When S.P. > C.P., using formula

Profit = S.P. - C.P.

By formula,

$\Rightarrow \text{Profit}$% $= \frac{\text{Profit}}{\text{C.P.}} \times 100$

$\Rightarrow \text{Profit}$% $= \frac{\text{S.P. - C.P.}}{\text{C.P.}} \times 100$

$\Rightarrow \text{Profit}$% $= \frac{\text{100 S.P. - 100 C.P.}}{\text{C.P.}}$

$\Rightarrow \text{Profit}$% $\times \text{C.P.} = \text{100 S.P. - 100 C.P.}$

$\Rightarrow \text{Profit}$% $\times \text{C.P.} + \text{100 C.P.} = \text{100 S.P.}$

$\Rightarrow \text{C.P. (Profit}$% $+ \space 100) = \text{100 S.P.}$

$\Rightarrow \text{C.P.} = \frac{\text{100 S.P.}}{\text{(Profit Percent + 100)}}$

$\Rightarrow \text{C.P.} = \frac{\text{100 S.P.}}{\text{(Profit Percent + 100)}}$

So, statement 1 is false.

When C.P. > S.P.,

Loss = C.P. - S.P.

By formula,

$\Rightarrow \text{Loss}$ % $= \frac{\text{Loss}}{\text{C.P.}} \times 100$

$\Rightarrow \text{Loss}$ % $= \frac{\text{C.P. - S.P.}}{\text{C.P.}} \times 100$

$\Rightarrow \text{Loss}$ % $= \frac{\text{100 C.P. - 100 S.P.}}{\text{C.P.}}$

$\Rightarrow \text{Loss}$ % $\times \text{C.P.} = \text{100 C.P. - 100 S.P.}$

$\Rightarrow \text{100 S.P.} = \text{100 C.P.} - \text{Loss}$ % $\times \text{C.P.}$

$\Rightarrow \text{100 S.P.} = \text{100 C.P.} - \text{Loss}$ % $\times \text{C.P.}$

$\Rightarrow \text{100 S.P.} = \text{C.P. (100 - Loss}$ % $)$

$\Rightarrow \text{S.P.} = \frac{\text{C.P. (100 - Loss Percent)}}{100}$

So, statement 2 is false.

Hence, option 2 is the correct option.

Let M.P. = ₹ 100

1st discount = 10% of ₹ 100

= ₹ $\frac{10}{100} \times 100$

= ₹ 10

Discounted price = ₹ 100 - ₹ 10 = ₹ 90

2nd discount = 5% of ₹90

= ₹ $\frac{5}{100} \times 90$

= ₹ 4.50

Final discounted price = ₹ 90 - ₹ 4.5 = ₹ 85.50

Total discount = M.P. - Final discounted price

= ₹ 100 - ₹ 85.5 = ₹ 14.5

Since the discount of ₹ 14.5 is on ₹ 100.

∴ Single equivalent discount%

$$\begin{aligned}= \frac{\text{Total discount}}{100} \times 100% \\[1em] = \frac{14.5}{100} \times 100% \\[1em] = 14.5%\end{aligned}$$

So, assertion (A) is true.

By formula,

Discount % = $\frac{\text{Discount}}{\text{M.P.}} \times 100%$

So, reason (R) is true.

Both A and R are correct, and R is not the correct explanation for A.

Hence, option 2 is the correct option.

Let the C.P. be ₹ a.

Gain = $\frac{1}{4}$ of its C.P = $\frac{1}{4}$ x a

Using the formula,

S.P. = Gain + C.P.

$$\begin{aligned}\Rightarrow 400 = \frac{1}{4} \times a + a \\[1em] \Rightarrow 400 = \frac{a + 4a}{4} \\[1em] \Rightarrow 400 = \frac{5a}{4} \\[1em] \Rightarrow a = \frac{4 \times 400}{5} \\[1em] \Rightarrow a = \frac{1600}{5} \\[1em] \Rightarrow a = ₹320\end{aligned}$$

Gain = S.P. - C.P. = ₹ 400 - ₹ 320 = ₹ 80.

$\text{Gain}$ % $= \frac{\text{Gain}}{\text{C.P.}} \times 100$%

$= \frac{80}{320} \times 100$%

$= \frac{8000}{320}$%

$= 25$%

So, assertion (A) is true.

By formula,

Loss% = $\frac{\text{C.P.} \times \text{Loss Percent}}{100}$

So, reason (R) is true but reason (R) does not explains assertion (A).

Hence, option 2 is the correct option.

Given,

M.P. = ₹ 1,200

Sales tax = 20%

Bill amount = M.P. + Tax amount

= ₹ 1,200 + 20% of 1,200

= ₹ 1,200 + $\frac{20}{100}$ x 1,200

= ₹ 1,200 + 20 x 12

= ₹ 1,200 + ₹ 240

= ₹ 1,440

So, assertion (A) is true.

Bill amount = M.P. + Sale tax amount

= M.P. + $\frac{\text{Rate of sale tax}}{100}$ x M.P.

= $M.P.\Big(1 + \frac{\text{Rate of sales tax}}{100}\Big)$

So, reason (R) is false.

Hence, option 3 is the correct option.

If 12 articles are bought for ₹1, then:

C.P. per article = $\frac{1}{12}$ rupees

If 8 articles are sold for ₹ 1, then:

S.P. per article = $\frac{1}{8}$ rupees

Profit = S.P. - C.P.

$$\begin{aligned}\text{Profit }= \frac{1}{8} - \frac{1}{12}\\[1em] = \frac{3 - 2}{24}\\[1em] = \frac{1}{24}\end{aligned}$$

Profit% = $\frac{\text{Profit}}{\text{C.P.}} \times 100$

$\text{Profit}$% $= \frac{\frac{1}{24}}{\frac{1}{12}} \times 100$%

$= \frac{1 \times 12}{24 \times 1} \times 100$%

$= \frac{12}{24} \times 100$%

$= \frac{1}{2} \times 100$%

$= 50$%

So, assertion (A) is true.

Profit % = $\Big(\frac{\text{Profit}}{\text{C.P.}} \times 100\Big)% \text{ and Loss}% = \Big(\frac{\text{Loss}}{\text{C.P.}} \times 100\Big)%$

These are the standard formula for finding profit% and loss%.

So, reason (R) is true but reason (R) does not clearly explains assertion (A) as there is no case of loss.

Hence, option 2 is the correct option.

(i) Given:

S.P. of the bicycle = ₹ 405

Loss = one-tenth of its C.P.

Let the C.P. be ₹ $x$.

Loss = $\frac{1}{10} \times x$

= $\frac{x}{10}$

As we know,

$$\begin{aligned}\text{Loss = C.P. - S.P.}\\[1em] \Rightarrow\frac{x}{10} = x - 405\\[1em] \Rightarrow x - \frac{x}{10} = 405\\[1em] \Rightarrow \frac{10x}{10} - \frac{x}{10} = 405\\[1em] \Rightarrow \frac{(10x - x)}{10} = 405\\[1em] \Rightarrow \frac{9x}{10} = 405\\[1em] \Rightarrow x = \frac{405 \times 10}{9} \\[1em] \Rightarrow x = \frac{4050}{9} \\[1em] \Rightarrow x = 450\end{aligned}$$

Hence, the cost price = ₹ 450.

(ii) Loss = one-tenth of the C.P.

= $\frac{1}{10} \times 450$

= $\frac{450}{10}$

= $45$

$\text{Loss}$ % $= \frac{\text{Loss}}{\text{C.P.}} \times 100$%

$= \frac{45}{450} \times 100$%

$= \frac{1}{10} \times 100$%

$= 10$%

Hence, the loss percent = 10%.

(i) Given:

S.P. of the radio set = ₹ 250

Gain = one-ninth of its C.P.

Let the C.P. be ₹ $x$.

Gain = $\frac{1}{9} \times x$

= $\frac{x}{9}$

As we know,

$$\begin{aligned}\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow\frac{x}{9} = 250 - x\\[1em] \Rightarrow \frac{x}{9} + x = 250\\[1em] \Rightarrow \frac{x}{9} + \frac{9x}{9} = 250\\[1em] \Rightarrow \frac{(x + 9x)}{9} = 250\\[1em] \Rightarrow \frac{10x}{9} = 250\\[1em] \Rightarrow x = \frac{250 \times 9}{10} \\[1em] \Rightarrow x = \frac{2250}{10} \\[1em] \Rightarrow x = 225\end{aligned}$$

Hence, the cost price = ₹ 225.

(ii) Gain = one-ninth of its C.P.

= $\frac{1}{9} \times 225$

= $\frac{225}{9}$

= $25$

$\text{Gain}$ % $= \frac{\text{Gain}}{\text{C.P.}} \times 100$%

$\Rightarrow \text{Gain}$ % $= \frac{25}{225} \times 100$%

$= \frac{1}{9} \times 100$%

$= \frac{100}{9}$%

$= 11\frac{1}{9}$%

Hence, the gain percent = $11\frac{1}{9}%$.

Given:

S.P. of tape recorder = ₹ 990

Gain% on one tape recorder = 10%

Loss% on one tape recorder = 10%

Lets take C.P. of tape recorder be ₹ $x$.

As we know,

$\text{Gain}$% $= \frac{\text{Gain}}{\text{C.P.}} \times 100$

$$\begin{aligned}\Rightarrow10 = \frac{\text{Gain}}{x} \times 100\\[1em] \Rightarrow\text{Gain} = \frac{10 \times x}{100}\\[1em] \Rightarrow\text{Gain} = \frac{x}{10}\end{aligned}$$

And,

$$\begin{aligned}\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow\frac{x}{10} = 990 - x\\[1em] \Rightarrow\frac{x}{10} + x = 990\\[1em] \Rightarrow\frac{x}{10} + \frac{10x}{10} = 990\\[1em] \Rightarrow\frac{(x + 10x)}{10} = 990\\[1em] \Rightarrow\frac{11x}{10} = 990\\[1em] \Rightarrow x = \frac{990\times10}{11}\\[1em] \Rightarrow x = \frac{9,900}{11}\\[1em] \Rightarrow x = 900\end{aligned}$$

When S.P. is ₹ 990 and gain% is 10%, then C.P. is ₹ 900.

Now, when loss% = 10%

As we know,

$\text{Loss}$% $= \frac{\text{Loss}}{\text{C.P.}} \times 100$

$$\begin{aligned}\Rightarrow10 = \frac{\text{Loss}}{x} \times 100\\[1em] \Rightarrow\text{Loss} = \frac{10 \times x}{100}\\[1em] \Rightarrow\text{Loss} = \frac{x}{10}\end{aligned}$$

And,

$$\begin{aligned}\text{Loss = C.P. - S.P.}\\[1em] \Rightarrow\frac{x}{10} = x - 990\\[1em] \Rightarrow x - \frac{x}{10} = 990\\[1em] \Rightarrow\frac{10x}{10} - \frac{x}{10} = 990\\[1em] \Rightarrow\frac{(10x - x)}{10} = 990\\[1em] \Rightarrow\frac{9x}{10} = 990\\[1em] \Rightarrow x = \frac{990\times10}{9}\\[1em] \Rightarrow x = \frac{9,900}{9}\\[1em] \Rightarrow x = 1,100\end{aligned}$$

When S.P. is ₹ 990 and loss% is 10%, then C.P. is ₹ 1,100.

Total C.P. of both tape recorder = ₹ 900 + ₹ 1,100

= ₹ 2,000

Total S.P. of both tape recorders = ₹ 990 + ₹ 990

= ₹ 1,980

($\because$ S.P. is lesser than C.P., means article is sold at loss.)

$$\begin{aligned}\text{Loss = C.P. - S.P.}\\[1em] \Rightarrow\text{Loss} = ₹ 2,000 - ₹ 1,980\\[1em] =₹ 20\end{aligned}$$

And,

$\text{Loss}$% $= \frac{\text{Loss}}{\text{C.P.}}\times100$

$= \frac{20}{2000}\times100$%

$= \frac{1}{100}\times100$%

$= \frac{1}{\cancel{100}}\times\cancel{100}$%

$= 1$%

Hence, the overall loss percent = 1%.

(i) Given:

S.P. of tape recorder = ₹ 2,760

Gain% on one tape recorder = 15%

Let C.P. of tape recorder = ₹ $x$.

As we know,

$\text{Gain}$% $= \frac{\text{Gain}}{\text{C.P.}} \times 100$

$$\begin{aligned}\Rightarrow15 = \frac{\text{Gain}}{x} \times 100\\[1em] \Rightarrow\text{Gain} = \frac{15 \times x}{100}\\[1em] \Rightarrow\text{Gain} = \frac{3x}{20}\end{aligned}$$

And,

$$\begin{aligned}\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow\frac{3x}{20} = 2,760 - x\\[1em] \Rightarrow\frac{3x}{20} + x = 2,760\\[1em] \Rightarrow\frac{3x}{20} + \frac{20x}{20} = 2,760\\[1em] \Rightarrow\frac{(3x + 20x)}{20} = 2,760\\[1em] \Rightarrow\frac{23x}{20} = 2,760\\[1em] \Rightarrow x = \frac{2,760\times20}{23}\\[1em] \Rightarrow x = \frac{55,200}{23}\\[1em] \Rightarrow x = 2,400\end{aligned}$$

Hence, the cost price of tape recorder = ₹ 2,400.

(ii) Given:

S.P. of the CD Player = ₹ 3,240

Loss% = 10%

Let the C.P. of the CD Player be ₹ $x$

As we know,

$\text{Loss}$% $= \frac{\text{Loss}}{\text{C.P.}} \times 100$

$$\begin{aligned}\Rightarrow10 = \frac{\text{Loss}}{x} \times 100\\[1em] \Rightarrow\text{Loss} = \frac{10 \times x}{100}\\[1em] \Rightarrow\text{Loss} = \frac{x}{10}\end{aligned}$$

And,

$$\begin{aligned}\text{Loss = C.P. - S.P.}\\[1em] \Rightarrow\frac{x}{10} = x - 3,240\\[1em] \Rightarrow x - \frac{x}{10} = 3,240\\[1em] \Rightarrow\frac{10x}{10} - \frac{x}{10} = 3,240\\[1em] \Rightarrow\frac{(10x - x)}{10} = 3,240\\[1em] \Rightarrow\frac{9x}{10} = 3,240\\[1em] \Rightarrow x = \frac{3,240 \times10}{9}\\[1em] \Rightarrow x = \frac{32,400}{9}\\[1em] \Rightarrow x = 3,600\end{aligned}$$

Hence, the cost price of CD Player = ₹ 3,600.

(iii) Total C.P. of both = ₹ 2,400 + ₹ 3,600

= ₹ 6,000

Total C.P. of both items = ₹ 6,000

(iv) Total S.P. of both = ₹ 2,760 + ₹ 3,240

= ₹ 6,000

Total S.P. of both items = ₹ 6,000

(v) As S.P. is equal to C.P., means article is sold at neither loss nor gain.

Hence, the overall gain percent or loss percent = 0%.

Let the cost John paid for the article be ₹ $x$.

John sold the article to Peter at profit = 20%

As we know

$\text{Profit}$% $= \frac{\text{Profit}}{\text{C.P.}} \times 100$

$$\begin{aligned}\Rightarrow 20 = \frac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \frac{20 \times x}{100}\\[1em] \Rightarrow \text{Profit} = \frac{x}{5}\\[1em]\end{aligned}$$

And

$$\begin{aligned}\text{Profit = S.P. - C.P.}\\[1em] \Rightarrow \frac{x}{5} = S.P. - x\\[1em] \Rightarrow S.P. = \frac{x}{5} + x\\[1em] \Rightarrow S.P. = \frac{x}{5} + \frac{5x}{5}\\[1em] \Rightarrow S.P. = \frac{(x + 5x)}{5}\\[1em] \Rightarrow S.P. = \frac{6x}{5}\\[1em]\end{aligned}$$

Now, S.P. for John will be C.P. for Peter and Peter sold it to Mohan.

C.P. of the article for Peter = $\frac{6x}{5}$

Loss% of the article for Peter = 5%

S.P. of the article for Peter = ₹ 912

As we know

$\text{Loss}$% $= \frac{\text{Loss}}{\text{C.P.}} \times 100$

$$\begin{aligned}\Rightarrow 5 = \frac{\text{Loss}}{\frac{6x}{5}} \times 100\\[1em] \Rightarrow \text{Loss} = \frac{5 \times 6x}{5 \times 100}\\[1em] \Rightarrow \text{Loss} = \frac{30x}{500}\\[1em] \Rightarrow \text{Loss} = \frac{3x}{50}\\[1em]\end{aligned}$$

And

$$\begin{aligned}\text{Loss = C.P. - S.P.}\\[1em] \Rightarrow \frac{3x}{50} = \frac{6x}{5} - 912\\[1em] \Rightarrow \frac{6x}{5} - \frac{3x}{50} = 912\\[1em] \Rightarrow \frac{60x}{50} - \frac{3x}{50} = 912\\[1em] \Rightarrow \frac{(60x - 3x)}{50} = 912\\[1em] \Rightarrow \frac{57x}{50} = 912\\[1em] \Rightarrow x = \frac{912 \times 50}{57}\\[1em] \Rightarrow x = \frac{45,600}{57}\\[1em] \Rightarrow x = 800\end{aligned}$$

Hence, John paid ₹ 800 for the article.

Given:

S.P. of an article = ₹ 1,200

Loss = one-fifth of C.P.

Let C.P. of the article = ₹ $x$.

Loss = $\frac{1}{5} \times x$

= $\frac{x}{5}$

As we know:

$$\begin{aligned}\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow \frac{x}{5} = x - 1,200\\[1em] \Rightarrow 1,200 = x - \frac{x}{5}\\[1em] \Rightarrow 1,200 = \frac{5x}{5} - \frac{x}{5}\\[1em] \Rightarrow 1,200 = \frac{(5x - x)}{5} \\[1em] \Rightarrow 1,200 = \frac{4x}{5}\\[1em] \Rightarrow x = \frac{1,200 \times 5}{4}\\[1em] \Rightarrow x = \frac{6,000}{4}\\[1em] \Rightarrow x = 1,500\end{aligned}$$

Hence, C.P. of the article = ₹ 1,500

Gain % = 30%

$\text{Gain}$ % $= \frac{\text{Gain}}{\text{C.P.}} \times \text{100}$

$$\begin{aligned}\Rightarrow 30 = \frac{\text{Gain}}{1,500} \times 100\\[1em] \Rightarrow \text{Gain} = \frac{30 \times 1,500}{100}\\[1em] \Rightarrow \text{Gain} = \frac{45,000}{100}\\[1em] \Rightarrow \text{Gain} = 450\end{aligned}$$

And,

$$\begin{aligned}\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow 450 = \text{S.P.} - 1,500\\[1em] \Rightarrow \text{S.P.} = 450 + 1,500\\[1em] \Rightarrow \text{S.P.} = 1,950\end{aligned}$$

Hence, New S.P. of the article = ₹ 1,950.

Given:

S.P. of an article = ₹ 1,200

Gain = one-fifth of C.P.

Let C.P. of the article = ₹ $x$.

Gain = $\frac{1}{5} \times x$

= $\frac{x}{5}$

As we know:

$$\begin{aligned}\text{Gain} = \text{S.P. - C.P.}\\[1em] \Rightarrow \frac{x}{5} = 1,200 - x\\[1em] \Rightarrow 1,200 = x + \frac{x}{5}\\[1em] \Rightarrow 1,200 = \frac{5x}{5} + \frac{x}{5}\\[1em] \Rightarrow 1,200 = \frac{(5x + x)}{5} \\[1em] \Rightarrow 1,200 = \frac{6x}{5}\\[1em] \Rightarrow x = \frac{1,200 \times 5}{6}\\[1em] \Rightarrow x = \frac{6,000}{6}\\[1em] \Rightarrow x = 1,000\end{aligned}$$

Hence, C.P. of the article = ₹ 1,000

Gain % = 30%

$\text{Gain}$% $= \frac{\text{Gain}}{\text{C.P.}} \times \text{100}$

$$\begin{aligned}\Rightarrow 30 = \frac{\text{Gain}}{1,000} \times 100\\[1em] \Rightarrow \text{Gain} = \frac{30 \times 1,000}{100}\\[1em] \Rightarrow \text{Gain} = \frac{30,000}{100}\\[1em] \Rightarrow \text{Gain} = ₹ 300\end{aligned}$$

And,

$$\begin{aligned}\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow 300 = \text{S.P.} - 1,000\\[1em] \Rightarrow \text{S.P.} = 300 + 1,000\\[1em] \Rightarrow \text{S.P.} = ₹ 1,300\end{aligned}$$

Hence, S.P. of the article = ₹ 1,300.

25% of the cost price of an article = ₹ 600

$\frac{1}{4}$ of the cost price of an article = ₹ 600

The cost price of an article = ₹ 600 x 4 = ₹ 2,400

Profit on the article = 25%

$\text{Profit}$% $= \frac{\text{Profit}}{\text{C.P.}} \times 100$

$$\begin{aligned}\Rightarrow 25 = \frac{\text{Profit}}{2400} \times 100\\[1em] \Rightarrow \text{Profit} = \frac{25 \times 2400}{100}\\[1em] \Rightarrow \text{Profit} = \frac{60000}{100}\\[1em] \Rightarrow \text{Profit} = 600\end{aligned}$$

And

$$\begin{aligned}\text{Gain} = \text{S.P. - C.P.}\\[1em] \Rightarrow 600 = \text{S.P.} - 2,400\\[1em] \Rightarrow \text{S.P.} = 600 + 2,400\\[1em] \Rightarrow \text{S.P.} = 3,000\end{aligned}$$

Hence, S.P. of the article = ₹ 3,000.

Let the C.P. of the bicycle be ₹ $100$.

Profit % = 5%

As we know

$\text{Profit }$% $= \frac{\text{Profit}}{\text{C.P.}} \times 100$

$$\begin{aligned}\Rightarrow 5 = \frac{\text{Profit}}{100} \times 100 \\[1em] \Rightarrow 5 = \frac{\text{Profit}}{\cancel{100}} \times \cancel{100} \\[1em] \Rightarrow \text{Profit} = ₹ 5\end{aligned}$$

And

$$\begin{aligned}\text{Profit = S.P. - C.P.}\\[1em] \Rightarrow 5 = \text{S.P.} - 100\\[1em] \Rightarrow \text{S.P.} = 100 + 5\\[1em] \Rightarrow \text{S.P.} = ₹ 105\end{aligned}$$

When C.P. of the bicycle is $30%$ less.

$$\begin{aligned}= 100 - \frac{30}{100} \times 100\\[1em] = 100 - \frac{30}{\cancel{100}} \times \cancel{100}\\[1em] = 100 - 30\\[1em] = ₹ 70\end{aligned}$$

∴ New C.P. = ₹ 70

New gain % = 30%.

As we know,

$\text{Gain }$% $= \frac{\text{Gain}}{\text{C.P.}} \times 100$

$$\begin{aligned}\Rightarrow 30 = \frac{\text{Gain}}{70} \times 100 \\[1em] \Rightarrow \text{Gain} = \frac{30 \times 70}{100}\\[1em] \Rightarrow \text{Gain} = \frac{2100}{100}\\[1em] \Rightarrow \text{Gain} = ₹ 21\end{aligned}$$

And

$$\begin{aligned}\text{New Gain = New S.P. - New C.P.}\\[1em] \Rightarrow 21 = \text{New S.P.} - 70\\[1em] \Rightarrow \text{New S.P.} = 21 + 70\\[1em] \Rightarrow \text{New S.P.} = ₹ 91\end{aligned}$$

Difference in Selling Price = Original S.P. - New S.P.

= ₹ 105 - ₹ 91 = ₹ 14

∴ New S.P. is ₹ 14 less than original S.P.

Applying unitary method:

When sold for ₹ 14 less, the C.P. of the bicycle = ₹ 100.

When sold for ₹ 63 less, the C.P. of the bicycle = ₹ $\frac{100}{14} \times 63 = ₹ 450$.

Hence, cost price of the bicycle = ₹ 450.

Let the C.P. of the article be ₹ $100$.

Loss% = 8%

As we know

$\text{Loss }$% $= \frac{\text{Loss}}{\text{C.P.}} \times 100$

$$\begin{aligned}\Rightarrow 8 = \frac{\text{Loss}}{100} \times 100 \\[1em] \Rightarrow 8 = \frac{\text{Loss}}{\cancel{100}} \times \cancel{100}\\[1em] \Rightarrow \text{Loss} = 8\end{aligned}$$

And

$$\begin{aligned}\text{Loss = C.P. - S.P.}\\[1em] \Rightarrow 8 = 100 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 100 - 8\\[1em] \Rightarrow \text{S.P.} = 92\end{aligned}$$

When C.P. of the article is 10% less.

$$\begin{aligned}= 100 - \frac{10}{100} \times 100\\[1em] = 100 - \frac{10}{\cancel{100}} \times \cancel{100}\\[1em] = 100 - 10\\[1em] = 90\end{aligned}$$

The gain % = 20%.

As we know

$\text{Gain}$% $= \frac{\text{Gain}}{\text{C.P.}} \times 100$

$$\begin{aligned}\Rightarrow 20 = \frac{\text{Gain}}{90} \times 100 \\[1em] \Rightarrow \text{Gain} = \frac{20 \times 90}{100}\\[1em] \Rightarrow \text{Gain} = \frac{1800}{100}\\[1em] \Rightarrow \text{Gain} = 18\end{aligned}$$

And

$$\begin{aligned}\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow 18 = \text{S.P.} - 90\\[1em] \Rightarrow \text{S.P.} = 18 + 90\\[1em] \Rightarrow \text{S.P.} = 108\end{aligned}$$

Difference in Selling Price = ₹ 108 - ₹ 92 = ₹ 16

Applying unitary method:

When sold for ₹ $16$ more, the C.P. of the article = ₹ $100$.

When sold for ₹ $36$ more, the C.P. of the article = ₹ $\frac{100}{16} \times 36 = ₹ 225$.

Hence, cost price of the article = ₹ $225$.

(i) Given:

C.P. = 25% below the M.P.

C.P. = ₹ 2,400

Let the M.P. be ₹ $x$.

$$\begin{aligned}x - \frac{25}{100} \times x = 2,400\\[1em] \Rightarrow x - \frac{1}{4} \times x = 2,400\\[1em] \Rightarrow \frac{4x}{4} - \frac{x}{4} = 2,400\\[1em] \Rightarrow \frac{(4x - x)}{4} = 2,400\\[1em] \Rightarrow \frac{3x}{4} = 2,400\\[1em] \Rightarrow x = \frac{2,400 \times 4}{3}\\[1em] \Rightarrow x = \frac{9,600}{3}\\[1em] \Rightarrow x = ₹ 3,200\end{aligned}$$

Hence, the marked price = ₹ 3,200.

(ii) M.P. of the article = ₹ 3,200

Discount = 15% of M.P.

$$\begin{aligned}\Rightarrow \frac{15}{100} \times ₹ 3,200\\[1em] \Rightarrow \frac{3}{20} \times ₹ 3,200\\[1em] \Rightarrow₹ \frac{9,600}{20}\\[1em] \Rightarrow₹ 480\end{aligned}$$

S.P. of the article = M.P. - Discount

= ₹ 3,200 - ₹480

= ₹ 2,720

Hence, the selling price = ₹ 2,720.

(iii) C.P. = ₹ 2,400

S.P. = ₹ 2,720

Profit = S.P. - C.P.

= $₹ 2,720 - ₹ 2,400$

= $₹ 320$

And,

$\text{Profit}$% $= \frac{\text{Profit}}{\text{C.P.}} \times 100$%

$= \frac{320}{2400} \times 100$%

$= \frac{32000}{2400}$%

$= \frac{40}{3}$%

$= 13\frac{1}{3}$%

Hence, the profit percent = $13\frac{1}{3}%$.

(i) Let M.P. be ₹ $100$.

1st discount % = 20%

$\text{Discount}$ % $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 20 = \frac{\text{Discount}}{100} \times 100\\[1em] \Rightarrow 20 = \frac{\text{Discount}}{\cancel{100}} \times \cancel{100}\\[1em] \Rightarrow \text{Discount} = 20\end{aligned}$$

And,

$$\begin{aligned}\text{S.P. = M.P. - Discount}\\[1em] \Rightarrow \text{S.P.} = 100 - 20\\[1em] \Rightarrow \text{S.P.} = 80\end{aligned}$$

New M.P. = ₹ 80

2nd Discount % = 12%

$\text{Discount}$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 12 = \frac{\text{Discount}}{80} \times 100\\[1em] \Rightarrow \text{Discount} = \frac{12 \times 80}{100}\\[1em] \Rightarrow \text{Discount} = \frac{960}{100}\\[1em] \Rightarrow \text{Discount} = 9.6\end{aligned}$$

And,

$$\begin{aligned}\text{S.P. = M.P. - Discount}\\[1em] \Rightarrow \text{S.P.} = 80 - 9.6\\[1em] \Rightarrow \text{S.P.} = 70.4\end{aligned}$$

Single equivalent discount = Initial M.P. - Final S.P.

= 100 - 70.4

= 29.6

$\text{Discount}$ % $= \frac{\text{Single Discount}}{\text{Initial M.P.}} \times 100$%

$\Rightarrow \text{Discount}$ % $= \frac{29.6}{100} \times 100$%

$\Rightarrow \text{Discount}$ % $= \frac{29.6}{\cancel{100}} \times \cancel{100}$%

$\Rightarrow \text{Discount}$ % $= 29.6$%

Hence, single equivalent discount = 29.6%.

(ii) Let M.P. be ₹ $100$.

1st discount % = 10%

$\text{Discount }$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 10 = \frac{\text{Discount}}{100} \times 100\\[1em] \Rightarrow 10 = \frac{\text{Discount}}{\cancel{100}} \times \cancel{100}\\[1em] \Rightarrow \text{Discount} = 10\end{aligned}$$

And,

$$\begin{aligned}\text{S.P. = M.P. - Discount}\\[1em] \Rightarrow \text{S.P.} = 100 - 10\\[1em] \Rightarrow \text{S.P.} = 90\end{aligned}$$

New M.P. = ₹ 90

2nd Discount % = 20%

$\text{Discount}$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 20 = \frac{\text{Discount}}{90} \times 100\\[1em] \Rightarrow \text{Discount} = \frac{20 \times 90}{100}\\[1em] \Rightarrow \text{Discount} = \frac{1800}{100}\\[1em] \Rightarrow \text{Discount} = 18\end{aligned}$$

And,

$$\begin{aligned}\text{S.P. = M.P. - Discount}\\[1em] \Rightarrow \text{S.P.} = 90 - 18\\[1em] \Rightarrow \text{S.P.} = 72\end{aligned}$$

New M.P. = ₹ 72

2nd Discount % = 20%

$\text{Discount}$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 20 = \frac{\text{Discount}}{72} \times 100\\[1em] \Rightarrow \text{Discount} = \frac{20 \times 72}{100}\\[1em] \Rightarrow \text{Discount} = \frac{1440}{100}\\[1em] \Rightarrow \text{Discount} = 14.4\end{aligned}$$

And,

$$\begin{aligned}\text{S.P. = M.P. - Discount}\\[1em] \Rightarrow \text{S.P.} = 72 - 14.4\\[1em] \Rightarrow \text{S.P.} = 57.6\end{aligned}$$

Single equivalent discount = Initial M.P. - Final S.P.

= 100 - 57.6

= 42.4

$\text{Discount}$% $= \frac{\text{Single Discount}}{\text{Initial M.P.}} \times 100$%

$\Rightarrow \text{Discount}$% $= \frac{42.4}{100} \times 100$%

$\Rightarrow \text{Discount}$% $= \frac{42.4}{\cancel{100}} \times \cancel{100}$%

$\Rightarrow \text{Discount}$% $= 42.4$%

Hence, single equivalent discount = 42.4%.

(iii) Let M.P. be ₹ $100$.

1st discount % = 20%

$\text{Discount}$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 20 = \frac{\text{Discount}}{100} \times 100\\[1em] \Rightarrow 20 = \frac{\text{Discount}}{\cancel{100}} \times \cancel{100}\\[1em] \Rightarrow \text{Discount} = 20\end{aligned}$$

And,

$$\begin{aligned}\text{S.P. = M.P. - Discount}\\[1em] \Rightarrow \text{S.P.} = 100 - 20\\[1em] \Rightarrow \text{S.P.} = 80\end{aligned}$$

New M.P. = ₹ 80

2nd Discount % = 10%

$\text{Discount}$% $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 10 = \frac{\text{Discount}}{80} \times 100\\[1em] \Rightarrow \text{Discount} = \frac{10 \times 80}{100}\\[1em] \Rightarrow \text{Discount} = \frac{800}{100}\\[1em] \Rightarrow \text{Discount} = 8\end{aligned}$$

And,

$$\begin{aligned}\text{S.P. = M.P. - Discount}\\[1em] \Rightarrow \text{S.P.} = 80 - 8\\[1em] \Rightarrow \text{S.P.} = 72\end{aligned}$$

New M.P. = ₹ 72

3rd Discount % = 5%

$\text{Discount}$ % $= \frac{\text{Discount}}{\text{M.P.}} \times 100$

$$\begin{aligned}\Rightarrow 5 = \frac{\text{Discount}}{72} \times 100\\[1em] \Rightarrow \text{Discount} = \frac{5 \times 72}{100}\\[1em] \Rightarrow \text{Discount} = \frac{360}{100}\\[1em] \Rightarrow \text{Discount} = 3.6\end{aligned}$$

And,

$$\begin{aligned}\text{S.P. = M.P. - Discount}\\[1em] \Rightarrow \text{S.P.} = 72 - 3.6\\[1em] \Rightarrow \text{S.P.} = 68.4\end{aligned}$$

Single equivalent discount = Initial M.P. - Final S.P.

= 100 - 68.4

= 31.6

$\text{Discount}$% $= \frac{\text{Single Discount}}{\text{Initial M.P.}} \times 100$%

$\Rightarrow \text{Discount}$% $= \frac{31.6}{100} \times 100$%

$\Rightarrow \text{Discount}$% $= \frac{31.6}{\cancel{100}} \times \cancel{100}$%

$\Rightarrow \text{Discount}$% $= 31.6$%

Hence, single equivalent discount = 31.6%.

Let the list price of the T.V. be ₹ $x$.

Original Tax % = 9%

∴ Original Tax = 9% of ₹ $x$

= $\frac{9}{100} \times ₹ x$

= $\frac{9x}{100}$

Selling price of the T.V. = ₹ x + ₹ $\frac{9x}{100}$

= ₹ $\frac{100x}{100} + ₹ \frac{9x}{100}$

= ₹ $\frac{(100x + 9x)}{100}$

= ₹ $\frac{109x}{100}$

Reduced Tax % = 6%

∴ Reduced Tax = 6% of ₹ $x$

= $\frac{6}{100} \times ₹ x$

= $\frac{6x}{100}$

New Selling price of the T.V. = $₹ x + ₹ \frac{6x}{100}$

= ₹ $\frac{100x}{100} + ₹ \frac{6x}{100}$

= ₹ $\frac{(100x + 6x)}{100}$

= ₹ $\frac{106x}{100}$

Given, difference in the selling price = ₹ 780 [∵ Mrs Geeta saves ₹ 780]

Original S.P. - New S.P. = 780

$$\begin{aligned}\Rightarrow \frac{109x}{100} - \frac{106x}{100} = 780\\[1em] \Rightarrow \frac{(109x - 106x)}{100} = 780\\[1em] \Rightarrow \frac{3x}{100} = 780\\[1em] \Rightarrow x = \frac{780 \times 100}{3}\\[1em] \Rightarrow x = \frac{78,000}{3}\\[1em] \Rightarrow x = 26,000\end{aligned}$$

Hence, the list price of the T.V. = ₹ 26,000.

S.P. of the article = ₹ 21,384

Tax = 10% on the M.P.

Let the M.P. be ₹$x$.

Tax = 10% on ₹ $x$

$$\begin{aligned}\Rightarrow \frac{10}{100} \times x\\[1em] \Rightarrow \frac{1}{10} \times x\\[1em] \Rightarrow \frac{x}{10}\end{aligned}$$

S.P. of the article = M.P. + Tax on M.P.

$$\begin{aligned}\Rightarrow x + \frac{x}{10} = 21,384\\[1em] \Rightarrow \frac{10x}{10} + \frac{x}{10} = 21,384\\[1em] \Rightarrow \frac{(10x + x)}{10} = 21,384\\[1em] \Rightarrow \frac{11x}{10} = 21,384\\[1em] \Rightarrow x = \frac{21,384 \times 10}{11}\\[1em] \Rightarrow x = \frac{2,13,840}{11}\\[1em] \Rightarrow x = 19,440\end{aligned}$$

M.P. = ₹ 19,440

Actual tax = 8% of the M.P.

$$\begin{aligned}\Rightarrow \frac{8}{100} \times 19,440\\[1em] \Rightarrow \frac{1,55,520}{100}\\[1em] \Rightarrow 1,555.20\end{aligned}$$

Actual S.P. of the article = M.P. + Tax on M.P.

= ₹ 19,440 + ₹ 1,555.20

= ₹ 20,995.20

Profit made by the dealer = S.P. charged by dealer - Actual S.P.

= ₹ (21,384 - 20,995.20)

= ₹388.80

Hence, the deal made the profit of ₹388.80

Let Marked Price of an article be ₹ $x$

Discount = 30% of ₹ x

$$\begin{aligned}\Rightarrow\frac{30}{100} \times ₹ x\\[1em] \Rightarrow\frac{3}{10} \times ₹ x\\[1em] \Rightarrow ₹ \frac{3x}{10}\end{aligned}$$

Taxable cost of article = ₹ $x - \frac{3x}{10}$

= ₹ $\frac{10x}{10} - \frac{3x}{10}$

= ₹ $\frac{7x}{10}$

IGST = 28% of ₹ $\frac{7x}{10}$

$$\begin{aligned}\Rightarrow ₹\Big(\frac{28}{100} \times \frac{7x}{10}\Big) \\[1em] \Rightarrow ₹\Big(\frac{7}{25} \times \frac{7x}{10}\Big) \\[1em] \Rightarrow ₹ \frac{49x}{250}\end{aligned}$$

Amount of bill = Taxable Cost + Tax = 1,792

$$\begin{aligned}\Rightarrow ₹ \frac{7x}{10} + ₹ \frac{49x}{250} = 1,792 \\[1em] \Rightarrow ₹ \frac{175x}{250} + ₹ \frac{49x}{250} = 1,792 \\[1em] \Rightarrow ₹ \frac{(175x + 49x)}{250} = 1,792 \\[1em] \Rightarrow ₹ \frac{224x}{250} = 1,792 \\[1em] \Rightarrow x = ₹\Big(\frac{1,792 \times 250}{224}\Big) \\[1em] \Rightarrow x = ₹\Big(\frac{4,48,000}{224}\Big) \\[1em] \Rightarrow x = ₹ 2,000 \\[1em]\end{aligned}$$

Hence, the marked price of the article = ₹ 2,000.

The list price of a bicycle = ₹ 4,000

Discount = 18% of ₹ 4,000

$$\begin{aligned}\Rightarrow\frac{18}{100} \times ₹ 4,000\\[1em] \Rightarrow\frac{9}{50} \times ₹ 4,000\\[1em] \Rightarrow ₹ \frac{36,000}{50}\\[1em] \Rightarrow ₹ 720\end{aligned}$$

Taxable cost of article = ₹ (4,000 - 720)

= ₹ 3,280

IGST = 18% of ₹ 3,280

$$\begin{aligned}\Rightarrow \frac{18}{100} \times ₹ 3,280\\[1em] \Rightarrow \frac{9}{50} \times ₹ 3,280\\[1em] \Rightarrow ₹ \frac{29,520}{50}\\[1em] \Rightarrow ₹ 590.40\end{aligned}$$

Amount of bill = ₹ 3,280 + ₹ 590.40 = ₹ 3,870.40

Hence, the selling price of the bicycle = ₹ 3,870.40