ICSE Class 8 Mathematics · Solutions for Class 8 RS Aggarwal ICSE Foundation Mathematics · 112 solved questions
Find the gain or loss per cent, when:
C.P. = ₹ 750, S.P. = ₹ 875
Given:
C.P. = ₹ 750 and S.P. = ₹ 875
Since S.P. > C.P., so there is a gain.
Gain = S.P. - C.P. = ₹ 875 - ₹ 750 = ₹ 125.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{125}{750} \times 100\Big)$%
= $\frac{50}{3}$%
= $16\frac{2}{3}$%
Hence, the gain per cent is $\mathbf{16\frac{2}{3}}$%.
Find the gain or loss per cent, when:
C.P. = ₹ 126, S.P. = ₹ 94.50
Given:
C.P. = ₹ 126 and S.P. = ₹ 94.50
Since C.P. > S.P., so there is a loss.
Loss = C.P. - S.P. = ₹ 126 - ₹ 94.50 = ₹ 31.50
Loss % = $\Big(\frac{\text{Loss}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{31.50}{126} \times 100\Big)$%
= $\frac{3150}{126}$%
= 25%
Hence, the loss per cent is 25%.
Find the gain or loss per cent, when:
C.P. = ₹ 80.40, S.P. = ₹ 68.34
Given:
C.P. = ₹ 80.40 and S.P. = ₹ 68.34
Since C.P. > S.P., so there is a loss.
Loss = C.P. - S.P. = ₹ 80.40 - ₹ 68.34 = ₹ 12.06
Loss % = $\Big(\frac{\text{Loss}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{12.06}{80.40} \times 100\Big)$%
= $\frac{1206}{80.40}$%
= 15%
Hence, the loss per cent is 15%.
Find the gain or loss per cent, when:
C.P. = ₹ 58.75, S.P. = ₹ 51.70
Given:
C.P. = ₹ 58.75 and S.P. = ₹ 51.70
Since C.P. > S.P., so there is a loss.
Loss = C.P. - S.P. = ₹ 58.75 - ₹ 51.70 = ₹ 7.05
Loss % = $\Big(\frac{\text{Loss}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{7.05}{58.75} \times 100\Big)$%
= $\frac{705}{58.75}$%
= 12%
Hence, the loss per cent is 12%.
Ranjit purchased an almirah for ₹ 5,248 and paid ₹ 127 for its transportation. He sold it for ₹ 6,020. Find his gain or loss per cent.
Given:
C.P. of the almirah = ₹ 5,248
Overhead expenses = ₹ 127
Actual C.P. = C.P. + Overhead expenses = ₹ (5,248 + 127) = ₹ 5,375.
S.P. = ₹ 6,020
Since S.P. > C.P., so there is a gain.
Gain = S.P. - C.P. = ₹ (6,020 - 5,375) = ₹ 645.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{645}{5375} \times 100\Big)$%
= $\frac{64500}{5375}$%
= 12%
Hence, Ranjit's gain per cent is 12%.
Ahmed purchased an old scooter for ₹ 14,625 and spent ₹ 3,225 on its repairs. Then, he sold it for ₹ 16,422. Find his gain or loss per cent.
Given:
C.P. of the scooter = ₹ 14,625
Overhead expenses (repairs) = ₹ 3,225
Actual C.P. = C.P. + Overhead expenses = ₹ (14,625 + 3,225) = ₹ 17,850.
S.P. = ₹ 16,422
Since C.P. > S.P., so there is a loss.
Loss = C.P. - S.P. = ₹ (17,850 - 16,422) = ₹ 1,428.
Loss % = $\Big(\frac{\text{Loss}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{1428}{17850} \times 100\Big)$%
= $\frac{142800}{17850}$%
= 8%
Hence, Ahmed's loss per cent is 8%.
A man buys two cricket bats, one for ₹ 1,360 and the other for ₹ 1,040. He sells the first bat at a gain of 15% and the second one at a loss of 15%. Find his gain or loss per cent in the whole transaction.
Given:
C.P. of the first bat = ₹ 1,360, Gain % = 15%
C.P. of the second bat = ₹ 1,040, Loss % = 15%
For the first bat:
$$\begin{aligned}\text{S.P.} = \frac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 + 15}{100} \times 1360\Big) \\[1em] = ₹ \Big(\frac{115}{100} \times 1360\Big) \\[1em] = ₹ 1564\end{aligned}$$
For the second bat:
$$\begin{aligned}\text{S.P.} = \frac{(100 - \text{loss percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 - 15}{100} \times 1040\Big) \\[1em] = ₹ \Big(\frac{85}{100} \times 1040\Big) \\[1em] = ₹ 884\end{aligned}$$
Total C.P. of the two bats = ₹ (1,360 + 1,040) = ₹ 2,400.
Total S.P. of the two bats = ₹ (1,564 + 884) = ₹ 2,448.
Since S.P. > C.P., so there is a gain.
Gain = ₹ (2,448 - 2,400) = ₹ 48.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{48}{2400} \times 100 \Big)$%
= $\frac{4800}{2400}$%
= 2%
Hence, the man gains 2% in the whole transaction.
Nandlal bought 20 dozen notebooks at ₹ 156 per dozen. He sold 8 dozen of them at 10% gain and the remaining 12 dozen at 20% gain. What is his gain per cent in the whole transaction?
Given:
Number of notebooks bought = 20 dozen, rate = ₹ 156 per dozen
Total C.P. = ₹ (156 × 20) = ₹ 3,120.
8 dozen are sold at a gain of 10%.
$$\begin{aligned}\text{S.P. of 8 dozen} = ₹ \Big(\frac{156 \times 110 \times 8}{100}\Big) \\[1em] = ₹ \frac{137280}{100} \\[1em] = ₹ 1372.80\end{aligned}$$
The remaining 12 dozen are sold at a gain of 20%.
$$\begin{aligned}\text{S.P. of 12 dozen} = ₹ \Big(\frac{156 \times 120 \times 12}{100}\Big) \\[1em] = ₹ \frac{224640}{100} \\[1em] = ₹ 2246.40\end{aligned}$$
Total S.P. = ₹ (1,372.80 + 2,246.40) = ₹ 3,619.20.
Since S.P. > C.P., so there is a gain.
Gain = ₹ (3,619.20 - 3,120) = ₹ 499.20.
Gain percentage = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{499.20}{3120} \times 100\Big)$%
= $\frac{49920}{3120}$%
= 16%
Hence, Nandlal's gain per cent in the whole transaction is 16%.
Heera bought 25 kg of rice at ₹ 48 per kg and 35 kg of rice at ₹ 60 per kg. He sold the mixture at ₹ 66 per kg. Find his gain per cent.
Given:
25 kg of rice at ₹ 48 per kg and 35 kg of rice at ₹ 60 per kg
C.P. of 25 kg of rice = ₹ (25 × 48) = ₹ 1,200.
C.P. of 35 kg of rice = ₹ (35 × 60) = ₹ 2,100.
Total C.P. of the mixture = ₹ (1,200 + 2,100) = ₹ 3,300.
Total weight of the mixture = (25 + 35) kg = 60 kg.
S.P. of the mixture = ₹ (60 × 66) = ₹ 3,960.
Since S.P. > C.P., so there is a gain.
Gain = ₹ (3,960 - 3,300) = ₹ 660.
Gain percentage = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{660}{3300} \times 100\Big)$%
= $\frac{66000}{3300}$%
= 20%
Hence, Heera's gain per cent is 20%.
If the selling price of an article is $\frac{4}{5}$th of its cost price, find the loss per cent.
Given:
S.P. = $\frac{4}{5}$ of C.P.
Since S.P. < C.P., so there is a loss.
Loss = C.P. - S.P.
= $\text{C.P.} - \frac{4}{5}\text{C.P.}$
= $\frac{\text{C.P.}}{5}$
Loss % = $\Big(\frac{\text{Loss}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{\frac{\text{C.P.}}{5}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{\text{C.P.}}{5} \times \frac{100}{\text{C.P.}}\Big)$%
= 20%
Hence, the loss per cent is 20%.
If the selling price of an article is $1\frac{1}{3}$ of its cost price, find the gain per cent.
Given:
S.P. = $1\frac{1}{3}$ of C.P. = $\frac{4}{3}$ of C.P.
Since S.P. > C.P., so there is a gain.
Gain = S.P. - C.P.
= $\frac{4}{3}\text{C.P.} - \text{C.P.}$
= $\frac{\text{C.P.}}{3}$
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{\text{C.P.}}{3} \times \frac{100}{\text{C.P.}}\Big)$%
= $\frac{100}{3}$%
= $33\frac{1}{3}$%
Hence, the gain per cent is $\mathbf{33\frac{1}{3}}$%.
A man sold a table for ₹ 2,250 and gained one-ninth of its cost price. Find:
(i) the cost price of the table
(ii) the gain per cent earned by the man.
Given:
S.P. of the table = ₹ 2,250 and Gain = $\frac{1}{9}$ of C.P.
(i) Let the cost price of the table be ₹ $x$.
Then, Gain = ₹ $\frac{x}{9}$.
$$\begin{aligned}\text{S.P.} = \text{C.P.} + \text{Gain} \\[1em] \Rightarrow 2250 = x + \frac{x}{9} \\[1em] \Rightarrow 2250 = \frac{10x}{9} \\[1em] \Rightarrow x = \frac{2250 \times 9}{10} \\[1em] \Rightarrow x = 2025\end{aligned}$$
Hence, the cost price of the table is ₹ 2,025.
(ii) Gain = ₹ (2,250 - 2,025) = ₹ 225.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{225}{2025} \times 100\Big)$%
= $\frac{100}{9}$%
= $11\frac{1}{9}$%
Hence, the gain per cent earned by the man is $\mathbf{11\frac{1}{9}}$%.
By selling a pen for ₹ 195, a man loses one-sixteenth of what it costs him. Find
(i) the cost price of the pen
(ii) loss per cent.
Given:
S.P. of the pen = ₹ 195 and Loss = $\frac{1}{16}$ of C.P.
(i) Let the cost price of the pen be ₹ $x$.
Then, Loss = ₹ $\frac{x}{16}$.
$$\begin{aligned}\text{S.P.} = \text{C.P.} - \text{Loss} \\[1em] \Rightarrow 195 = x - \frac{x}{16} \\[1em] \Rightarrow 195 = \frac{15x}{16} \\[1em] \Rightarrow x = \frac{195 \times 16}{15} \\[1em] \Rightarrow x = 208\end{aligned}$$
Hence, the cost price of the pen is ₹ 208.
(ii) Loss = ₹ (208 - 195) = ₹ 13.
Loss % = $\Big(\frac{\text{Loss}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{13}{208} \times 100\Big)$%
= $\frac{100}{16}$%
= $\frac{25}{4}$%
= $6\frac{1}{4}$%
Hence, the loss per cent is $\mathbf{6\frac{1}{4}}$%.
A cycle was sold at a gain of 10%. Had it been sold for ₹ 99 more, the gain would have been 12%. Find the cost price of the cycle.
Let the cost price of the cycle be ₹ $x$.
When the gain is 10%, then S.P. = ₹ ($x$ + 10% of $x$) = ₹ $\frac{11x}{10}$.
When the gain is 12%, then S.P. = ₹ ($x$ + 12% of $x$) = ₹ $\frac{28x}{25}$.
Now, the difference between the two S.P.s = ₹ 99.
$$\begin{aligned}\Rightarrow \frac{28x}{25} - \frac{11x}{10} = 99 \\[1em] \Rightarrow \frac{56x - 55x}{50} = 99 \\[1em] \Rightarrow \frac{x}{50} = 99 \\[1em] \Rightarrow x = 50 \times 99 \\[1em] \Rightarrow x = 4950\end{aligned}$$
Hence, the cost price of the cycle is ₹ 4,950.
A bucket was sold at a loss of 8%. Had it been sold for ₹ 56 more, there would have been a gain of 8%. What is the cost price of the bucket?
Let the cost price of the bucket be ₹ $x$.
When the loss is 8%, then S.P. = ₹ ($x$ - 8% of $x$) = ₹ $\frac{23x}{25}$.
When the gain is 8%, then S.P. = ₹ ($x$ + 8% of $x$) = ₹ $\frac{27x}{25}$.
Now, the difference between the two S.P.s = ₹ 56.
$$\begin{aligned}\Rightarrow \frac{27x}{25} - \frac{23x}{25} = 56 \\[1em] \Rightarrow \frac{4x}{25} = 56 \\[1em] \Rightarrow x = \frac{56 \times 25}{4} \\[1em] \Rightarrow x = 350\end{aligned}$$
Hence, the cost price of the bucket is ₹ 350.
The selling price of 18 books is equal to the cost price of 21 books. Find the gain or loss per cent.
Let the cost price of 1 book be ₹ 1.
Then, C.P. of 21 books = ₹ 21.
S.P. of 18 books = C.P. of 21 books = ₹ 21.
⇒ S.P. of 1 book = ₹ $\frac{21}{18} = ₹ \frac{7}{6}$.
Since S.P. of 1 book > C.P. of 1 book, so there is a gain.
Gain on 1 book = ₹ $\Big(\frac{7}{6} - 1\Big) = ₹ \frac{1}{6}$.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{1}{6} \times \frac{100}{1}\Big)$%
= $\frac{50}{3}$%
= $16\frac{2}{3}$%
Hence, the gain per cent is $\mathbf{16\frac{2}{3}}$%.
The cost price of 12 fans is equal to the selling price of 16 fans. Find the gain or loss per cent.
Let the cost price of 1 fan be ₹ 1.
Then, C.P. of 12 fans = ₹ 12.
S.P. of 16 fans = C.P. of 12 fans = ₹ 12.
⇒ S.P. of 1 fan = ₹ $\frac{12}{16} = ₹ \frac{3}{4}$.
Since S.P. of 1 fan < C.P. of 1 fan, so there is a loss.
Loss on 1 fan = ₹ $\Big(1 - \frac{3}{4}\Big) = ₹ \frac{1}{4}$.
Loss % = $\Big(\frac{\text{Loss}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{1}{4} \times \frac{100}{1}\Big)$%
= 25%
Hence, the loss per cent is 25%.
On selling 250 cassettes, a man had a gain equal to the selling price of 25 cassettes. Find his gain per cent.
We have:
Gain on selling 250 cassettes = (S.P. of 250 cassettes) - (C.P. of 250 cassettes)
⇒ S.P. of 25 cassettes = (S.P. of 250 cassettes) - (C.P. of 250 cassettes)
⇒ C.P. of 250 cassettes = (S.P. of 250 cassettes) - (S.P. of 25 cassettes)
⇒ C.P. of 250 cassettes = S.P. of 225 cassettes
Let the selling price of 1 cassette be ₹ 1.
Then, C.P. of 250 cassettes = ₹ 225 and S.P. of 250 cassettes = ₹ 250.
Since S.P. > C.P., so there is a gain.
Gain = ₹ (250 - 225) = ₹ 25.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{25}{225} \times 100\Big)$%
= $\frac{100}{9}$%
= $11\frac{1}{9}$%
Hence, the gain per cent is $\mathbf{11\frac{1}{9}}$%.
On selling 36 oranges, a vendor loses the selling price of 4 oranges. Find his loss per cent.
We have:
Loss on selling 36 oranges = (C.P. of 36 oranges) - (S.P. of 36 oranges)
⇒ S.P. of 4 oranges = (C.P. of 36 oranges) - (S.P. of 36 oranges)
⇒ C.P. of 36 oranges = (S.P. of 36 oranges) + (S.P. of 4 oranges)
⇒ C.P. of 36 oranges = S.P. of 40 oranges
Let the selling price of 1 orange be ₹ 1.
Then, C.P. of 36 oranges = ₹ 40 and S.P. of 36 oranges = ₹ 36.
Since C.P. > S.P., so there is a loss.
Loss = ₹ (40 - 36) = ₹ 4.
Loss % = $\Big(\frac{\text{Loss}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{4}{40} \times 100\Big)$%
= 10%
Hence, the loss per cent is 10%.
Toffees are bought at 2 for a rupee and sold at 5 for ₹ 3. Find the gain or loss per cent.
Suppose the number of toffees bought = L.C.M. of 2 and 5 = 10.
C.P. of 2 toffees = ₹ 1.
C.P. of 1 toffee = ₹ $\frac{1}{2}$.
C.P. of 10 toffees = ₹ $\Big(\frac{1}{2} \times 10\Big)$ = ₹ 5.
S.P. of 5 toffees = ₹ 3.
S.P. of 1 toffee = ₹ $\frac{3}{5}$.
S.P. of 10 toffees = ₹ $\Big(\frac{3}{5} \times 10\Big)$ = ₹ 6.
Since S.P. > C.P., so there is a gain.
Gain = ₹ (6 - 5) = ₹ 1.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{1}{5} \times 100\Big)$%
= 20%
Hence, the gain per cent is 20%.
Coffee costing ₹ 450 per kg was mixed with Chicory costing ₹ 225 per kg in the ratio 5 : 2 for a certain blend. If the mixture was sold at ₹ 405 per kg; find the gain or loss per cent.
Let 5 kg of coffee be mixed with 2 kg of chicory.
C.P. of 5 kg of coffee = ₹ (450 × 5) = ₹ 2,250.
C.P. of 2 kg of chicory = ₹ (225 × 2) = ₹ 450.
Total C.P. of the blend = ₹ (2,250 + 450) = ₹ 2,700.
Total weight of the blend = (5 + 2) kg = 7 kg.
Total S.P. of the blend = ₹ (405 × 7) = ₹ 2,835.
Since S.P. > C.P., so there is a gain.
Gain = ₹ (2,835 - 2,700) = ₹ 135.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{135}{2700} \times 100\Big)$%
= $\frac{13500}{2700}$%
= 5%
Hence, the gain per cent is 5%.
Find the selling price when:
C.P. = ₹ 7,640, Gain = 15%
Given:
C.P. = ₹ 7,640, Gain % = 15%
$$\begin{aligned}\text{S.P.} = \frac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 + 15}{100} \times 7640\Big) \\[1em] = ₹ \Big(\frac{115}{100} \times 7640\Big) \\[1em] = ₹ 8786\end{aligned}$$
Hence, the selling price is ₹ 8,786.
Find the selling price when:
C.P. = ₹ 4,850, Loss = 12%
Given:
C.P. = ₹ 4,850, Loss % = 12%
$$\begin{aligned}\text{S.P.} = \frac{(100 - \text{loss percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 - 12}{100} \times 4850\Big) \\[1em] = ₹ \Big(\frac{88}{100} \times 4850\Big) \\[1em] = ₹ 4268\end{aligned}$$
Hence, the selling price is ₹ 4,268.
Find the selling price when:
C.P. = ₹ 720, Loss = $8\frac{3}{4}$%
Given:
C.P. = ₹ 720, Loss % = $8\frac{3}{4}$% = $\frac{35}{4}$%
$$\begin{aligned}\text{S.P.} = \frac{(100 - \text{loss percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 - \frac{35}{4}}{100} \times 720\Big) \\[1em] = ₹ \Big(\frac{365}{4 \times 100} \times 720\Big) \\[1em] = ₹ \Big(\frac{365}{400} \times 720\Big) \\[1em] = ₹ 657\end{aligned}$$
Hence, the selling price is ₹ 657.
Find the selling price when:
C.P. = ₹ 2,652, Gain = $16\frac{2}{3}$%
Given:
C.P. = ₹ 2,652, Gain % = $16\frac{2}{3}$% = $\frac{50}{3}$%
$$\begin{aligned}\text{S.P.} = \frac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 + \frac{50}{3}}{100} \times 2652\Big) \\[1em] = ₹ \Big(\frac{350}{3 \times 100} \times 2652\Big) \\[1em] = ₹ \Big(\frac{350}{300} \times 2652\Big) \\[1em] = ₹ 3094\end{aligned}$$
Hence, the selling price is ₹ 3,094.
Find the cost price when:
S.P. = ₹ 207, Gain = 15%
Given:
S.P. = ₹ 207, Gain % = 15%
$$\begin{aligned}\text{C.P.} = \frac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{100 + 15} \times 207\Big) \\[1em] = ₹ \Big(\frac{100}{115} \times 207\Big) \\[1em] = ₹ 180\end{aligned}$$
Hence, the cost price is ₹ 180.
Find the cost price when:
S.P. = ₹ 448.20, Loss = 17%
Given:
S.P. = ₹ 448.20, Loss % = 17%
$$\begin{aligned}\text{C.P.} = \frac{100}{(100 - \text{loss percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{100 - 17} \times 448.20\Big) \\[1em] = ₹ \Big(\frac{100}{83} \times 448.20\Big) \\[1em] = ₹ 540\end{aligned}$$
Hence, the cost price is ₹ 540.
Find the cost price when:
S.P. = ₹ 1,479, Gain = $6\frac{1}{4}$%
Given:
S.P. = ₹ 1,479, Gain % = $6\frac{1}{4}$% = $\frac{25}{4}$%
$$\begin{aligned}\text{C.P.} = \frac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{100 + \frac{25}{4}} \times 1479\Big) \\[1em] = ₹ \Big(\frac{100}{\frac{425}{4}} \times 1479\Big) \\[1em] = ₹ \Big(\frac{100 \times 4}{425} \times 1479\Big) \\[1em] = ₹ \Big(\frac{400}{425} \times 1479\Big) \\[1em] = ₹ 1392\end{aligned}$$
Hence, the cost price is ₹ 1,392.
Find the cost price when:
S.P. = ₹ 611.80, Loss = 8%
Given:
S.P. = ₹ 611.80, Loss % = 8%
$$\begin{aligned}\text{C.P.} = \frac{100}{(100 - \text{loss percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{100 - 8} \times 611.80\Big) \\[1em] = ₹ \Big(\frac{100}{92} \times 611.80\Big) \\[1em] = ₹ 665\end{aligned}$$
Hence, the cost price is ₹ 665.
A sells a bicycle to B at a profit of 20% and B sells it to C at a profit of 5%. If C pays ₹ 3,780, what did A pay for it?
Given:
C pays ₹ 3,780 for the bicycle.
For B,
S.P. = ₹ 3,780 and Profit % = 5%.
$$\begin{aligned}\text{C.P. of B} = \frac{100}{(100 + \text{profit percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{100 + 5} \times 3780\Big) \\[1em] = ₹ \Big(\frac{100}{105} \times 3780\Big) \\[1em] = ₹ 3600\end{aligned}$$
For A,
S.P. = ₹ 3,600 and Profit % = 20%.
$$\begin{aligned}\text{C.P. of A} = \frac{100}{(100 + \text{profit percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{100 + 20} \times 3600\Big) \\[1em] = ₹ \Big(\frac{100}{120} \times 3600\Big) \\[1em] = ₹ 3000\end{aligned}$$
Hence, A paid ₹ 3,000 for the bicycle.
Raju sold a watch to Sonu at 12% gain and Sonu had to sell it to Manu at a loss of 5%. If Manu paid ₹ 5,320, how much did Raju pay for it?
Given:
Manu paid ₹ 5,320 for the watch.
For Sonu,
S.P. = ₹ 5,320 and Loss % = 5%.
$$\begin{aligned}\text{C.P. of Sonu} = \frac{100}{(100 - \text{loss percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{100 - 5} \times 5320\Big) \\[1em] = ₹ \Big(\frac{100}{95} \times 5320\Big) \\[1em] = ₹ 5600\end{aligned}$$
For Raju, S.P. = ₹ 5,600 and Gain % = 12%.
$$\begin{aligned}\text{C.P. of Raju} = \frac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{100 + 12} \times 5600\Big) \\[1em] = ₹ \Big(\frac{100}{112} \times 5600\Big) \\[1em] = ₹ 5000\end{aligned}$$
Hence, Raju paid ₹ 5,000 for the watch.
A grocer purchased 80 kg of rice at ₹ 27 per kg and mixed it with 120 kg of rice purchased at ₹ 32 per kg. At what rate per kg should he sell the mixture to gain 16%?
Given:
A grocer purchased 80 kg of rice at ₹ 27 per kg and 120 kg of rice at ₹ 32 per kg.
C.P. of 80 kg of rice = ₹ (80 × 27) = ₹ 2,160.
C.P. of 120 kg of rice = ₹ (120 × 32) = ₹ 3,840.
Total C.P. of the mixture = ₹ (2,160 + 3,840) = ₹ 6,000.
Total weight of the mixture = (80 + 120) kg = 200 kg.
Gain % = 16%.
$$\begin{aligned}\text{S.P. of the mixture} = \frac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 + 16}{100} \times 6000\Big) \\[1em] = ₹ \Big(\frac{116}{100} \times 6000\Big) \\[1em] = ₹ 6,960\end{aligned}$$
Selling price per kg = ₹ $\frac{6960}{200}$ = ₹ 34.80
Hence, he should sell the mixture at ₹ 34.80 per kg.
Mrs. Harjeet bought two bags for ₹ 1,150 each. She sold one of them at a gain of 6% and the other at a loss of 2%. How much did she gain?
Given:
C.P. of each bag = ₹ 1,150
For the first bag, Gain % = 6%.
Gain = 6% of ₹ 1,150 = ₹ $\Big(\frac{6}{100} \times 1150\Big)$ = ₹ 69.
For the second bag, Loss % = 2%.
Loss = 2% of ₹ 1,150 = ₹ $\Big(\frac{2}{100} \times 1150\Big)$ = ₹ 23.
Since the gain is more than the loss, there is a net gain.
Net gain = ₹ (69 - 23) = ₹ 46.
Hence, Mrs. Harjeet gained ₹ 46.
A trader purchased a wall clock and a watch for a sum of ₹ 5,070. He sold them making a profit of 10% on the wall clock and 15% on the watch. He earns a profit of ₹ 669.50. Find the cost price of the wall clock and that of the watch.
Let the cost price of the wall clock be ₹ $x$.
Then, the cost price of the watch = ₹ (5070 - $x$).
Profit on the wall clock = 10% of ₹ $x = ₹ \frac{10x}{100}$.
Profit on the watch = 15% of ₹ (5070 - $x$) = ₹ $\frac{15(5070 - x)}{100}$.
Total profit = ₹ 669.50.
$$\begin{aligned}\Rightarrow \frac{10x}{100} + \frac{15(5070 - x)}{100} = 669.50 \\[1em] \Rightarrow 10x + 76050 - 15x = 66950 \\[1em] \Rightarrow -5x = 66950 - 76050 \\[1em] \Rightarrow -5x = -9100 \\[1em] \Rightarrow x = 1820\end{aligned}$$
C.P. of the wall clock = ₹ 1,820.
C.P. of the watch = ₹ (5,070 - 1,820) = ₹ 3,250.
Hence, the cost price of the wall clock is ₹ 1,820 and that of the watch is ₹ 3,250.
Toffees are bought at 15 for ₹ 20. How many toffees would be sold for ₹ 20 so as to gain 25%?
Given:
C.P. of 15 toffees = ₹ 20 and Gain % = 25%
$$\begin{aligned}\text{S.P. of 15 toffees} = \frac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 + 25}{100} \times 20\Big) \\[1em] = ₹ \Big(\frac{125}{100} \times 20\Big) \\[1em] = ₹ 25\end{aligned}$$
So, for ₹ 25 he sells 15 toffees.
⇒ For ₹ 20 he should sell $\Big(\frac{15}{25} \times 20\Big)$ = 12 toffees.
Hence, 12 toffees would be sold for ₹ 20 so as to gain 25%.
Two-thirds of a consignment was sold at a profit of 5% and the remainder at a loss of 2%. If the total profit was ₹ 4,000, find the value at which the consignment was purchased.
Let the cost price of the consignment be ₹ 100.
C.P. of $\frac{2}{3}$ of the consignment = ₹ $\frac{200}{3}$, sold at a profit of 5%.
Gain = ₹ $\Big(\frac{200}{3} \times \frac{5}{100}\Big) = ₹ \frac{10}{3}$.
C.P. of the remaining $\Big(1 - \frac{2}{3}\Big) = \frac{1}{3}$ of the consignment = ₹ $\frac{100}{3}$, sold at a loss of 2%.
Loss = ₹ $\Big(\frac{100}{3} \times \frac{2}{100}\Big) = ₹ \frac{2}{3}$.
Net profit = ₹ $\Big(\frac{10}{3} - \frac{2}{3}\Big) = ₹ \frac{8}{3}$.
If the profit is ₹ $\frac{8}{3}$, then C.P. = ₹ 100.
$$\begin{aligned}\Rightarrow \text{If the profit is ₹ 4000, then C.P.} = ₹ \Big(100 \times \frac{3}{8} \times 4000\Big) \\[1em] = ₹ \frac{1200000}{8} \\[1em] = ₹ 150000\end{aligned}$$
Hence, the consignment was purchased for ₹ 1,50,000.
A grocer bought sugar worth of ₹ 4,500. He sold one-third of it at 10% gain. At what gain per cent, the remaining sugar be sold to have a 12% gain on the whole?
Given:
Total C.P. of the sugar = ₹ 4,500
C.P. of one-third of the sugar = ₹ $\Big(\frac{1}{3} \times 4500\Big)$ = ₹ 1,500, sold at a gain of 10%.
$$\begin{aligned}\text{S.P. of this part} = ₹ \Big(\frac{100 + 10}{100} \times 1500\Big) \\[1em] = ₹ \Big(\frac{110}{100} \times 1500\Big) \\[1em] = ₹ 1650\end{aligned}$$
For a gain of 12% on the whole,
$$\begin{aligned}\text{Total S.P.} = ₹ \Big(\frac{100 + 12}{100} \times 4500\Big) \\[1em] = ₹ \Big(\frac{112}{100} \times 4500\Big) \\[1em] = ₹ 5040\end{aligned}$$
S.P. of the remaining sugar = ₹ (5,040 - 1,650) = ₹ 3,390.
C.P. of the remaining sugar = ₹ (4,500 - 1,500) = ₹ 3,000.
Since S.P. > C.P., so there is a gain.
Gain = ₹ (3,390 - 3,000) = ₹ 390.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{390}{3000} \times 100\Big)$%
= $\frac{39000}{3000}$%
= 13%
Hence, the remaining sugar should be sold at a gain of 13%.
A man buys a piece of land for ₹ 3,84,000. He sells two-fifths of it at a loss of 6%. At what gain per cent should he sell the remaining piece of land to gain 10% on the whole?
Given:
Total C.P. of the land = ₹ 3,84,000
C.P. of two-fifths of the land = ₹ $\Big(\frac{2}{5} \times 384000\Big)$ = ₹ 1,53,600, sold at a loss of 6%.
$$\begin{aligned}\text{S.P. of this part} = ₹ \Big(\frac{100 - 6}{100} \times 153600\Big) \\[1em] = ₹ \Big(\frac{94}{100} \times 153600\Big) \\[1em] = ₹ 144384\end{aligned}$$
For a gain of 10% on the whole,
$$\begin{aligned}\text{Total S.P.} = ₹ \Big(\frac{100 + 10}{100} \times 384000\Big) \\[1em] = ₹ \Big(\frac{110}{100} \times 384000\Big) \\[1em] = ₹ 422400\end{aligned}$$
S.P. of the remaining land = ₹ (4,22,400 - 1,44,384) = ₹ 2,78,016.
C.P. of the remaining land = ₹ (3,84,000 - 1,53,600) = ₹ 2,30,400.
Since S.P. > C.P., so there is a gain.
Gain = ₹ (2,78,016 - 2,30,400) = ₹ 47,616.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{47616}{230400} \times 100\Big)$%
= $\frac{4761600}{230400}$%
= $\frac{62}{3}$%
= $20\frac{2}{3}$%
Hence, he should sell the remaining piece of land at a gain of $\mathbf{20\frac{2}{3}}$%.
By selling an almirah for ₹ 10,416, a man gains 12%. What will be his gain or loss per cent if it is sold for ₹ 9,114?
Given:
S.P. of the almirah = ₹ 10,416 and Gain % = 12%
$$\begin{aligned}\text{C.P.} = \frac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{100 + 12} \times 10416\Big) \\[1em] = ₹ \Big(\frac{100}{112} \times 10416\Big) \\[1em] = ₹ 9300\end{aligned}$$
Now, the new S.P. = ₹ 9,114.
Since C.P. > S.P., so there is a loss.
Loss = ₹ (9,300 - 9,114) = ₹ 186.
Loss % = $\Big(\frac{\text{Loss}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{186}{9300} \times 100\Big)$%
= $\frac{18600}{9300}$%
= 2%
Hence, there will be a loss of 2%.
A chair was sold for ₹ 2,142 at a gain of 5%. At what price it should have been sold to gain 10%?
Given:
S.P. of the chair = ₹ 2,142 and Gain % = 5%
$$\begin{aligned}\text{C.P.} = \frac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{100 + 5} \times 2142\Big) \\[1em] = ₹ \Big(\frac{100}{105} \times 2142\Big) \\[1em] = ₹ 2040\end{aligned}$$
Now, C.P. = ₹ 2,040 and the gain required = 10%.
$$\begin{aligned}\text{Required S.P.} = \frac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 + 10}{100} \times 2040\Big) \\[1em] = ₹ \Big(\frac{110}{100} \times 2040\Big) \\[1em] = ₹ 2244\end{aligned}$$
Hence, the chair should have been sold for ₹ 2,244 to gain 10%.
A television is sold for ₹ 9,360 at a loss of 4%. For how much it should have been sold to gain 4%?
Given:
S.P. of the television = ₹ 9,360 and Loss % = 4%
$$\begin{aligned}\text{C.P.} = \frac{100}{(100 - \text{loss percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{100 - 4} \times 9360\Big) \\[1em] = ₹ \Big(\frac{100}{96} \times 9360\Big) \\[1em] = ₹ 9,750\end{aligned}$$
Now, C.P. = ₹ 9,750 and the gain required = 4%.
$$\begin{aligned}\text{Required S.P.} = \frac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 + 4}{100} \times 9750\Big) \\[1em] = ₹ \Big(\frac{104}{100} \times 9750\Big) \\[1em] = ₹ 10,140\end{aligned}$$
Hence, the television should have been sold for ₹ 10,140 to gain 4%.
A shopkeeper sold two fans at ₹ 1,980 each. On one he gained 10%, while on the other he lost 10%. Calculate the gain or loss per cent on the whole transaction.
Given:
S.P. of each fan = ₹ 1,980
For the first fan, S.P. = ₹ 1,980 and Gain % = 10%.
$$\begin{aligned}\text{C.P.} = \frac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{110} \times 1980\Big) \\[1em] = ₹ 1800\end{aligned}$$
For the second fan, S.P. = ₹ 1,980 and Loss % = 10%.
$$\begin{aligned}\text{C.P.} = \frac{100}{(100 - \text{loss percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{90} \times 1980\Big) \\[1em] = ₹ 2200\end{aligned}$$
Total C.P. of the two fans = ₹ (1,800 + 2,200) = ₹ 4,000.
Total S.P. of the two fans = ₹ (1,980 + 1,980) = ₹ 3,960.
Since C.P. > S.P., so there is a loss.
Loss = ₹ (4,000 - 3,960) = ₹ 40.
Loss % = $\Big(\frac{\text{Loss}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{40}{4000} \times 100\Big)$%
= 1%
Hence, there is a loss of 1% on the whole transaction.
Shanti sold two cameras for ₹ 6,555 each. On one she lost 5%, while on the other she gained 15%. Find the gain or loss per cent in the whole transaction.
Given:
S.P. of each camera = ₹ 6,555
For the first camera, S.P. = ₹ 6,555 and Loss % = 5%.
$$\begin{aligned}\text{C.P.} = \frac{100}{(100 - \text{loss percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{95} \times 6555\Big) \\[1em] = ₹ 6900\end{aligned}$$
For the second camera, S.P. = ₹ 6,555 and Gain % = 15%.
$$\begin{aligned}\text{C.P.} = \frac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{115} \times 6555\Big) \\[1em] = ₹ 5700\end{aligned}$$
Total C.P. of the two cameras = ₹ (6,900 + 5,700) = ₹ 12,600.
Total S.P. of the two cameras = ₹ (6,555 + 6,555) = ₹ 13,110.
Since S.P. > C.P., so there is a gain.
Gain = ₹ (13,110 - 12,600) = ₹ 510.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{510}{12600} \times 100\Big)$%
= $\frac{51000}{12600}$%
= $\frac{85}{21}$%
= $4\frac{1}{21}$%
Hence, there is a gain of $\mathbf{4\frac{1}{21}}$% in the whole transaction.
By selling 45 lemons for ₹ 40, a man loses 20%. How many should he sell for ₹ 24 to gain 20% on the transaction?
Given:
S.P. of 45 lemons = ₹ 40 and Loss % = 20%
$$\begin{aligned}\text{C.P. of 45 lemons} = \frac{100}{(100 - \text{loss percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{80} \times 40\Big) \\[1em] = ₹ 50\end{aligned}$$
Now, the gain required = 20%.
$$\begin{aligned}\text{S.P. of 45 lemons} = \frac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{120}{100} \times 50\Big) \\[1em] = ₹ 60\end{aligned}$$
So, for ₹ 60 he sells 45 lemons.
⇒ For ₹ 24 he should sell $\Big(\frac{45}{60} \times 24\Big)$ = 18 lemons.
Hence, he should sell 18 lemons for ₹ 24 to gain 20%.
Rajni sold a pressure cooker at a loss of 8%. Had she bought it at 10% less and sold for ₹ 176 more, she would have gained 20%. Find the cost price of the pressure cooker.
Let the cost price of the pressure cooker be ₹ $x$.
When the loss is 8%, then S.P. = ₹ ($x$ - 8% of $x$) = ₹ $\frac{23x}{25}$.
New C.P. = ₹ ($x$ - 10% of $x$) = ₹ $\frac{9x}{10}$.
New S.P. = ₹ $\Big(\frac{23x}{25} + 176\Big)$.
On the new cost price, the gain is 20%.
$$\begin{aligned}\Rightarrow \frac{23x}{25} + 176 = \frac{(100 + 20)}{100} \times \frac{9x}{10} \\[1em] \Rightarrow \frac{23x}{25} + 176 = \frac{120}{100} \times \frac{9x}{10} \\[1em] \Rightarrow \frac{23x}{25} + 176 = \frac{27x}{25} \\[1em] \Rightarrow \frac{27x}{25} - \frac{23x}{25} = 176 \\[1em] \Rightarrow \frac{4x}{25} = 176 \\[1em] \Rightarrow x = \frac{176 \times 25}{4} \\[1em] \Rightarrow x = 1100\end{aligned}$$
Hence, the cost price of the pressure cooker is ₹ 1,100.
A man sold a toaster at a profit of 10%. Had he purchased it for 5% less and sold it for ₹ 56 more, he could have gained 25%. For how much did he buy it?
Let the cost price of the toaster be ₹ $x$.
When the profit is 10%, then S.P. = ₹ ($x$ + 10% of $x$) = ₹ $\frac{11x}{10}$.
New C.P. = ₹ ($x$ - 5% of $x$) = ₹ $\frac{19x}{20}$.
New S.P. = ₹ $\Big(\frac{11x}{10} + 56\Big)$.
On the new cost price, the gain is 25%.
$$\begin{aligned}\Rightarrow \frac{11x}{10} + 56 = \frac{(100 + 25)}{100} \times \frac{19x}{20} \\[1em] \Rightarrow \frac{11x}{10} + 56 = \frac{125}{100} \times \frac{19x}{20} \\[1em] \Rightarrow \frac{11x}{10} + 56 = \frac{19x}{16} \\[1em] \Rightarrow \frac{19x}{16} - \frac{11x}{10} = 56 \\[1em] \Rightarrow \frac{95x - 88x}{80} = 56 \\[1em] \Rightarrow \frac{7x}{80} = 56 \\[1em] \Rightarrow x = \frac{56 \times 80}{7} \\[1em] \Rightarrow x = 640\end{aligned}$$
Hence, the man bought the toaster for ₹ 640.
A shopkeeper sells each of his goods at a gain of $22\frac{1}{2}$%. If on any day, his total sale was of ₹ 9,408, what was (i) the total cost of all the goods sold on that day (ii) his profit of that day.
Given:
Total S.P. of the goods = ₹ 9,408 and Gain % = $22\frac{1}{2}$% = $\frac{45}{2}$%
(i) Total cost of the goods:
$$\begin{aligned}\text{C.P.} = \frac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{100 + \frac{45}{2}} \times 9408\Big) \\[1em] = ₹ \Big(\frac{100}{\frac{245}{2}} \times 9408\Big) \\[1em] = ₹ \Big(\frac{100 \times 2}{245} \times 9408\Big) \\[1em] = ₹ \Big(\frac{200}{245} \times 9408\Big) \\[1em] = ₹ 7680\end{aligned}$$
Hence, the total cost of all the goods sold on that day is ₹ 7,680.
(ii) Profit = S.P. - C.P. = ₹ (9,408 - 7,680) = ₹ 1,728.
Hence, his profit of that day is ₹ 1,728.
The marked price of a refrigerator is ₹ 16,450. The shopkeeper offers an off-season discount of 16% on it. Find its selling price.
Given:
Marked price = ₹ 16,450, Discount % = 16%
Discount = 16% of M.P.
= 16% of ₹ 16,450
= ₹ $\Big(\frac{16}{100} \times 16450\Big)$
= ₹ 2,632.
S.P. of the refrigerator = M.P. - Discount = ₹ (16,450 - 2,632) = ₹ 13,818.
Hence, the selling price of the refrigerator is ₹ 13,818.
The price of a sweater was slashed down by a shopkeeper from ₹ 850 to ₹ 731. Find the rate of discount given by him.
Given:
M.P. = ₹ 850, S.P. = ₹ 731
Discount given = M.P. - S.P. = ₹ (850 - 731) = ₹ 119.
Rate of discount = $\Big(\frac{\text{Discount}}{\text{M.P.}} \times 100\Big)$%
= $\Big(\frac{119}{850} \times 100\Big)$%
= $\frac{11900}{850}$%
= 14%
Hence, the rate of discount given by him is 14%.
Find the rate of discount being given on a mini toy-gun whose selling price is ₹ 345 after deducting a discount of ₹ 30 on its marked price.
Given:
S.P. = ₹ 345, Discount = ₹ 30
M.P. = S.P. + Discount = ₹ (345 + 30) = ₹ 375.
Rate of discount = $\Big(\frac{\text{Discount}}{\text{M.P.}} \times 100\Big)$%
= $\Big(\frac{30}{375} \times 100\Big)$%
= $\frac{3000}{375}$%
= 8%
Hence, the rate of discount is 8%.
After allowing a discount of 15%, a baby-suit was sold for ₹ 1,156. Find its marked price.
Given:
Discount % = 15%, S.P. = ₹ 1,156
Let the marked price be ₹ $x$.
Discount = 15% of ₹ $x = ₹ \frac{15x}{100}$.
$$\begin{aligned}\text{S.P.} = \text{M.P.} - \text{Discount} \\[1em] \Rightarrow 1156 = x - \frac{15x}{100} \\[1em] \Rightarrow 1156 = \frac{85x}{100} \\[1em] \Rightarrow x = \frac{1156 \times 100}{85} \\[1em] \Rightarrow x = 1360\end{aligned}$$
Hence, the marked price of the baby-suit is ₹ 1,360.
A calculator was bought for ₹ 435 after getting a discount of 13%. Find the marked price of the calculator.
Given:
Discount % = 13%, S.P. = ₹ 435
Let the marked price be ₹ $x$.
Discount = 13% of ₹ $x = ₹ \frac{13x}{100}$.
$$\begin{aligned}\text{S.P.} = \text{M.P.} - \text{Discount} \\[1em] \Rightarrow 435 = x - \frac{13x}{100} \\[1em] \Rightarrow 435 = \frac{87x}{100} \\[1em] \Rightarrow x = \frac{435 \times 100}{87} \\[1em] \Rightarrow x = 500\end{aligned}$$
Hence, the marked price of the calculator is ₹ 500.
A dealer marked his goods 35% above cost price and allowed a discount of 20% on the marked price. Find his gain or loss per cent.
Let the cost price of the goods be ₹ 100.
Then, its marked price = ₹ $\Big(100 + \frac{35}{100} \times 100\Big)$ = ₹ (100 + 35) = ₹ 135.
Discount = 20% of M.P. = 20% of ₹ 135 = ₹ $\Big(\frac{20}{100} \times 135\Big)$ = ₹ 27.
Selling price = M.P. - Discount = ₹ (135 - 27) = ₹ 108.
Since S.P. > C.P., so there is a gain.
Gain = S.P. - C.P. = ₹ (108 - 100) = ₹ 8.
On a cost price of ₹ 100, the gain is ₹ 8.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{8}{100} \times 100\Big)$%
= 8%
Hence, the dealer gains 8%.
An article was marked 40% above cost price and a discount of 35% was given on its marked price. Find the gain or loss per cent made by the shopkeeper.
Let the cost price of the article be ₹ 100.
Then, its marked price = ₹ $\Big(100 + \frac{40}{100} \times 100\Big)$ = ₹ (100 + 40) = ₹ 140.
Discount = 35% of M.P. = 35% of ₹ 140 = ₹ $\Big(\frac{35}{100} \times 140\Big)$ = ₹ 49.
Selling price = M.P. - Discount = ₹ (140 - 49) = ₹ 91.
Since C.P. > S.P., so there is a loss.
Loss = C.P. - S.P. = ₹ (100 - 91) = ₹ 9.
On a cost price of ₹ 100, the loss is ₹ 9.
Loss % = $\Big(\frac{\text{Loss}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{9}{100} \times 100\Big)$%
= 9%
Hence, the shopkeeper makes a loss of 9%.
A dealer purchased a washing machine for ₹ 7,660. After allowing a discount of 12% on its marked price, he gains 10%. Find the marked price.
Given:
C.P. = ₹ 7,660, Gain % = 10%, Discount % = 12%
$$\begin{aligned}\text{S.P.} = \frac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 + 10}{100} \times 7660\Big) \\[1em] = ₹ \Big(\frac{110}{100} \times 7660\Big) \\[1em] = ₹ 8,426\end{aligned}$$
Let the marked price be ₹ $x$.
Discount = 12% of ₹ $x = ₹ \frac{12x}{100}$.
$$\begin{aligned}\text{S.P.} = \text{M.P.} - \text{Discount} \\[1em] \Rightarrow 8426 = x - \frac{12x}{100} \\[1em] \Rightarrow 8426 = \frac{88x}{100} \\[1em] \Rightarrow x = \frac{8426 \times 100}{88} \\[1em] \Rightarrow x = 9575\end{aligned}$$
Hence, the marked price of the washing machine is ₹ 9,575.
A shopkeeper bought a sewing machine for ₹ 3,750. After allowing a discount of 10% on its marked price, he gains 26%. Find the marked price of the sewing machine.
Given:
C.P. = ₹ 3,750, Gain % = 26%, Discount % = 10%
$$\begin{aligned}\text{S.P.} = \frac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 + 26}{100} \times 3750\Big) \\[1em] = ₹ \Big(\frac{126}{100} \times 3750\Big) \\[1em] = ₹ 4725\end{aligned}$$
Let the marked price be ₹ $x$.
Discount = 10% of ₹ $x = ₹ \frac{10x}{100}$.
$$\begin{aligned}\text{S.P.} = \text{M.P.} - \text{Discount} \\[1em] \Rightarrow 4725 = x - \frac{10x}{100} \\[1em] \Rightarrow 4725 = \frac{90x}{100} \\[1em] \Rightarrow x = \frac{4725 \times 100}{90} \\[1em] \Rightarrow x = 5250\end{aligned}$$
Hence, the marked price of the sewing machine is ₹ 5,250.
After allowing a discount of 10% on the marked price, a trader still makes a profit of 17%. By what per cent is the marked price above cost price?
Let the cost price be ₹ 100.
Since the profit is 17%, S.P. = ₹ (100 + 17) = ₹ 117.
Let the marked price be ₹ $x$.
Discount = 10% of ₹ $x$, so S.P. = 90% of M.P.
$$\begin{aligned}\Rightarrow \frac{90x}{100} = 117 \\[1em] \Rightarrow x = \frac{117 \times 100}{90} \\[1em] \Rightarrow x = 130\end{aligned}$$
M.P. = ₹ 130 and C.P. = ₹ 100.
M.P. is above C.P. by ₹ (130 - 100) = ₹ 30.
On a cost price of ₹ 100, the marked price is ₹ 30 above.
Required per cent = $\Big(\frac{\text{M.P.} - \text{C.P.}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{30}{100} \times 100\Big)$%
= 30%
Hence, the marked price is 30% above the cost price.
After allowing a discount of 12% on the marked price, a shopkeeper still gains 21%. By what per cent is the marked price above cost price?
Let the cost price be ₹ 100.
Since the gain is 21%, S.P. = ₹ (100 + 21) = ₹ 121.
Let the marked price be ₹ $x$.
Discount = 12% of ₹ $x$, so S.P. = 88% of M.P.
$$\begin{aligned}\Rightarrow \frac{88x}{100} = 121 \\[1em] \Rightarrow x = \frac{121 \times 100}{88} \\[1em] \Rightarrow x = \frac{275}{2} \\[1em] \Rightarrow x = 137.50\end{aligned}$$
M.P. = ₹ 137.50 and C.P. = ₹ 100.
M.P. is above C.P. by ₹ (137.50 - 100) = ₹ 37.50.
On a cost price of ₹ 100, the marked price is ₹ 37.50 above.
Required per cent = $\Big(\frac{\text{M.P.} - \text{C.P.}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{37.50}{100} \times 100\Big)$%
= $37\frac{1}{2}$%
Hence, the marked price is $\mathbf{37\frac{1}{2}}$% above the cost price.
Find a single discount equivalent to two successive discounts of 20% and 10%.
Let the marked price be ₹ 100.
First discount = 20% of ₹ 100 = ₹ $\Big(\frac{20}{100} \times 100\Big)$ = ₹ 20.
Price after the first discount = ₹ (100 - 20) = ₹ 80.
Second discount = 10% of ₹ 80 = ₹ $\Big(\frac{10}{100} \times 80\Big)$ = ₹ 8.
Price after the second discount = ₹ (80 - 8) = ₹ 72.
Net discount = ₹ (100 - 72) = ₹ 28.
On a marked price of ₹ 100, the discount is ₹ 28.
Discount % = $\Big(\frac{\text{Discount}}{\text{M.P.}} \times 100\Big)$%
= $\Big(\frac{28}{100} \times 100\Big)$%
= 28%
Hence, the single discount equivalent to the given successive discounts is 28%.
Find a single discount equivalent to two successive discounts of 40% and 5%.
Let the marked price be ₹ 100.
First discount = 40% of ₹ 100 = ₹ $\Big(\frac{40}{100} \times 100\Big)$ = ₹ 40.
Price after the first discount = ₹ (100 - 40) = ₹ 60.
Second discount = 5% of ₹ 60 = ₹ $\Big(\frac{5}{100} \times 60\Big)$ = ₹ 3.
Price after the second discount = ₹ (60 - 3) = ₹ 57.
Net discount = ₹ (100 - 57) = ₹ 43.
On a marked price of ₹ 100, the discount is ₹ 43.
Discount % = $\Big(\frac{\text{Discount}}{\text{M.P.}} \times 100\Big)$%
= $\Big(\frac{43}{100} \times 100\Big)$%
= 43%
Hence, the single discount equivalent to the given successive discounts is 43%.
Find a single discount equivalent to three successive discounts of 20%, 5% and 1%.
Let the marked price be ₹ 100.
First discount = 20% of ₹ 100 = ₹ $\Big(\frac{20}{100} \times 100\Big)$ = ₹ 20.
Price after the first discount = ₹ (100 - 20) = ₹ 80.
Second discount = 5% of ₹ 80 = ₹ $\Big(\frac{5}{100} \times 80\Big)$ = ₹ 4.
Price after the second discount = ₹ (80 - 4) = ₹ 76.
Third discount = 1% of ₹ 76 = ₹ $\Big(\frac{1}{100} \times 76\Big)$ = ₹ 0.76.
Price after the third discount = ₹ (76 - 0.76) = ₹ 75.24.
Net discount = ₹ (100 - 75.24) = ₹ 24.76.
On a marked price of ₹ 100, the discount is ₹ 24.76.
Discount % = $\Big(\frac{\text{Discount}}{\text{M.P.}} \times 100\Big)$%
= $\Big(\frac{24.76}{100} \times 100\Big)$%
= 24.76%
Hence, the single discount equivalent to the given successive discounts is 24.76%.
The marked price of a watch is ₹ 1,375. If tax is charged at the rate of 4%, find the total cost of the watch.
Given:
Marked price of the watch = ₹ 1,375, Rate of tax = 4%
Tax = 4% of ₹ 1,375 = ₹ $\Big(\frac{4}{100} \times 1375\Big)$ = ₹ 55.
Total amount to be paid = ₹ (1,375 + 55) = ₹ 1,430.
Hence, the total cost of the watch is ₹ 1,430.
Ravi buys a bicycle with a marked price of ₹ 12,500. He gets a rebate of 10% on it. After getting the rebate, tax is charged at the rate of 6%. Find the amount he will have to pay for the bicycle.
Given:
Marked price of the bicycle = ₹ 12,500, Rebate = 10%, Rate of tax = 6%
Rebate = 10% of ₹ 12,500 = ₹ $\Big(\frac{10}{100} \times 12500\Big)$ = ₹ 1,250.
Sale price of the bicycle = ₹ (12,500 - 1,250) = ₹ 11,250.
Tax = 6% of ₹ 11,250 = ₹ $\Big(\frac{6}{100} \times 11250\Big)$ = ₹ 675.
Total amount paid by Ravi = ₹ (11,250 + 675) = ₹ 11,925.
Hence, Ravi will have to pay ₹ 11,925 for the bicycle.
The list price of a washing machine is ₹ 25,000 and the shopkeeper gives a discount of 12% on the list price. On the remaining amount, he charges a tax of 10%.
Find:
(i) the amount of tax, a customer has to pay, and
(ii) the final price he has to pay for the washing machine.
Given:
List price of the washing machine = ₹ 25,000, Discount = 12%, Rate of tax = 10%
Discount = 12% of ₹ 25,000 = ₹ $\Big(\frac{12}{100} \times 25000\Big)$ = ₹ 3,000.
Sale price of the washing machine = ₹ (25,000 - 3,000) = ₹ 22,000.
(i) Tax = 10% of ₹ 22,000 = ₹ $\Big(\frac{10}{100} \times 22000\Big)$ = ₹ 2,200.
Hence, the amount of tax the customer has to pay is ₹ 2,200.
(ii) Final price = ₹ (22,000 + 2,200) = ₹ 24,200.
Hence, the final price he has to pay for the washing machine is ₹ 24,200.
Reena purchased a face cream for ₹ 113.40 including tax. If the printed price of the face cream is ₹ 105, find the rate of tax on it.
Given:
Printed price of the face cream = ₹ 105, Price paid including tax = ₹ 113.40
Tax = ₹ (113.40 - 105) = ₹ 8.40.
Rate of tax = $\Big(\frac{\text{Tax}}{\text{Printed price}} \times 100\Big)$%
= $\Big(\frac{8.40}{105} \times 100\Big)$%
= $\frac{840}{105}$%
= 8%
Hence, the rate of tax on the face cream is 8%.
Vivek purchased a laptop for ₹ 34,164, which includes 10% rebate on the marked price and then 4% tax on the remaining price. Find the marked price of the laptop.
Let the marked price of the laptop be ₹ $x$.
Rebate = 10% of ₹ $x = ₹ \frac{10x}{100}$.
Price after rebate = ₹ $\Big(x - \frac{10x}{100}\Big) = ₹ \frac{90x}{100} = ₹ \frac{9x}{10}$.
Tax = 4% of ₹ $\frac{9x}{10} = ₹ \Big(\frac{4}{100} \times \frac{9x}{10}\Big) = ₹ \frac{9x}{250}$.
Total price paid = ₹ $\Big(\frac{9x}{10} + \frac{9x}{250}\Big) = ₹ \frac{225x + 9x}{250} = ₹ \frac{234x}{250}$.
$$\begin{aligned}\Rightarrow \frac{234x}{250} = 34164 \\[1em] \Rightarrow x = \frac{34164 \times 250}{234} \\[1em] \Rightarrow x = \frac{8541000}{234} \\[1em] \Rightarrow x = 36500\end{aligned}$$
Hence, the marked price of the laptop is ₹ 36,500.
Tanya buys an electric iron for ₹ 712.80, which includes two successive discounts of 10% and 4% respectively on the marked price and then 10% tax on the remaining price. Find the marked price of the electric iron.
Let the marked price be ₹ 100.
$$\begin{aligned}\text{Price after the two discounts} = ₹ \Big[\Big(1 - \frac{10}{100}\Big)\Big(1 - \frac{4}{100}\Big) \times 100\Big] \\[1em] = ₹ \Big(\frac{90}{100} \times \frac{96}{100} \times 100\Big) \\[1em] = ₹ 86.40\end{aligned}$$
Tax = 10% of ₹ 86.40 = ₹ $\Big(\frac{10}{100} \times 86.40\Big)$ = ₹ 8.64.
S.P. = ₹ (86.40 + 8.64) = ₹ 95.04.
If the S.P. is ₹ 95.04, then M.P. = ₹ 100.
$$\begin{aligned}\Rightarrow \text{If the S.P. is ₹ 712.80, then M.P.} = ₹ \Big(\frac{100}{95.04} \times 712.80\Big) \\[1em] \Rightarrow \text{M.P.} = ₹ \frac{71280}{95.04} \\[1em] \Rightarrow \text{M.P.} = ₹ 750\end{aligned}$$
Hence, the marked price of the electric iron is ₹ 750.
The price of a food processor inclusive of tax of 5% is ₹ 6,930. If the tax is increased to 8%, how much more does the customer pay for it?
Given:
Price of the food processor inclusive of 5% tax = ₹ 6,930
Let the sale price of the food processor be ₹ $x$.
Tax = 5% of ₹ $x = ₹ \frac{5x}{100}$.
$$\begin{aligned}\Rightarrow x + \frac{5x}{100} = 6930 \\[1em] \Rightarrow \frac{105x}{100} = 6930 \\[1em] \Rightarrow x = \frac{6930 \times 100}{105} \\[1em] \Rightarrow x = 6600\end{aligned}$$
When the tax is increased to 8%,
New tax = 8% of ₹ 6,600 = ₹ $\Big(\frac{8}{100} \times 6600\Big)$ = ₹ 528.
New price of the food processor = ₹ (6,600 + 528) = ₹ 7,128.
Extra amount paid = ₹ (7,128 - 6,930) = ₹ 198.
Hence, the customer pays ₹ 198 more for the food processor.
The price of a laser printer including 7% tax, is ₹ 17,334. How much less does a customer pay for it, if the tax on it is reduced to 4%?
Given:
Price of the laser printer inclusive of 7% tax = ₹ 17,334
Let the sale price of the laser printer be ₹ $x$.
Tax = 7% of ₹ $x = ₹ \frac{7x}{100}$.
$$\begin{aligned}\Rightarrow x + \frac{7x}{100} = 17334 \\[1em] \Rightarrow \frac{107x}{100} = 17334 \\[1em] \Rightarrow x = \frac{17334 \times 100}{107} \\[1em] \Rightarrow x = 16200\end{aligned}$$
When the tax is reduced to 4%,
New tax = 4% of ₹ 16,200 = ₹ $\Big(\frac{4}{100} \times 16200\Big)$ = ₹ 648.
New price of the laser printer = ₹ (16,200 + 648) = ₹ 16,848.
Amount saved = ₹ (17,334 - 16,848) = ₹ 486.
Hence, the customer pays ₹ 486 less for the laser printer.
In an intrastate transaction, goods worth ₹ 16,000 are bought. If the rate of GST is 5%. Find the amount of the bill.
Given:
Value of the goods = ₹ 16,000 and Rate of GST = 5%
GST = 5% of ₹ 16,000 = ₹ $\Big(\frac{5}{100} \times 16000\Big)$ = ₹ 800.
Amount of the bill = ₹ (16,000 + 800) = ₹ 16,800.
Hence, the amount of the bill is ₹ 16,800.
A customer buys a suitcase from a dealer at a discount of 8% on the marked price of ₹ 5,000. If the rate of GST is 12%, calculate:
(i) the tax (GST) that the customer has to pay for the purchase.
(ii) the total amount that the customer has to pay for the suitcase.
Given:
Marked price of the suitcase = ₹ 5,000, Discount = 8%, Rate of GST = 12%
Discount = 8% of ₹ 5,000 = ₹ $\Big(\frac{8}{100} \times 5000\Big)$ = ₹ 400.
Price after discount = ₹ (5,000 - 400) = ₹ 4,600.
(i) GST = 12% of ₹ 4,600 = ₹ $\Big(\frac{12}{100} \times 4600\Big)$ = ₹ 552.
Hence, the tax (GST) that the customer has to pay is ₹ 552.
(ii) Total amount paid by the customer = ₹ (4,600 + 552) = ₹ 5,152.
Hence, the total amount that the customer has to pay for the suitcase is ₹ 5,152.
A dealer in Jaipur sells a monitor to a customer in Jaipur at ₹ 7,200. If the rate of GST is 18%, find:
(i) IGST
(ii) CGST
(iii) SGST
(iv) the amount paid by the customer for the monitor.
Given:
Sale price of the monitor = ₹ 7,200 and Rate of GST = 18%
Since the dealer and the customer are both in Jaipur, it is a case of intrastate transaction.
(i) Since it is the case of intrastate transaction, so IGST = 0.
Hence, IGST = 0.
(ii) GST rate = 18%
⇒ CGST rate = 9% and SGST rate = 9%.
CGST = 9% of ₹ 7,200
= ₹ $\Big(\frac{9}{100} \times 7200\Big)$
= ₹ 648.
Hence, CGST = ₹ 648.
(iii) GST rate = 18%
SGST = 9% of ₹ 7,200
= ₹ $\Big(\frac{9}{100} \times 7200\Big)$
= ₹ 648.
Hence, SGST = ₹ 648.
(iv) Amount paid by the customer = Sale price + CGST + SGST
= ₹ (7,200 + 648 + 648) = ₹ 8,496.
Hence, the amount paid by the customer for the monitor is ₹ 8,496.
In an interstate transaction, goods worth ₹ 42,000 are bought at 25% discount. If the rate of GST is 12%, find:
(i) IGST
(ii) the amount of the bill.
Given:
Marked price of the goods = ₹ 42,000, Discount = 25%, Rate of GST = 12%
Discount = 25% of ₹ 42,000 = ₹ $\Big(\frac{25}{100} \times 42000\Big)$ = ₹ 10,500.
Price after discount = ₹ (42,000 - 10,500) = ₹ 31,500.
Since it is a case of interstate transaction, the whole GST is charged as IGST.
(i) IGST = 12% of ₹ 31,500 = ₹ $\Big(\frac{12}{100} \times 31500\Big)$ = ₹ 3,780.
Hence, IGST = ₹ 3,780.
(ii) Amount of the bill = ₹ (31,500 + 3,780) = ₹ 35,280.
Hence, the amount of the bill is ₹ 35,280.
An AC mechanic in Mumbai charges repairing cost from three different customers in Mumbai as below:
| Customers | I | II | III |
|---|---|---|---|
| Repairing cost (in ₹) | 3,000 | 4,000 | 2,500 |
| Discount | 10% | 5% | 8% |
If the rate of GST is 18%, find:
(i) IGST
(ii) CGST
(iii) SGST
(iv) total amount of bill paid by each customer.
Given:
Rate of GST = 18%
Since the mechanic and all the three customers are in Mumbai, it is a case of intrastate transaction.
Let us first find the repairing cost of each customer after discount.
For Customer I:
Discount = 10% of ₹ 3,000 = ₹ $\Big(\frac{10}{100} \times 3000\Big)$ = ₹ 300.
Cost after discount = ₹ (3,000 - 300) = ₹ 2,700.
For Customer II:
Discount = 5% of ₹ 4,000 = ₹ $\Big(\frac{5}{100} \times 4000\Big)$ = ₹ 200.
Cost after discount = ₹ (4,000 - 200) = ₹ 3,800.
For Customer III:
Discount = 8% of ₹ 2,500 = ₹ $\Big(\frac{8}{100} \times 2500\Big)$ = ₹ 200.
Cost after discount = ₹ (2,500 - 200) = ₹ 2,300.
Total cost after discount = ₹ (2,700 + 3,800 + 2,300) = ₹ 8,800.
(i) Since it is the case of intrastate transaction, so IGST = 0.
Hence, IGST = 0.
(ii) GST rate = 18%
⇒ CGST rate = 9% and SGST rate = 9%.
CGST = 9% of ₹ 8,800
= ₹ $\Big(\frac{9}{100} \times 8800\Big)$
= ₹ 792.
Hence, CGST = ₹ 792.
(iii) GST rate = 18%
SGST = 9% of ₹ 8,800
= ₹ $\Big(\frac{9}{100} \times 8800\Big)$
= ₹ 792.
Hence, SGST = ₹ 792.
(iv) For Customer I:
CGST = 9% of ₹ 2,700 = ₹ 243 and SGST = 9% of ₹ 2,700 = ₹ 243.
Amount of the bill = ₹ (2,700 + 243 + 243) = ₹ 3,186.
For Customer II:
CGST = 9% of ₹ 3,800 = ₹ 342 and SGST = 9% of ₹ 3,800 = ₹ 342.
Amount of the bill = ₹ (3,800 + 342 + 342) = ₹ 4,484.
For Customer III:
CGST = 9% of ₹ 2,300 = ₹ 207 and SGST = 9% of ₹ 2,300 = ₹ 207.
Amount of the bill = ₹ (2,300 + 207 + 207) = ₹ 2,714.
Hence, the total amount of bill paid is ₹ 3,186 by Customer I, ₹ 4,484 by Customer II and ₹ 2,714 by Customer III.
A wholesaler in Agra (U.P) bought goods from a dealer in Ranchi (Jharkhand). He bought:
(a) 50 rings, marked ₹ 4,000 each, at a discount of 40%.
(b) 40 necklaces, marked ₹ 2,400 each, at a discount of 25%.
If the rate of GST on both the items is 18%, how much will the wholesaler at Agra pay to the dealer in Ranchi?
Given:
Rate of GST = 18%
Since Agra (U.P.) and Ranchi (Jharkhand) are in different states, it is a case of interstate transaction. So, the whole GST is charged as IGST.
For the rings:
Marked price of 50 rings = ₹ (4,000 × 50) = ₹ 2,00,000.
Discount = 40% of ₹ 2,00,000 = ₹ $\Big(\frac{40}{100} \times 200000\Big)$ = ₹ 80,000.
Price after discount = ₹ (2,00,000 - 80,000) = ₹ 1,20,000.
For the necklaces:
Marked price of 40 necklaces = ₹ (2,400 × 40) = ₹ 96,000.
Discount = 25% of ₹ 96,000 = ₹ $\Big(\frac{25}{100} \times 96000\Big)$ = ₹ 24,000.
Price after discount = ₹ (96,000 - 24,000) = ₹ 72,000.
Total price after discount = ₹ (1,20,000 + 72,000) = ₹ 1,92,000.
IGST = 18% of ₹ 1,92,000 = ₹ $\Big(\frac{18}{100} \times 192000\Big)$ = ₹ 34,560.
Amount of the bill = ₹ (1,92,000 + 34,560) = ₹ 2,26,560.
Hence, the wholesaler at Agra will pay ₹ 2,26,560 to the dealer in Ranchi.
By selling an article for ₹ 100, one gains ₹ 10. The gain per cent is
S.P. = ₹ 100 and Gain = ₹ 10.
C.P. = S.P. - Gain = ₹ (100 - 10) = ₹ 90.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{10}{90} \times 100\Big)$%
= $\frac{100}{9}$%
= $11\frac{1}{9}$%
Hence, option 4 is the correct option.
By selling an article for ₹ 100, one loses ₹ 10. The loss per cent is
S.P. = ₹ 100 and Loss = ₹ 10.
C.P. = S.P. + Loss = ₹ (100 + 10) = ₹ 110.
Loss % = $\Big(\frac{\text{Loss}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{10}{110} \times 100\Big)$%
= $\frac{100}{11}$%
= $9\frac{1}{11}$%
Hence, option 2 is the correct option.
A man sold his cow for ₹ 7,920 and gained 10%. The cow was bought for
S.P. = ₹ 7,920 and Gain % = 10%.
$$\begin{aligned}\text{C.P.} = \frac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{110} \times 7920\Big) \\[1em] = ₹ 7200\end{aligned}$$
Hence, option 2 is the correct option.
A watch is sold for ₹ 1,080 at a loss of 10%. The cost price of the watch is
S.P. = ₹ 1,080 and Loss % = 10%.
$$\begin{aligned}\text{C.P.} = \frac{100}{(100 - \text{loss percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{90} \times 1080\Big) \\[1em] = ₹ 1,200\end{aligned}$$
Hence, option 2 is the correct option.
By selling an article for ₹ 240, a trader loses 4%. In order to gain 10% he must sell that article for
S.P. = ₹ 240 and Loss % = 4%.
$$\begin{aligned}\text{C.P.} = \frac{100}{(100 - \text{loss percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{96} \times 240\Big) \\[1em] = ₹ 250\end{aligned}$$
Now, C.P. = ₹ 250 and the gain required = 10%.
$$\begin{aligned}\text{Required S.P.} = \frac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{110}{100} \times 250\Big) \\[1em] = ₹ 275\end{aligned}$$
Hence, option 3 is the correct option.
A man loses ₹ 20 by selling some articles at the rate of ₹ 3 per piece and gains ₹ 30, if he sells them at ₹ 3.25 per piece. The number of pieces sold by him is
Let the number of pieces be $x$ and the cost price of all the pieces be ₹ $y$.
When sold at ₹ 3 per piece, there is a loss of ₹ 20.
$\Rightarrow 3x = y - 20$ .....(1)
When sold at ₹ 3.25 per piece, there is a gain of ₹ 30.
$\Rightarrow 3.25x = y + 30$ .....(2)
Subtracting equation (1) from equation (2),
$$\begin{aligned}\Rightarrow 3.25x - 3x = (y + 30) - (y - 20) \\[1em] \Rightarrow 0.25x = 50 \\[1em] \Rightarrow x = \frac{50}{0.25} \\[1em] \Rightarrow x = 200\end{aligned}$$
Hence, option 3 is the correct option.
The per cent profit made when an article is sold for ₹ 78 is twice as when it is sold for ₹ 69. The cost price of the article is
Let the cost price of the article be ₹ $x$.
Profit when sold for ₹ 78 = ₹ (78 - $x$).
Profit when sold for ₹ 69 = ₹ (69 - $x$).
According to the question, the per cent profit in the first case is twice that in the second case.
$$\begin{aligned}\Rightarrow \frac{78 - x}{x} \times 100 = 2 \times \Big(\frac{69 - x}{x} \times 100\Big) \\[1em] \Rightarrow 78 - x = 2(69 - x) \\[1em] \Rightarrow 78 - x = 138 - 2x \\[1em] \Rightarrow 2x - x = 138 - 78 \\[1em] \Rightarrow x = 60\end{aligned}$$
Hence, option 4 is the correct option.
A vendor buys oranges at ₹ 2 for 3 oranges and sells them at a rupee each. To make a profit of ₹ 10 he must sell
C.P. of 3 oranges = ₹ 2.
C.P. of 1 orange = ₹ $\frac{2}{3}$.
S.P. of 1 orange = ₹ 1.
Profit on 1 orange = ₹ $\Big(1 - \frac{2}{3}\Big) = ₹ \frac{1}{3}$.
For a profit of ₹ $\frac{1}{3}$, he must sell 1 orange.
⇒ For a profit of ₹ 10, he must sell $(10 \times 3)$ = 30 oranges.
Hence, option 3 is the correct option.
A man gains 10% by selling an article for a certain price. If he sells it at double the price the profit made is
Let the cost price of the article be ₹ 100.
Since the gain is 10%, S.P. = ₹ (100 + 10) = ₹ 110.
New S.P. = double of ₹ 110 = ₹ 220.
New profit = ₹ (220 - 100) = ₹ 120.
On a cost price of ₹ 100, the profit is ₹ 120.
Profit % = $\Big(\frac{\text{Profit}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{120}{100} \times 100\Big)$%
= 120%
Hence, option 4 is the correct option.
If an article is sold at a gain of 6% instead of at a loss of 6%, then the seller gets ₹ 6 more. The cost price of the article is
Let the cost price of the article be ₹ $x$.
When the gain is 6%, then S.P. = ₹ ($x$ + 6% of $x$) = ₹ $\frac{53x}{50}$.
When the loss is 6%, then S.P. = ₹ ($x$ - 6% of $x$) = ₹ $\frac{47x}{50}$.
Now, the difference between the two S.P.s = ₹ 6.
$$\begin{aligned}\Rightarrow \frac{53x}{50} - \frac{47x}{50} = 6 \\[1em] \Rightarrow \frac{6x}{50} = 6 \\[1em] \Rightarrow x = \frac{6 \times 50}{6} \\[1em] \Rightarrow x = 50\end{aligned}$$
Hence, option 1 is the correct option.
A radio is sold at a gain of 16%. If it had been sold for ₹ 20 more, 20% would have been gained. The cost price of the radio is
Let the cost price of the radio be ₹ $x$.
When the gain is 16%, then S.P. = ₹ ($x$ + 16% of $x$) = ₹ $\frac{29x}{25}$.
When the gain is 20%, then S.P. = ₹ ($x$ + 20% of $x$) = ₹ $\frac{6x}{5}$.
Now, the difference between the two S.P.s = ₹ 20.
$$\begin{aligned}\Rightarrow \frac{6x}{5} - \frac{29x}{25} = 20 \\[1em] \Rightarrow \frac{30x - 29x}{25} = 20 \\[1em] \Rightarrow \frac{x}{25} = 20 \\[1em] \Rightarrow x = 500\end{aligned}$$
Hence, option 3 is the correct option.
Profit after selling an article for ₹ 425 is the same as loss after selling it for ₹ 355. The cost of the article is
Let the cost price of the article be ₹ $x$.
Profit when sold for ₹ 425 = ₹ (425 - $x$).
Loss when sold for ₹ 355 = ₹ ($x$ - 355).
According to the question, the profit is equal to the loss.
$$\begin{aligned}\Rightarrow 425 - x = x - 355 \\[1em] \Rightarrow 425 + 355 = 2x \\[1em] \Rightarrow 2x = 780 \\[1em] \Rightarrow x = \frac{780}{2} \\[1em] \Rightarrow x = 390\end{aligned}$$
Hence, option 2 is the correct option.
A sold a watch to B at a gain of 5% and B sold it to C at a gain of 4%. If C paid ₹ 1,092 for it the price paid by A is
For B, S.P. = ₹ 1,092 and Gain % = 4%.
$$\begin{aligned}\text{C.P. of B} = \frac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{104} \times 1092\Big) \\[1em] = ₹ 1050\end{aligned}$$
For A, S.P. = ₹ 1,050 and Gain % = 5%.
$$\begin{aligned}\text{C.P. of A} = \frac{100}{(100 + \text{gain percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{105} \times 1050\Big) \\[1em] = ₹ 1000\end{aligned}$$
Hence, option 4 is the correct option.
A bicycle is sold at a gain of 16%. If it had been sold for ₹ 60 more, 20% would have been gained. The cost price of the bicycle is
Let the cost price of the bicycle be ₹ $x$.
When the gain is 16%, then S.P. = ₹ ($x$ + 16% of $x$) = ₹ $\frac{29x}{25}$.
When the gain is 20%, then S.P. = ₹ ($x$ + 20% of $x$) = ₹ $\frac{6x}{5}$.
Now, the difference between the two S.P.s = ₹ 60.
$$\begin{aligned}\Rightarrow \frac{6x}{5} - \frac{29x}{25} = 60 \\[1em] \Rightarrow \frac{30x - 29x}{25} = 60 \\[1em] \Rightarrow \frac{x}{25} = 60 \\[1em] \Rightarrow x = 1500\end{aligned}$$
Hence, option 3 is the correct option.
If the cost price of 15 tables be equal to selling price of 20 tables, the loss per cent is
Let the cost price of 1 table be ₹ 1.
Then, C.P. of 15 tables = ₹ 15.
S.P. of 20 tables = C.P. of 15 tables = ₹ 15.
⇒ S.P. of 1 table = ₹ $\frac{15}{20} = ₹ \frac{3}{4}$.
Since S.P. of 1 table < C.P. of 1 table, so there is a loss.
Loss on 1 table = ₹ $\Big(1 - \frac{3}{4}\Big) = ₹ \frac{1}{4}$.
Loss % = $\Big(\frac{\text{Loss}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{1}{4} \times \frac{100}{1}\Big)$%
= 25%
Hence, option 2 is the correct option.
A fruit seller buys lemons at 2 for a rupee and sells them at 5 for ₹ 3. His gain per cent is
Suppose the number of lemons bought = L.C.M. of 2 and 5 = 10.
C.P. of 2 lemons = ₹ 1.
C.P. of 10 lemons = ₹ $\Big(\frac{1}{2} \times 10\Big)$ = ₹ 5.
S.P. of 5 lemons = ₹ 3.
S.P. of 10 lemons = ₹ $\Big(\frac{3}{5} \times 10\Big)$ = ₹ 6.
Since S.P. > C.P., so there is a gain.
Gain = ₹ (6 - 5) = ₹ 1.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{1}{5} \times 100\Big)$%
= 20%
Hence, option 3 is the correct option.
By selling 45 oranges for ₹ 80 a man loses 20%. How many should he sell for ₹ 48 so as to gain 20% in the transaction?
S.P. of 45 oranges = ₹ 80 and Loss % = 20%.
$$\begin{aligned}\text{C.P. of 45 oranges} = \frac{100}{(100 - \text{loss percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{80} \times 80\Big) \\[1em] = ₹ 100\end{aligned}$$
Now, the gain required = 20%.
$$\begin{aligned}\text{S.P. of 45 oranges} = \frac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{120}{100} \times 100\Big) \\[1em] = ₹ 120\end{aligned}$$
So, for ₹ 120 he sells 45 oranges.
⇒ For ₹ 48 he should sell $\Big(\frac{45}{120} \times 48\Big)$ = 18 oranges.
Hence, option 2 is the correct option.
A trader lists his articles 20% above cost price and allows a discount of 10% on cash payment. His gain per cent is
Let the cost price of the article be ₹ 100.
Then, its marked price = ₹ $\Big(100 + \frac{20}{100} \times 100\Big)$ = ₹ (100 + 20) = ₹ 120.
Discount = 10% of ₹ 120 = ₹ $\Big(\frac{10}{100} \times 120\Big)$ = ₹ 12.
Selling price = M.P. - Discount = ₹ (120 - 12) = ₹ 108.
Gain = S.P. - C.P. = ₹ (108 - 100) = ₹ 8.
On a cost price of ₹ 100, the gain is ₹ 8.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{8}{100} \times 100\Big)$%
= 8%
Hence, option 3 is the correct option.
At what percent above the cost price must an article be marked so as to gain 22.5% after allowing a discount of 2%?
Let the cost price be ₹ 100.
Since the gain is 22.5%, S.P. = ₹ (100 + 22.5) = ₹ 122.50.
Let the marked price be ₹ $x$.
Discount = 2% of ₹ $x$, so S.P. = 98% of M.P.
$$\begin{aligned}\Rightarrow \frac{98x}{100} = 122.50 \\[1em] \Rightarrow x = \frac{122.50 \times 100}{98} \\[1em] \Rightarrow x = 125\end{aligned}$$
M.P. = ₹ 125 and C.P. = ₹ 100.
M.P. is above C.P. by ₹ (125 - 100) = ₹ 25.
On a cost price of ₹ 100, the marked price is ₹ 25 above.
Required per cent = $\Big(\frac{\text{M.P.} - \text{C.P.}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{25}{100} \times 100\Big)$%
= 25%
Hence, option 3 is the correct option.
Arun buys an article with 25% discount on its marked price. He makes a profit of 10% by selling it at ₹ 660. The marked price is
For Arun, S.P. = ₹ 660 and Profit % = 10%.
$$\begin{aligned}\text{C.P. of Arun} = \frac{100}{(100 + \text{profit percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{110} \times 660\Big) \\[1em] = ₹ 600\end{aligned}$$
Arun bought the article at a discount of 25% on the marked price.
Let the marked price be ₹ $x$.
$$\begin{aligned}\Rightarrow \frac{(100 - 25)}{100} \times x = 600 \\[1em] \Rightarrow \frac{75x}{100} = 600 \\[1em] \Rightarrow x = \frac{600 \times 100}{75} \\[1em] \Rightarrow x = 800\end{aligned}$$
Hence, option 3 is the correct option.
An umbrella marked at ₹ 80 is sold for ₹ 68. The rate of discount is
M.P. = ₹ 80 and S.P. = ₹ 68.
Discount given = M.P. - S.P. = ₹ (80 - 68) = ₹ 12.
Rate of discount = $\Big(\frac{\text{Discount}}{\text{M.P.}} \times 100\Big)$%
= $\Big(\frac{12}{80} \times 100\Big)$%
= $\frac{1200}{80}$%
= 15%
Hence, option 2 is the correct option.
A tradesman marks his goods 30% above cost price. If he allows a discount of $6\frac{1}{4}$%, then his gain per cent is
Let the cost price of the goods be ₹ 100.
Then, its marked price = ₹ $\Big(100 + \frac{30}{100} \times 100\Big)$ = ₹ (100 + 30) = ₹ 130.
Discount = $6\frac{1}{4}$% of ₹ 130 = ₹ $\Big(\frac{25}{4} \times \frac{1}{100} \times 130\Big)$ = ₹ $\frac{65}{8}$.
Selling price = M.P. - Discount = ₹ $\Big(130 - \frac{65}{8}\Big) = ₹ \frac{975}{8}$.
Gain = S.P. - C.P. = ₹ $\Big(\frac{975}{8} - 100\Big) = ₹ \frac{175}{8}$.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{175}{8} \times \frac{1}{100} \times 100\Big)$%
= $\frac{175}{8}$%
= $21\frac{7}{8}$%
Hence, option 1 is the correct option.
A discount series of 10%, 20% and 40% is equivalent to a single discount of
Let the marked price be ₹ 100.
First discount = 10% of ₹ 100 = ₹ 10.
Price after the first discount = ₹ (100 - 10) = ₹ 90.
Second discount = 20% of ₹ 90 = ₹ 18.
Price after the second discount = ₹ (90 - 18) = ₹ 72.
Third discount = 40% of ₹ 72 = ₹ 28.80.
Price after the third discount = ₹ (72 - 28.80) = ₹ 43.20.
Net discount = ₹ (100 - 43.20) = ₹ 56.80.
On a marked price of ₹ 100, the discount is ₹ 56.80.
Discount % = $\Big(\frac{\text{Discount}}{\text{M.P.}} \times 100\Big)$%
= $\Big(\frac{56.80}{100} \times 100\Big)$%
= 56.8%
Hence, option 2 is the correct option.
The difference between a discount of 40% on ₹ 500 and two successive discounts of 36% and 4% on the same amount is
For a single discount of 40%:
Discount = 40% of ₹ 500 = ₹ $\Big(\frac{40}{100} \times 500\Big)$ = ₹ 200.
Price after discount = ₹ (500 - 200) = ₹ 300.
For two successive discounts of 36% and 4%:
First discount = 36% of ₹ 500 = ₹ $\Big(\frac{36}{100} \times 500\Big)$ = ₹ 180.
Price after the first discount = ₹ (500 - 180) = ₹ 320.
Second discount = 4% of ₹ 320 = ₹ $\Big(\frac{4}{100} \times 320\Big)$ = ₹ 12.80.
Price after the second discount = ₹ (320 - 12.80) = ₹ 307.20.
Required difference = ₹ (307.20 - 300) = ₹ 7.20.
Hence, option 4 is the correct option.
On an article with marked price ₹ 20,000, a customer has a choice between three successive discounts of 20%, 20% and 10% and three successive discounts of 40%, 5% and 5%. By choosing the better offer he can save
Marked price of the article = ₹ 20,000
If $d_1$%, $d_2$% and $d_3$% are three successive discounts, then :
Price = $\frac{(100 - d_1)}{100} \times \frac{(100 - d_2)}{100} \times \frac{(100 - d_3)}{100} \times \text{M.P.}$
For the successive discounts of 20%, 20% and 10%:
$$\begin{aligned}\text{Price} = ₹ \Big[\Big(1 - \frac{20}{100}\Big)\Big(1 - \frac{20}{100}\Big)\Big(1 - \frac{10}{100}\Big) \times 20000\Big] \\[1em] = ₹ \Big(\frac{80}{100} \times \frac{80}{100} \times \frac{90}{100} \times 20000\Big) \\[1em] = ₹ (0.8 \times 0.8 \times 0.9 \times 20000) \\[1em] = ₹ 11520\end{aligned}$$
For the successive discounts of 40%, 5% and 5%:
$$\begin{aligned}\text{Price} = ₹ \Big[\Big(1 - \frac{40}{100}\Big)\Big(1 - \frac{5}{100}\Big)\Big(1 - \frac{5}{100}\Big) \times 20000\Big] \\[1em] = ₹ \Big(\frac{60}{100} \times \frac{95}{100} \times \frac{95}{100} \times 20000\Big) \\[1em] = ₹ (0.6 \times 0.95 \times 0.95 \times 20000) \\[1em] = ₹ 10830\end{aligned}$$
Since ₹ 10,830 < ₹ 11,520, the second offer is better.
Saving = ₹ (11,520 - 10,830) = ₹ 690.
Hence, option 2 is the correct option.
Fill in the blanks:
(i) ......... = $\frac{(100 + \text{gain percentage})}{100}$ × ......... .
(ii) Discount is always allowed on the ......... price.
(iii) ......... = M.P. - Discount.
(iv) If the S.P of an article is $\frac{6}{5}$ of its cost price, then the gain per cent is ......... .
(v) A shopkeeper incurs a ......... if he sells 15 articles at the cost price of 12 articles.
(i) When an article is sold at a gain, the selling price is obtained from the cost price by the formula $\text{S.P.} = \frac{(100 + \text{gain percentage})}{100} \times \text{C.P.}$
Hence, S.P. = $\frac{(100 + \text{gain percentage})}{100}$ × C.P.
(ii) Discount is a reduction given by the shopkeeper on the price marked on the article.
Hence, discount is always allowed on the marked price.
(iii) The price at which an article is finally sold is obtained by subtracting the discount from the marked price.
Hence, S.P. = M.P. - Discount.
(iv) $\text{S.P.} = \frac{6}{5}$ of C.P.
Since S.P. > C.P., so there is a gain.
$$\begin{aligned}\text{Gain} = \text{S.P.} - \text{C.P.} \\[1em] = \frac{6}{5}\text{C.P.} - \text{C.P.} \\[1em] = \frac{\text{C.P.}}{5}\end{aligned}$$
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{\text{C.P.}}{5} \times \frac{100}{\text{C.P.}}\Big)$%
= 20%
Hence, the gain per cent is 20%.
(v) Let the cost price of 1 article be ₹ 1.
Then, C.P. of 15 articles = ₹ 15.
S.P. of 15 articles = C.P. of 12 articles = ₹ 12.
Since S.P. < C.P., the shopkeeper incurs a loss.
Hence, a shopkeeper incurs a loss if he sells 15 articles at the cost price of 12 articles.
Write true (T) or false (F):
(i) Gain or loss is always reckoned on the S.P. .........
(ii) If a shopkeeper buys an article for ₹ 75 and sells it for ₹ 100, then his gain is 25%. .........
(iii) C.P. = $\frac{100}{(100 - \text{loss percentage})}$ × S.P. .........
(iv) If no discount is given, then cost price becomes equal to selling price. .........
(i) Gain or loss is always reckoned on the S.P.
Gain or loss is always reckoned on the cost price, and not on the selling price.
Hence, the statement is False.
(ii) If a shopkeeper buys an article for ₹ 75 and sells it for ₹ 100, then his gain is 25%.
C.P. = ₹ 75 and S.P. = ₹ 100.
Gain = ₹ (100 - 75) = ₹ 25.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{25}{75} \times 100\Big)$%
= $\frac{100}{3}$%
= $33\frac{1}{3}$%
Since the gain per cent is $33\frac{1}{3}$% and not 25%, the statement is false.
Hence, the statement is False.
(iii) C.P. = $\frac{100}{(100 - \text{loss percentage})}$ × S.P.
When an article is sold at a loss, $\text{S.P.} = \frac{(100 - \text{loss percentage})}{100} \times \text{C.P.}$, and so $\text{C.P.} = \frac{100}{(100 - \text{loss percentage})} \times \text{S.P.}$
Hence, the statement is True.
(iv) If no discount is given, then cost price becomes equal to selling price.
If no discount is given, the article is sold at its marked price, so the selling price becomes equal to the marked price and not to the cost price.
Hence, the statement is False.
Assertion (A): Aman bought a new motorcycle for ₹ 2,50,000. Next year, its price decreased by 10% and further next year, it decreased by 12%. The overall decrease in the price of the motorcycle is 20.8%.
Reason (R): SP = $\frac{(100 - \text{loss percentage})}{100}$ × CP.
Original price of the motorcycle = ₹ 2,50,000.
Price after a decrease of 10% = ₹ $\Big(\frac{100 - 10}{100} \times 250000\Big) = ₹ \Big(\frac{90}{100} \times 250000\Big)$ = ₹ 2,25,000.
Price after a further decrease of 12% = ₹ $\Big(\frac{100 - 12}{100} \times 225000\Big) = ₹ \Big(\frac{88}{100} \times 225000\Big)$ = ₹ 1,98,000.
Total decrease in the price = ₹ (2,50,000 - 1,98,000) = ₹ 52,000.
Overall decrease % = $\Big(\frac{\text{Total decrease}}{\text{Original price}} \times 100\Big)$%
= $\Big(\frac{52000}{250000} \times 100\Big)$%
= $\frac{5200000}{250000}$%
= 20.8%
So, Assertion (A) is true.
The formula $\text{SP} = \frac{(100 - \text{loss percentage})}{100} \times \text{CP}$ is a correct statement, so Reason (R) is true.
However, this formula applies to a single transaction only. The overall decrease of 20.8% arises because the second decrease is calculated on the already reduced price, and this successive effect is not explained by the formula in Reason (R).
So, Reason (R) is true but it is not the correct explanation of Assertion (A).
Hence, option 2 is the correct option.
Assertion (A): Selling price of 9 articles is equal to the cost price of 15 articles. In this transaction, there is a profit of $66\frac{2}{3}$%.
Reason (R): Gain% = $\frac{\text{Actual gain}}{100}$ × CP.
Let the cost price of 1 article be ₹ 1.
Then, C.P. of 15 articles = ₹ 15.
S.P. of 9 articles = C.P. of 15 articles = ₹ 15.
⇒ S.P. of 1 article = ₹ $\frac{15}{9} = ₹ \frac{5}{3}$.
Since S.P. of 1 article > C.P. of 1 article, so there is a profit.
Profit on 1 article = ₹ $\Big(\frac{5}{3} - 1\Big) = ₹ \frac{2}{3}$.
Profit % = $\Big(\frac{\text{Profit}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{2}{3} \times \frac{100}{1}\Big)$%
= $\frac{200}{3}$%
= $66\frac{2}{3}$%
So, Assertion (A) is true.
The correct formula is $\text{Gain percentage} = \frac{\text{Actual gain}}{\text{CP}} \times 100$, and not $\frac{\text{Actual gain}}{100} \times \text{CP}$ as given.
So, Reason (R) is false.
Hence, option 3 is the correct option.
Which of the following does mean a 100% profit?
A profit of 100% means that the profit is equal to the cost price, i.e. S.P. = 2 × C.P.
Let us check each option:
Option 1: C.P. = ₹ 100 and S.P. = ₹ 50. Here S.P. < C.P., so there is a loss of 50%.
Option 2: C.P. = ₹ 100 and S.P. = ₹ 100. Here S.P. = C.P., so there is neither profit nor loss.
Option 3: C.P. = ₹ 50 and S.P. = ₹ 100. Profit = ₹ 50 and Profit % = $\Big(\frac{50}{50} \times 100\Big)$% = 100%.
Option 4: C.P. = ₹ 50 and S.P. = ₹ 150. Profit = ₹ 100 and Profit % = $\Big(\frac{100}{50} \times 100\Big)$% = 200%.
Hence, option 3 is the correct option.
A shopkeeper buys a ball and a bat for ₹ 200 and ₹ 500 respectively. For selling, he marks the bat at ₹ 525. What price should he ask for the ball, if he wants to make a profit of 5% on the whole transaction?
Total C.P. of the ball and the bat = ₹ (200 + 500) = ₹ 700.
For a profit of 5% on the whole transaction,
$$\begin{aligned}\text{Total S.P.} = \frac{(100 + \text{profit percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 + 5}{100} \times 700\Big) \\[1em] = ₹ \Big(\frac{105}{100} \times 700\Big) \\[1em] = ₹ 735\end{aligned}$$
S.P. of the bat = ₹ 525.
S.P. of the ball = ₹ (735 - 525) = ₹ 210.
Hence, option 3 is the correct option.
A shopkeeper bought an item and plans to sells it in two ways:
(i) The shopkeeper gives a discount of $x$% on the marked price and adds $x$% tax on the discounted price of the item.
(ii) The shopkeeper hikes the marked price by $x$% and then gives $x$% discount on the hiked price of the item.
Which option is better for the shopkeeper?
Let the marked price of the item be ₹ $M$.
For option (i):
Price after a discount of $x$% = ₹ $M\Big(1 - \frac{x}{100}\Big)$.
Price after adding $x$% tax on it = ₹ $M\Big(1 - \frac{x}{100}\Big)\Big(1 + \frac{x}{100}\Big)$ = ₹ $M\Big(1 - \frac{x^2}{10000}\Big)$.
For option (ii):
Price after a hike of $x$% = ₹ $M\Big(1 + \frac{x}{100}\Big)$.
Price after a discount of $x$% on it = ₹ $M\Big(1 + \frac{x}{100}\Big)\Big(1 - \frac{x}{100}\Big)$ = ₹ $M\Big(1 - \frac{x^2}{10000}\Big)$.
The final price is the same in both the options.
Hence, option 3 is the correct option.
Amazon offers you 10% cashback (discount) on an article of ₹ 500 and adds 15% delivery charges on the discounted amount of the article. How much do you need to pay?
Marked price of the article = ₹ 500.
Cashback (discount) = 10% of ₹ 500 = ₹ 50.
Discounted amount = ₹ (500 - 50) = ₹ 450, which is ₹ 500 - 10% of ₹ 500.
The delivery charges are added on the discounted amount, so
Delivery charges = 15% of ₹ 450.
Amount to be paid = ₹ 500 - 10% of ₹ 500 + 15% of ₹ 450.
Hence, option 4 is the correct option.
A shopkeeper sells an item for 25% discount and still makes 25% profit. The discount he needs to offer to achieve a profit of 36% is:
Let the marked price of the item be ₹ 100.
Discount = 25% of ₹ 100 = ₹ 25.
S.P. = ₹ (100 - 25) = ₹ 75, and on this the profit is 25%.
$$\begin{aligned}\text{C.P.} = \frac{100}{(100 + \text{profit percentage})} \times \text{S.P.} \\[1em] = ₹ \Big(\frac{100}{125} \times 75\Big) \\[1em] = ₹ 60\end{aligned}$$
For a profit of 36%,
$$\begin{aligned}\text{Required S.P.} = \frac{(100 + 36)}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{136}{100} \times 60\Big) \\[1em] = ₹ 81.60\end{aligned}$$
Required discount = ₹ (100 - 81.60) = ₹ 18.40.
On a marked price of ₹ 100, the discount is ₹ 18.40.
Discount % = $\Big(\frac{\text{Discount}}{\text{M.P.}} \times 100\Big)$%
= $\Big(\frac{18.40}{100} \times 100\Big)$%
= 18.4%
Hence, option 3 is the correct option.
A teacher buys a book of cost price ₹ 100. As she goes to school next day, her friend asks her to sells that book to her. As a friend, she sells the book at 20% loss to her. And then her friend sells that book at 20% gain to some other colleague. The final selling price of the book is:
For the teacher, C.P. = ₹ 100 and Loss % = 20%.
$$\begin{aligned}\text{S.P.} = \frac{(100 - \text{loss percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 - 20}{100} \times 100\Big) \\[1em] = ₹ 80\end{aligned}$$
For the friend, C.P. = ₹ 80 and Gain % = 20%.
$$\begin{aligned}\text{S.P.} = \frac{(100 + \text{gain percentage})}{100} \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 + 20}{100} \times 80\Big) \\[1em] = ₹ 96\end{aligned}$$
Hence, option 3 is the correct option.
A dealer allows a discount of 10% on the marked price. How much above the cost price must he mark his goods to make a profit of 8%?
Let the cost price of the goods be ₹ 100.
Since the profit is 8%, S.P. = ₹ (100 + 8) = ₹ 108.
Let the marked price be ₹ $x$.
Discount = 10% of ₹ $x$, so S.P. = 90% of M.P.
$$\begin{aligned}\Rightarrow \frac{90x}{100} = 108 \\[1em] \Rightarrow x = \frac{108 \times 100}{90} \\[1em] \Rightarrow x = 120\end{aligned}$$
M.P. = ₹ 120 and C.P. = ₹ 100.
M.P. is above C.P. by ₹ (120 - 100) = ₹ 20.
On a cost price of ₹ 100, the marked price is ₹ 20 above.
Required per cent = $\Big(\frac{\text{M.P.} - \text{C.P.}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{20}{100} \times 100\Big)$%
= 20%
Hence, option 4 is the correct option.
A dishonest seller sells fruits with a 960 g weight instead of a 1 kg weight. If he sold the fruits at the cost price, his gain is:
Let the cost price of the fruits be ₹ 1 per gram.
The seller uses a weight of 960 g in place of 1 kg = 1000 g.
So, he actually gives 960 g of fruits but charges the price of 1000 g.
C.P. of the fruits sold = ₹ 960.
S.P. of the fruits sold = ₹ 1,000.
Since S.P. > C.P., so there is a gain.
Gain = ₹ (1,000 - 960) = ₹ 40.
Gain % = $\Big(\frac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%
= $\Big(\frac{40}{960} \times 100\Big)$%
= $\frac{4000}{960}$%
= $\frac{25}{6}$%
= $4\frac{1}{6}$%
Hence, option 4 is the correct option.
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