Profit & Loss

Given:

C.P. = ₹ 960

S.P. = ₹ 1104

Gain = S.P. - C.P.

Substituting the values in above, we get:

Gain = ₹ 1104 - ₹ 960

Gain = ₹ 144

And

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

= $\Big(\frac{144}{960} \times 100\Big)$%

= $\Big(\frac{144}{48} \times 5\Big)$% $\quad$ [Dividing 100 and 960 by 20]

= $\Big(\frac{3}{1} \times 5\Big)$% $\quad$ [Dividing 144 and 48 by 48]

= 15%

Gain = ₹ 144, Gain % = 15%

Given:

C.P. = ₹ 2350

S.P. = ₹ 2538

Gain = S.P. - C.P.

Substituting the values in above, we get:

Gain = ₹ 2538 - ₹ 2350

Gain = ₹ 188

And

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

= $\Big(\frac{188}{2350} \times 100\Big)$%

= $\Big(\frac{188}{47} \times 2\Big)$% $\quad$ [Dividing 100 and 2350 by 50]

= $\Big(\frac{4}{1} \times 2\Big)$% $\quad$ [Dividing 188 and 47 by 47]

= 8%

Gain = ₹ 188, Gain % = 8%

Given:

C.P. = ₹ 6250

S.P. = ₹ 5875

Loss = C.P. - S.P.

Substituting the values in above, we get:

Loss = ₹ 6250 - ₹ 5875

Loss = ₹ 375

And

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

= $\Big(\frac{375}{6250} \times 100\Big)$%

= $\Big(\frac{375}{125} \times 2\Big)$% $\quad$ [Dividing 100 and 6250 by 50]

= $\Big(\frac{3}{1} \times 2\Big)$% $\quad$ [Dividing 375 and 125 by 125]

= 6%

Loss = ₹ 375, Loss % = 6%

Given:

C.P. of computer = ₹ 24000

C.P. of accessories = ₹ 1750

Total C.P. = ₹ 24000 + ₹ 1750 = ₹ 25750

S.P. = ₹ 26780.

Gain = S.P. - C.P.

Substituting the values in above, we get:

Gain = ₹ 26780 - ₹ 25750

Gain = ₹ 1030

And

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

= $\Big(\frac{1030}{25750} \times 100\Big)$%

= $\Big(\frac{1030}{515} \times 2\Big)$% $\quad$ [Dividing 100 and 25750 by 50]

= $\Big(\frac{2}{1} \times 2\Big)$% $\quad$ [Dividing 1030 and 515 by 515]

= 4%

Gain = ₹ 1030, Gain % = 4%

Given:

C.P. of refrigerator = ₹ 35615

Transportation fee = ₹ 125

Total C.P. = ₹ 35615 + ₹ 125 = ₹ 35740

S.P. = ₹ 33953.

Loss = C.P. - S.P.

Substituting the values in above, we get:

Loss = ₹ 35740 - ₹ 33953

Loss = ₹ 1787

And

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

= $\Big(\frac{1787}{35740} \times 100\Big)$%

= $\Big(\frac{1787}{1787} \times 5\Big)$% $\quad$ [Dividing 100 and 35740 by 20]

= $\Big(\frac{1}{1} \times 5\Big)$%

= 5%

Loss % = 5%

Given:

S.P. = ₹ 5670

Gain = ₹ 270

Gain = S.P. - C.P.

⇒ C.P. = S.P. - Gain

Substituting the values in above, we get:

⇒ C.P. = 5670 - 270

⇒ C.P. = ₹ 5400

And

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

= $\Big(\frac{270}{5400} \times 100\Big)$%

= $\Big(\frac{270}{54} \times 1\Big)$% $\quad$ [Dividing 100 and 5400 by 100]

= $\Big(\frac{5}{1} \times 1\Big)$% $\quad$ [Dividing 270 and 54 by 54]

= 5%

Gain % = 5%

Given:

S.P. = ₹ 1410

Loss = ₹ 90.

Loss = C.P. - S.P.

⇒ C.P. = S.P. + Loss

Substituting the values in above, we get:

⇒ C.P. = ₹ 1410 + ₹ 90

⇒ C.P. = ₹ 1500

And

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

= $\Big(\frac{90}{1500} \times 100\Big)$%

= $\Big(\frac{90}{15} \times 1\Big)$%

= $\Big(\frac{6}{1} \times 1\Big)$%

= 6%

Loss % = 6%

Given:

C.P. → 3 bananas = ₹ 8

C.P. of 1 banana = ₹ $\frac{8}{3}$

S.P. → 2 bananas = ₹ 7

S.P. of 1 banana = ₹ $\frac{7}{2}$

L.C.M. of 3 and 2 = 6 so let him buy 6 bananas.

C.P. of 6 bananas = ₹ $\frac{8}{3} \times 6 = ₹ 16$

S.P. of 6 bananas = ₹ $\frac{7}{2} \times 6 = ₹ 21$

Since S.P. > C.P., it is a gain.

Gain = S.P. - C.P.

Gain = ₹ 21 - ₹ 16 = ₹ 5

And

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

= $\Big(\frac{5}{16} \times 100\Big)$%

= $\Big(\frac{5}{4} \times 25\Big)$% $\quad$ [Dividing 100 and 16 by 4]

= $\frac{125}{4}$%

= $31\frac{1}{4}$%

Gain % = $31\frac{1}{4}$%

Given:

C.P. of 3 lemons = ₹ 4

C.P. of 1 lemon = ₹ $\frac{4}{3}$

Gain % = 20%

S.P. of 1 lemon = $\Big( \frac{100 + \text{Gain percentage}}{100}\Big) \times \text{C.P.}$

$$\begin{aligned}= ₹ \Big( \frac{100 + 20}{100} \Big) \times \frac{4}{3} \\[1em] = ₹ \Big(\frac{120}{100} \times \frac{4}{3}\Big) \\[1em] = ₹ \Big(\frac{6}{5} \times \frac{4}{3}\Big) \quad \text{[Dividing 120 and 100 by 20]} \\[1em] = ₹ \Big(\frac{2}{5} \times \frac{4}{1}\Big) \quad \text{[Dividing 6 and 3 by 3]} \\[1em] = ₹ \frac{8}{5}\end{aligned}$$

S.P. of 1 lemon = ₹ $\frac{8}{5}$

∴ S.P. of 5 lemons = ₹ $5 \times \frac{8}{5}$ = ₹ 8

Rate = 5 for ₹ 8

Given:

S.P. of 12 = C.P. of 14

Let C.P. of 1 pen = ₹ 1.

Then C.P. of 14 pens = ₹ 14.

S.P. of 12 pens = ₹ 14.

C.P. of 12 pens = ₹ 12.

Gain = S.P. - C.P.

Substituting the values in above, we get:

Gain = ₹ 14 - ₹ 12 = ₹ 2

And

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

= $\Big(\frac{2}{12} \times 100\Big)$%

= $\Big(\frac{2}{3} \times 25\Big)$% $\quad$ [Dividing 100 and 12 by 4]

= $\frac{50}{3}$%

= $16\frac{2}{3}$%

Gain % = $16\frac{2}{3}$%

Given:

C.P. of 12 oranges = S.P. of 15 oranges

Let C.P. of 1 orange = ₹ 1.

Then C.P. of 15 oranges = ₹ 15.

S.P. of 15 oranges = ₹ 12.

Loss = C.P. - S.P.

Substituting the values in above, we get:

Loss = ₹ 15 - ₹ 12 = ₹ 3

And

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

= $\Big(\frac{3}{15} \times 100\Big)$%

= $\Big(\frac{1}{5} \times 100\Big)$%

= 20%

Loss % = 20%

Given:

S.P. of plot of land = ₹ 143000

Gain percentage = 4%

C.P. = ?

We have the formula,

$$\begin{aligned}\text {C.P.} = \Big( \frac{100}{100 + \text{Gain percentage}} \times \text{S.P.}\Big) \\[1em] = ₹ \Big(\frac{100}{100 + 4} \times 143000\Big) \\[1em] = ₹ \Big(\frac{100}{104} \times 143000\Big) \\[1em] = ₹ \Big(\frac{25}{26} \times 143000\Big) \quad \text{[Dividing 100 and 104 by 4]} \\[1em] = ₹ \Big(\frac{25}{1} \times 5500\Big) \quad \text{[Dividing 143000 and 26 by 26]} \\[1em] = ₹ 25 \times 5500 \\[1em] = ₹ 137500\end{aligned}$$

Hence, Vinay purchased the plot for ₹ 137500.

Given:

S.P. of the T.V. = ₹ 14100

Loss percentage = 6%

C.P. = ?

We have the formula,

$$\begin{aligned}\text {C.P.} = \Big( \frac{100}{100 - \text{Loss percentage}} \times \text{S.P.} \Big) \\[1em] = ₹ \Big(\frac{100}{100 - 6} \times 14100\Big) \\[1em] = ₹ \Big(\frac{100}{94} \times 14100\Big) \\[1em] = ₹ \Big(\frac{50}{47} \times 14100\Big) \quad \text{[Dividing 100 and 94 by 2]} \\[1em] = ₹ \Big(\frac{50}{1} \times 300\Big) \quad \text{[Dividing 14100 and 47 by 47]} \\[1em] = ₹ 50 \times 300 \\[1em] = ₹ 15000\end{aligned}$$

Hence, John purchased the T.V. set for ₹ 15000.

Given:

Initial S.P. = ₹ 10800

Initial Loss percentage = 10%

Desired Gain percentage = 5%

Let us find the Cost Price (C.P.):

We have the formula,

$$\begin{aligned}\text {C.P.} = \Big( \frac{100}{100 - \text{Loss percentage}} \times \text{S.P.} \Big) \\[1em] = ₹ \Big(\frac{100}{100 - 10} \times 10800\Big) \\[1em] = ₹ \Big(\frac{100}{90} \times 10800\Big) \\[1em] = ₹ \Big(\frac{10}{9} \times 10800\Big) \quad \text{[Dividing 100 and 90 by 10]} \\[1em] = ₹ \Big(\frac{10}{1} \times 1200\Big) \quad \text{[Dividing 10800 and 9 by 9]} \\[1em] = ₹ 10 \times 1200 \\[1em] = ₹ 12000\end{aligned}$$

C.P. = ₹ 12000

Now, let us find the New Selling Price for 5% Gain:

We have the formula:

$$\begin{aligned}\text {S.P.} = \Big( \frac{100 + \text{Gain percentage}}{100} \Big) \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 + 5}{100} \times 12000\Big) \\[1em] = ₹ \Big(\frac{105}{100} \times 12000\Big) \\[1em] = ₹ \Big(\frac{105}{1} \times 120\Big) \quad \text{[Dividing 12000 and 100 by 100]} \\[1em] = ₹ 105 \times 120 \\[1em] = ₹ 12600\end{aligned}$$

∴ New S.P. = ₹ 12600

Hence, he should sell the bed for ₹ 12600.

Given:

Case 1: S.P. = ₹ 20350 and Gain = 10%

Case 2: New S.P. = ₹ 19610 and Gain % = ?

Let us find the Cost Price (C.P.):

We have the formula,

$$\begin{aligned}\text {C.P.} = \Big( \frac{100}{100 + \text{Gain percentage}} \times \text{S.P.} \Big) \\[1em] = ₹ \Big(\frac{100}{100 + 10} \times 20350\Big) \\[1em] = ₹ \Big(\frac{100}{110} \times 20350\Big) \\[1em] = ₹ \Big(\frac{100}{1} \times 185\Big) \quad \text{[Dividing 20350 and 110 by 110]} \\[1em] = ₹ 100 \times 185 \\[1em] = ₹ 18500\end{aligned}$$

C.P. = ₹ 18500

Now, let us find the Gain Percentage for New S.P.

New Gain = New S.P. - C.P.

New Gain = ₹ 19610 - ₹ 18500 = ₹ 1110

And

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

= $\Big(\frac{1110}{18500} \times 100\Big)$%

= $\Big(\frac{1110}{185} \times 1\Big)$% $\quad$ [Dividing 100 and 18500 by 100]

= $\Big(\frac{1110}{185}\Big)$% $\quad$ [Dividing 1110 and 185 by 185]

= 6%

On selling the almirah for ₹ 19610, he gains 6%.

Given:

Initial Selling Price (S.P.) = ₹ 4700

Initial Loss percentage = 6%

Desired Gain percentage = 6%

Let us find the Cost Price (C.P.):

We have the formula,

$$\begin{aligned}\text {C.P.} = \Big( \frac{100}{100 - \text{Loss percentage}} \times \text{S.P.} \Big) \\[1em] = ₹ \Big(\frac{100}{100 - 6} \times 4700\Big) \\[1em] = ₹ \Big(\frac{100}{94} \times 4700\Big) \\[1em] = ₹ \Big(\frac{100}{1} \times 50\Big) \quad \text{[Dividing 4700 and 94 by 94]} \\[1em] = ₹ 5000\end{aligned}$$

C.P. = ₹ 5000

Now, let us find the New Selling Price for 6% Gain:

We have the formula,

$$\begin{aligned}\text {S.P.} = \Big( \frac{100 + \text{Gain percentage}}{100} \Big) \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 + 6}{100} \times 5000\Big) \\[1em] = ₹ \Big(\frac{106}{100} \times 5000\Big) \\[1em] = ₹ \Big(\frac{106}{1} \times 50\Big) \quad \text{[Dividing 5000 and 100 by 100]} \\[1em] = ₹ 106 \times 50 \\[1em] = ₹ 5300\end{aligned}$$

Hence, he must sell the fan for ₹ 5300 to gain 6%.

Given:

S.P. of each scooter = ₹ 19800

Scooter 1 Gain = 10%

Scooter 2 Loss = 10%

First, let us find C.P. of both scooters:

For first scooter (10% gain) :

$$\begin{aligned}\text {C.P.}_1 = \Big( \frac{100}{100 + \text{Gain percentage}} \times \text{S.P.} \Big) \\[1em] = ₹ \Big(\frac{100}{100 + 10} \times 19800\Big) \\[1em] = ₹ \Big(\frac{100}{110} \times 19800\Big) \\[1em] = ₹ \Big(\frac{100}{1} \times 180\Big) \quad \text{[Dividing 19800 and 110 by 110]} \\[1em] = ₹ 18000 \\[1em]\end{aligned}$$

C.P.₁ = ₹ 18000

For second scooter (10% loss) :

$$\begin{aligned}\text {C.P.}_2 = \Big( \frac{100}{100 - \text{Loss percentage}} \times \text {S.P.} \Big) \\[1em] = ₹ \Big(\frac{100}{100 - 10} \times 19800\Big) \\[1em] = ₹ \Big(\frac{100}{90} \times 19800\Big) \\[1em] = ₹ \Big(\frac{100}{1} \times 220\Big) \quad \text{[Dividing 19800 and 90 by 90]} \\[1em] = ₹ 22000\end{aligned}$$

C.P.₂ = ₹ 22000

Now, let us find Total C.P. and Total S.P.

Total C.P. = C.P.₁ + C.P.₂

Total C.P. = ₹ 18000 + ₹ 22000 = ₹ 40000

Total S.P. = ₹ 19800 + ₹ 19800 = ₹ 39600

Since Total C.P. > Total S.P., there is an overall loss.

Loss = C.P. - S.P.

Loss = ₹ 40000 - ₹ 39600 = ₹ 400

We have the formula,

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

= $\Big( \frac{400}{40000} \times 100 \Big)$%

= $\Big( \frac{400}{400} \times 1 \Big)$% $\quad$ [Dividing 400 and 40000 by 100]

= $\Big( \frac{1}{1}\Big)$% $\quad$ [Dividing 400 and 400 by 400]

= 1%

Hence, Kamal suffered a 1% loss on the whole transaction.

Given:

A's Cost Price = ₹ 650

Profit from A to B = 20%

Loss from B to C = 20%

First, let us find A's S.P. (which is B's Cost Price):

A sells to B at 20% profit:

$\text {S.P.}_\text A ​= ₹ 650 + 20$% $\text { of } ₹ 650$

$$\begin{aligned}= ₹ 650 + ₹ \Big(\frac{\overset{1}{\cancel{20}}}{\underset{5}{\cancel{100}}} \times 650\Big) \\[1em] = ₹ 650 + ₹ \Big(\frac{1}{\underset{1}{\cancel{5}}} \times \overset{130}{\cancel{650}}\Big) \\[1em] = ₹ 650 + ₹ \Big(\frac{1}{1} \times 130\Big) \\[1em] = ₹ 650 + ₹ 130 \\[1em] = ₹ 780\end{aligned}$$

∴ S.P._A ​= ₹ 780

Now, let us find B's S.P. (which is C's Cost Price):

B sells to C at 20% loss :

$\text {S.P.}_\text B ​= ₹ 780 - 20$% $\text { of } ₹ 780$

$$\begin{aligned}= ₹ 780 - ₹ \Big(\frac{\overset{1}{\cancel{20}}}{\underset{5}{\cancel{100}}} \times 780\Big) \\[1em] = ₹ 780 - ₹ \Big(\frac{1}{\underset{1}{\cancel{5}}} \times \overset{156}{\cancel{780}}\Big) \\[1em] = ₹ 780 - ₹ \Big(\frac{1}{1} \times 156\Big) \\[1em] = ₹ 780 - ₹ 156 \\[1em] = ₹ 624\end{aligned}$$

∴ S.P._B ​= ₹ 624

Hence, C pays ₹ 624 for the article.

Gain occurs when the selling price is higher than the cost price.

Hence, option 3 is the correct option.

Loss is calculated as (Cost Price - Selling Price). The percentage is always calculated based on the Cost Price (C.P.).

Hence, option 1 is the correct option.

Profit or loss is always calculated on the cost price.

Hence, option 2 is the correct option.

Given:

C.P. = ₹ 80

S.P. = ₹ 100

Gain = S.P. - C.P.

Gain = 100 - 80 = ₹ 20

And

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

= $\Big(\frac{20}{80} \times 100\Big)$%

= $\Big(\frac{1}{4} \times 100\Big)$%

= 25%

Hence, option 3 is the correct option.

Given:

S.P. = ₹ 105

Loss = ₹ 15

Loss = C.P. - S.P.

⇒ C.P. = S.P. + Loss

⇒ C.P. = ₹ 105 + ₹ 15 = ₹ 120

And

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

= $\Big(\frac{15}{120} \times 100\Big)$%

= $\Big(\frac{1}{8} \times 100\Big)$%

= $12\frac{1}{2}$%

Hence, option 2 is the correct option.

Given:

S.P. = ₹ 720

Gain = 20%

Then

$$\begin{aligned}\text {C.P.} = \Big( \frac{100}{100 + \text{Gain percentage}} \times \text{S.P.} \Big) \\[1em] = ₹ \Big(\frac{100}{100 + 20} \times 720\Big) \\[1em] = ₹ \Big(\frac{100}{120} \times 720\Big) \\[1em] = ₹ 100 \times 6 \\[1em] = ₹ 600\end{aligned}$$

Hence, option 1 is the correct option.

Given:

C.P. of 15 chairs = S.P. of 20 chairs

Let C.P. of 1 chair = ₹ 1.

Then C.P. of 15 = ₹ 15 = S.P. of 20

S.P. of 1 chair = ₹ $\frac{15}{20}$ = ₹ $\frac{3}{4}$

Loss = C.P. of 1 chair - S.P. of 1 chair

Loss = ₹ 1 - ₹ $\frac{3}{4}$

Loss = ₹ $\frac{1}{4}$

And

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

= $\Big(\frac{1/ 4}{1} \times 100\Big)$%

= $\Big(\frac{1}{4} \times 100\Big)$%

= $\Big(\frac{1}{1} \times 25\Big)$%

= 25%

Hence, option 2 is the correct option.

Given:

C.P. of 15 pens = S.P. of 12 pens

Let C.P. of 1 pen = ₹ 1

Then C.P. of 15 pens = ₹ 15 = S.P. of 12 pens

S.P. of 1 pen = ₹ $\frac{15}{12}$ = ₹ $\frac{5}{4}$

Gain = S.P. of 1 pen - C.P. of 1 pen

Gain = ₹ $\frac{5}{4}$ - ₹ 1

Gain = ₹ $\frac{1}{4}$

And

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

= $\Big(\frac{1/ 4}{1} \times 100\Big)$%

= $\Big(\frac{1}{4} \times 100\Big)$%

= $\Big(\frac{1}{1} \times 25\Big)$%

= 25%

Hence, option 4 is the correct option.

Given:

Initial S.P. = ₹ 465

Initial Loss percentage = 7%

Desired Gain percentage = 7%

First, let us find the Cost Price (C.P.):

We have,

$$\begin{aligned}\text {C.P.} = \Big( \frac{100}{100 - \text{Loss percentage}} \times \text{S.P.} \Big) \\[1em] = ₹ \Big(\frac{100}{100 - 7} \times 465\Big) \\[1em] = ₹ \Big(\frac{100}{93} \times 465\Big) \\[1em] = ₹ \Big(\frac{100}{1} \times 5\Big) \quad \text{[Dividing 465 and 93 by 93]} \\[1em] = ₹ 500\end{aligned}$$

C.P. = ₹ 500

Now, let us find the New Selling Price to gain 7%:

We have:

$$\begin{aligned}\text {S.P.} = \Big( \frac{100 + \text{Gain percentage}}{100} \Big) \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 + 7}{100} \times 500\Big) \\[1em] = ₹ \Big(\frac{107}{100} \times 500\Big) \\[1em] = ₹ \Big(\frac{107}{1} \times 5\Big) \quad \text{[Dividing 500 and 100 by 100]} \\[1em] = ₹ 107 \times 5 \\[1em] = ₹ 535\end{aligned}$$

New S.P. = ₹ 535

Hence, option 4 is the correct option.

Given:

Initial (S.P.) = ₹ 144

Loss = $\frac{1}{7}$ of the Outlay (Outlay means Cost Price)

New Selling Price (New S.P.) = ₹ 189

First, let us find the Cost Price (C.P.):

If the loss is $\frac{1}{7}$ of the C.P., then the Selling Price is what is left after subtracting that fraction.

S.P. = C.P. - Loss

144 = C.P. - $\frac{1}{7}$ C.P

144 = $\frac{7 \text{ C.P.} - \text{ C.P.}}{7}$

144 = $\frac{6}{7}$ C.P.

⇒ C.P. = ₹ $\frac{144 \times 7}{6}$

⇒ C.P. = ₹ 24 x 7

⇒ C.P. = ₹ 168

Now, let us find the Gain Percentage for the New S.P.

New Gain = New S.P. - C.P.

New Gain = ₹ 189 - ₹ 168 = ₹ 21

We have,

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

= $\Big(\frac{21}{168} \times 100\Big)$%

= $\Big(\frac{1}{8} \times 100\Big)$% $\quad$ [Dividing 21 and 168 by 21]

= $\Big(\frac{1}{2} \times 25\Big)$% $\quad$ [Dividing 100 and 8 by 4]

= 12.5%

Hence, option 1 is the correct option.

(i) Net C.P. of an article = Actual C.P. + overhead expenses.

(ii) If S.P. < C.P., then the seller has a loss.

(iii) Profit % or loss % is always calculated on cost price.

(iv) A man spends ₹ 4590 and saves 15% of his income. His income is ₹ 5400.

(v) Ayush sold his scooter for ₹ 38400 and lost 20%. He had bought the scooter for ₹ 48000.

Explanation

(i) Any extra money spent on repairs, transportation, or labor after buying an item is added to the original price to find the total (Net) Cost Price.

(ii) When the amount you receive from a sale is less than the amount you originally paid, you have lost money.

(iii) The C.P. is your "starting point" or original investment. We measure our gain or loss against what we first spent.

(iv)

Given:

Amount spent (Expenditure) = ₹ 4590

Percentage saved (Savings %) = 15%

Total Income is always 100%. If the man saves 15%, the rest of his income is spent.

Expenditure % = 100% - 15% = 85%

Let the total income be x. Since ₹ 4590 represents 85% of his income:

85% of x = ₹ 4590

$$\begin{aligned}\Rightarrow ₹ \frac{85}{100} \times \text x = 4590 \\[1em] \Rightarrow \text x = ₹ \Big(\frac{4590 \times 100}{85}\Big) \\[1em] \Rightarrow \text x = ₹ \Big(\frac{4590 \times 100}{85}\Big) \\[1em] \Rightarrow \text x = ₹ 54 \times 100 \quad \text{[Dividing 4590 and 85 by 85]} \\[1em] \Rightarrow \text x = ₹ 5400\end{aligned}$$

∴ Total income = ₹ 5400

(v)

Given:

Selling Price (S.P.) = ₹ 38400

Loss percentage = 20%

The Cost Price (C.P.) is the original 100%. Because he sold it at a loss, the Selling Price is less than 100%.

S.P.% = 100% - 20% = 80%

This means ₹ 38,400 is exactly 80% of what he originally paid.

Let the Cost Price be x

80% of x = ₹ 38400

$$\begin{aligned}\Rightarrow \frac{80}{100} \times \text x = 38400 \\[1em] \Rightarrow \text x = \frac{38400 \times 100}{80} \\[1em] \Rightarrow \text x = 480 \times 100 \quad \text{[Dividing 38400 and 80 by 80]} \\[1em] \Rightarrow \text x = ₹ 48,000\end{aligned}$$

He had bought the scooter for ₹ 48,000.

(i) True
Reason — The Cost Price (C.P.) is the "starting line" or original investment. All gains or losses are measured against what we originally spent.

(ii) False
Reason — Overhead expenses (like repairs or transport) are added to the actual C.P., not subtracted. The correct formula is:

Net C.P. = Actual C.P. + Overhead expenses

(iii) False
Reason — If the Cost Price is greater than the Selling Price, you have spent more than you earned, which results in a Loss. A gain only happens when S.P. > C.P.

(iv) True
Reason — Since Loss = (C.P. - S.P.),

Loss % = $\Big(\frac{C.P. - S.P.}{C.P.} \times 100\Big)$% correctly calculates the loss as a part of the original Cost Price.

(v) True
Reason — $\text{S.P.}. = \Big(\frac{100 - \text{Loss percentage}}{100}\Big) \times C.P.$

This formula correctly finds the remaining percentage of the C.P. after a loss.

For example, a 10% loss means the S.P. is 90% of the C.P.

(vi) True
Reason — $\text{C.P.} = \frac{100}{100 + \text{Gain percentage}} \times S.P.$

This is the correct standard formula to "reverse-calculate" the original Cost Price when you know the Selling Price and the Gain Percentage.

(1)

Given:

Purchase rate (C.P.) : 8 pears for ₹ 75

Desired Gain: 20%

Total Selling Price (S.P.): ₹ 90

C.P. of 1 pear = ₹ $\frac{75}{8}$

Let us find the required S.P. of 1 pear to gain 20%:

$$\begin{aligned}\text {S.P.} = \Big( \frac{100 + \text{Gain percentage}}{100} \Big) \times \text{C.P.} \\[1em] = ₹ \Big( \frac{100 + 20}{100} \Big) \times \frac{75}{8} \\[1em] = ₹ \Big( \frac{120}{100} \times \frac{75}{8}\Big) \\[1em] = ₹ \Big( \frac{15}{100} \times \frac{75}{1}\Big) \\[1em] = ₹ \Big( \frac{15}{4} \times \frac{3}{1}\Big) \\[1em] = ₹ \Big( \frac{45}{4}\Big) \\[1em] = ₹ 11.25\end{aligned}$$

S.P. of 1 pear = ₹ 11.25

Now, let us calculate how many pears to sell for ₹ 90:

Number of pears = $\frac{\text{Total S.P.}}{\text{S.P. of 1}}$

Number of pears = $\frac{90}{11.25} = 8$

Hence, option 3 is the correct option.

(2)

Given:

Wholesale C.P. (for everyone): 8 pears for ₹ 75

Ghanshyam’s S.P. rate : 9 pears for ₹ 90

⇒ S.P. of 1 pear = ₹ $\frac{90}{9} = ₹ 10$

C.P. of 1 pear = ₹ $\frac{75}{8} = ₹ 9.375 \quad \text{[From previous step]}$

Gain per pear = S.P. - C.P.

Gain per pear = ₹ 10 - ₹ 9.375 = ₹ 0.625

And

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

= $\Big(\frac{0.625}{9.375} \times 100\Big)$%

= $\Big(\frac{1}{15} \times 100\Big)$% $\quad$ [Dividing 0.625 and 9.375 by 0.625]

= $\Big(\frac{1}{3} \times 20\Big)$% $\quad$ [Dividing 100 and 15 by 5]

= $6\frac{2}{3}$%

Hence, option 1 is the correct option.

(3)

Given:

C.P. of 8 pears = ₹ 75

S.P. of 8 pears = ₹ 90

Gain = S.P. - C.P.

Gain = ₹ 90 - ₹ 75 = ₹ 15

And

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

= $\Big(\frac{15}{75} \times 100\Big)$%

= $\Big(\frac{1}{5} \times 100\Big)$% $\quad$ [Dividing 15 and 75 by 15]

= $\Big(\frac{1}{1} \times 20\Big)$% $\quad$ [Dividing 100 and 5 by 5]

= 20%

Hence, option 3 is the correct option.

(4)

Given:

Total pears = 120

Rotten pears = 24

Wholesale (C.P.) : 8 for ₹ 75

⇒ C.P. of 1 pear = ₹ $\frac{75}{8}$

Selling rate : 8 for ₹ 90

⇒ S.P. of 1 pear = ₹ $\frac{90}{8}$

Let us find Total C.P. of 120 pears:

Total C.P. = (C.P. of 1 pear) x (Total number of pears)

Total C.P. = $\frac{75}{8} \times 120$

Total C.P. = 75 x 15 = ₹ 1125

Now, let us find Total S.P. of remaining pears:

Remaining pears = 120 - 24 = 96

Total S.P. = (S.P. of 1 pear) x (Remaining pears)

Total S.P. = $\frac{90}{8} \times 96$

Total S.P. = 90 x 12 = ₹ 1080

Since C.P. > S.P., there is a loss.

Loss = C.P. - S.P.

Loss = ₹ 1125 - ₹ 1080 = ₹ 45

And

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

= $\Big(\frac{45}{1125} \times 100\Big)$%

= $\Big(\frac{1}{25} \times 100\Big)$% $\quad$ [Dividing 45 and 1125 by 45]

= $\Big(\frac{1}{1} \times 4\Big)$% $\quad$ [Dividing 100 and 25 by 25]

= 4%

Hence, option 2 is the correct option.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Explanation

Given:

S.P. = ₹3320,

Gain = ₹320

Find C.P. first:

C.P. = S.P. - Gain

C.P. = 3320 - 320 = ₹ 3000

Calculate target S.P. for 10% gain:

110% of 3000 = $\frac{110}{100} \times 3000 = ₹ 3300$

The Assertion matches the calculation. So, it is True.

Reason:

S.P. = $\frac{(100 + \text{gain percentage})}{100} \times \text{C.P.}$

This is the correct formula and explains how we got ₹3300.

Hence, option 1 is the correct option.

Assertion (A) is true but Reason (R) is false.

Explanation

Given:

Total C.P. of onions = 20 x 50 = ₹ 1000

S.P. of remaining onion = ₹ 60 per kg

Remaining onions = 20 - 5% of 20

$$\begin{aligned}= 20 - \Big(\frac{5}{100} \times 20\Big)\text{ kg} \\[1em] = 20 - \Big(\frac{1}{20} \times 20\Big) \text{ kg} \\[1em] = 20 - \Big(\frac{1}{1} \times 1\Big) \text{ kg} \\[1em] = 20 - 1 \text{ kg} \\[1em] = 19\text{ kg} \\[1em]\end{aligned}$$

Remaining onions = 19 kg

Total S.P. = (Remaining onions) x (S.P.)

Total S.P. = 19 x 60 = ₹ 1140

Gain = S.P. - C.P.

Gain = 1140 - 1000 = ₹ 140

And

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

= $\Big(\frac{140}{1000} \times 100\Big)$%

= $\Big(\frac{140}{10} \times 1\Big)$%

= 14%

The Assertion is correct. So, it is True.

Reason:

Gain% = $\frac{\text{CP}}{\text{gain}}\times 100$%

This is incorrect. Correct formula is:

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

Hence, option 3 is the correct option.

Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

Explanation

If loss is 10%, then S.P. is 90% of C.P.

90% of C.P. = ₹ 1440

$\frac{90}{100} \times \text{C.P.} = ₹ 1440$

⇒ C.P. = $\frac{1440 \times 100}{90}$

⇒ C.P. = $\frac{16 \times 100}{1}$

⇒ C.P. = 16 x 100

⇒ C.P. = ₹ 1600

The Assertion is correct. So, it is true.

Reason:

Profit or loss percentage are always calculated on CP.

This is the fundamental rule of Profit and Loss. Reason is True.

While the Reason is a true statement, it doesn't explain the calculation (the formula) used to arrive at ₹ 1600.

Hence, option 2 is the correct option.

Given:

C.P. of 11 oranges = ₹ 10

C.P. of 1 orange = ₹ $\frac{10}{11}$

S.P. of 10 oranges = ₹ 11

S.P. of 1 orange = ₹ $\frac{11}{10}$

L.C.M. of 11 and 10 = 110, so let him buy 110 oranges.

C.P. of 110 oranges = ₹ $\frac{10}{11} \times 110 = ₹ 100$

S.P. of 110 oranges = ₹ $\frac{11}{10} \times 110 = ₹ 121$

Since S.P. > C.P., it is a gain.

Gain = S.P. - C.P.

Gain = ₹ 121 - ₹ 100 = ₹ 21

And

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

= $\Big(\frac{21}{100} \times 100\Big)$%

= 21%

Hence, option 3 is the correct option.

Given:

C.P. of 400 textbooks = ₹ 18000

C.P. of 1 textbook = ₹ $\frac{18000}{400} = ₹ 45$

For the bookseller to get 40 books free, his profit must be equal to the cost price of 40 books.

Profit = C.P. of 40 books

Profit = 40 × 45 = ₹ 1800

And

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

= $\Big(\frac{1800}{18000} \times 100\Big)$%

= $\Big(\frac{1800}{180} \times 1\Big)$% $\quad$ [Dividing 100 and 18000 by 100]

= $\Big(\frac{10}{1} \times 1\Big)$% $\quad$ [Dividing 1800 and 180 by 180]

= 10%

Hence, option 1 is the correct option.

Given:

S.P. of each goat = ₹ 4000

Total S.P. = ₹ 4000 + ₹ 4000 = ₹ 8000

Since there is neither loss nor gain on the whole transaction,

Total C.P. = Total S.P. = ₹ 8000

For first goat (sold at 25% gain) :

$$\begin{aligned}\text {C.P.}_1 = \Big( \frac{100}{100 + \text{Gain percentage}} \times \text{S.P.} \Big) \\[1em] = ₹ \Big(\frac{100}{100 + 25} \times 4000\Big) \\[1em] = ₹ \Big(\frac{100}{125} \times 4000\Big) \\[1em] = ₹ \Big(\frac{4}{5} \times 4000\Big) \quad \text{[Dividing 100 and 125 by 25]} \\[1em] = ₹ \Big(\frac{4}{1} \times 800\Big) \quad \text{[Dividing 4000 and 5 by 5]} \\[1em] = ₹ 3200\end{aligned}$$

C.P.₁ = ₹ 3200

For second goat :

C.P.₂ = Total C.P. - C.P.₁

C.P.₂ = ₹ 8000 - ₹ 3200 = ₹ 4800

S.P.₂ = ₹ 4000

Since C.P.₂ > S.P.₂, there is a loss on the second goat.

Loss = C.P.₂ - S.P.₂

Loss = ₹ 4800 - ₹ 4000 = ₹ 800

And

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

= $\Big(\frac{800}{4800} \times 100\Big)$%

= $\Big(\frac{1}{6} \times 100\Big)$% $\quad$ [Dividing 800 and 4800 by 800]

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

= $\frac{50}{3}$%

= $16\frac{2}{3}$%

Hence, option 2 is the correct option.

Given:

C.P. of 80 pears = ₹ 40

Spoiled pears = 25

Profit percentage = 10%

Remaining pears = 80 - 25 = 55

Let us find the Total S.P. of remaining pears:

$$\begin{aligned}\text {Total S.P.} = \Big( \frac{100 + \text{Gain percentage}}{100} \Big) \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 + 10}{100} \times 40\Big) \\[1em] = ₹ \Big(\frac{110}{100} \times 40\Big) \\[1em] = ₹ \Big(\frac{11}{10} \times 40\Big) \quad \text{[Dividing 110 and 100 by 10]} \\[1em] = ₹ \Big(\frac{11}{1} \times 4\Big) \quad \text{[Dividing 40 and 10 by 10]} \\[1em] = ₹ 44\end{aligned}$$

Total S.P. of 55 pears = ₹ 44

S.P. of 1 pear = $\frac{\text{Total S.P.}}{\text{Number of pears}}$

S.P. of 1 pear = ₹ $\frac{44}{55} = ₹ \frac{4}{5} = ₹ 0.80$

Hence, option 2 is the correct option.

We will use the formula:

$\text {S.P.} = \Big( \frac{100 + \text{Gain percentage}}{100} \Big) \times \text{C.P.}$ for profit

$\text {S.P.} = \Big( \frac{100 - \text{Loss percentage}}{100} \Big) \times \text{C.P.}$ for loss

Option 1 (Book) : C.P. = ₹ 80, Profit = 20%

$$\begin{aligned}\text {S.P.} = \Big( \frac{100 + 20}{100} \times 80 \Big) \\[1em] = ₹ \Big(\frac{120}{100} \times 80\Big) \\[1em] = ₹ \Big(\frac{6}{5} \times 80\Big) \quad \text{[Dividing 120 and 100 by 20]} \\[1em] = ₹ \Big(\frac{6}{1} \times 16\Big) \quad \text{[Dividing 80 and 5 by 5]} \\[1em] = ₹ 96\end{aligned}$$

This matches the given S.P. of ₹ 96. So, the match is correct.

Option 2 (Table) : C.P. = ₹ 8000, Loss = $12\frac{1}{2}$% = $\frac{25}{2}$%

$$\begin{aligned}\text {S.P.} = \Big( \frac{100 - 25/2}{100} \times 8000 \Big) \\[1em] = ₹ \Big(\frac{175/2}{100} \times 8000\Big) \\[1em] = ₹ \Big(\frac{175}{200} \times 8000\Big) \\[1em] = ₹ \Big(\frac{175}{1} \times 40\Big) \quad \text{[Dividing 8000 and 200 by 200]} \\[1em] = ₹ 7000\end{aligned}$$

This matches the given S.P. of ₹ 7000. So, the match is correct.

Option 3 (Watch) : C.P. = ₹ 7812, Loss = 13%

$$\begin{aligned}\text {S.P.} = \Big( \frac{100 - 13}{100} \times 7812 \Big) \\[1em] = ₹ \Big(\frac{87}{100} \times 7812\Big) \\[1em] = ₹ \frac{679644}{100} \\[1em] = ₹ 6796.44\end{aligned}$$

This does not match the given S.P. of ₹ 6786. So, the match is incorrect.

Option 4 (Bat) : C.P. = ₹ 1400, Profit = 9%

$$\begin{aligned}\text {S.P.} = \Big( \frac{100 + 9}{100} \times 1400 \Big) \\[1em] = ₹ \Big(\frac{109}{100} \times 1400\Big) \\[1em] = ₹ \Big(\frac{109}{1} \times 14\Big) \quad \text{[Dividing 1400 and 100 by 100]} \\[1em] = ₹ 1526\end{aligned}$$

This matches the given S.P. of ₹ 1526. So, the match is correct.

Hence, option 3 is the correct option.

For Garima :

C.P. = ₹ 60

S.P. = ₹ 84

Gain = S.P. - C.P.

Gain = ₹ 84 - ₹ 60 = ₹ 24

And

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

= $\Big(\frac{24}{60} \times 100\Big)$%

= $\Big(\frac{2}{5} \times 100\Big)$% $\quad$ [Dividing 24 and 60 by 12]

= $\Big(\frac{2}{1} \times 20\Big)$% $\quad$ [Dividing 100 and 5 by 5]

= 40%

Garima's Gain % = 40%

For Kajal :

C.P. = ₹ 90

S.P. = ₹ 150

Gain = S.P. - C.P.

Gain = ₹ 150 - ₹ 90 = ₹ 60

And

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

= $\Big(\frac{60}{90} \times 100\Big)$%

= $\Big(\frac{2}{3} \times 100\Big)$% $\quad$ [Dividing 60 and 90 by 30]

= $\frac{200}{3}$%

= $66\frac{2}{3}$%

Kajal's Gain % = $66\frac{2}{3}$% ≈ 66.6%

Since 66.6% > 40%, Kajal's profit per cent is more.

Difference = $66\frac{2}{3}$% - 40%

Difference = $\frac{200}{3}$% - 40%

Difference = $\frac{200 - 120}{3}$%

Difference = $\frac{80}{3}$% = $26\frac{2}{3}$% ≈ 26.6%

Hence, option 3 is the correct option.

Given:

Initial S.P. = ₹ 12000

Initial Loss percentage = 4%

Desired Gain percentage = 10%

Let us find the Cost Price (C.P.):

We have the formula,

$$\begin{aligned}\text {C.P.} = \Big( \frac{100}{100 - \text{Loss percentage}} \times \text{S.P.} \Big) \\[1em] = ₹ \Big(\frac{100}{100 - 4} \times 12000\Big) \\[1em] = ₹ \Big(\frac{100}{96} \times 12000\Big) \\[1em] = ₹ \Big(\frac{25}{24} \times 12000\Big) \quad \text{[Dividing 100 and 96 by 4]} \\[1em] = ₹ \Big(\frac{25}{1} \times 500\Big) \quad \text{[Dividing 12000 and 24 by 24]} \\[1em] = ₹ 12500\end{aligned}$$

C.P. = ₹ 12500

Now, let us find the New Selling Price for 10% Gain:

We have the formula,

$$\begin{aligned}\text {S.P.} = \Big( \frac{100 + \text{Gain percentage}}{100} \Big) \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 + 10}{100} \times 12500\Big) \\[1em] = ₹ \Big(\frac{110}{100} \times 12500\Big) \\[1em] = ₹ \Big(\frac{110}{1} \times 125\Big) \quad \text{[Dividing 12500 and 100 by 100]} \\[1em] = ₹ 110 \times 125 \\[1em] = ₹ 13750\end{aligned}$$

Hence, option 3 is the correct option.

Given:

Loss on selling 48 apples = S.P. of 6 apples

Let the S.P. of 1 apple = ₹ s and C.P. of 1 apple = ₹ c.

S.P. of 48 apples = 48s

C.P. of 48 apples = 48c

Loss = C.P. - S.P.

Loss = 48c - 48s

Also, Loss = S.P. of 6 apples = 6s

Equating both:

48 c - 48s = 6s

⇒ 48 c = 48s + 6s

⇒ 48 c = 54s

⇒ c = $\frac{54s}{48} = \frac{9s}{8}$

Loss per apple = c - s = $\frac{9s}{8} - s = \frac{9s - 8s}{8} = \frac{s}{8}$

And

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

= $\Big(\frac{s/8}{9s/8} \times 100\Big)$%

= $\Big(\frac{s}{8} \times \frac{8}{9s} \times 100\Big)$%

= $\Big(\frac{1}{9} \times 100\Big)$%

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

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

Hence, option 4 is the correct option.

Given:

Final Selling Price = ₹ 594

Manufacturer's profit = 25%

Agency's profit = 10%

Shopkeeper's profit = 20%

Let the manufacturing price (C.P. of manufacturer) = ₹ x

Step 1 : Manufacturer to Agency (25% profit) :

$$\begin{aligned}\text {S.P. of manufacturer} = \Big( \frac{100 + 25}{100} \Big) \times x \\[1em] = \frac{125}{100} \times x \\[1em] = \frac{5x}{4}\end{aligned}$$

So, Agency's C.P. = ₹ $\frac{5x}{4}$

Step 2 : Agency to Shopkeeper (10% profit) :

$$\begin{aligned}\text {S.P. of agency} = \Big( \frac{100 + 10}{100} \Big) \times \frac{5x}{4} \\[1em] = \frac{110}{100} \times \frac{5x}{4} \\[1em] = \frac{11}{10} \times \frac{5x}{4} \\[1em] = \frac{11x}{8}\end{aligned}$$

So, Shopkeeper's C.P. = ₹ $\frac{11x}{8}$

Step 3 : Shopkeeper to Customer (20% profit) :

$$\begin{aligned}\text {S.P. of shopkeeper} = \Big( \frac{100 + 20}{100} \Big) \times \frac{11x}{8} \\[1em] = \frac{120}{100} \times \frac{11x}{8} \\[1em] = \frac{6}{5} \times \frac{11x}{8} \\[1em] = \frac{66x}{40} \\[1em] = \frac{33x}{20}\end{aligned}$$

Final S.P. = ₹ $\frac{33x}{20}$

According to the question, Final S.P. = ₹ 594

$$\begin{aligned}\frac{33x}{20} = 594 \\[1em] \Rightarrow 33x = 594 \times 20 \\[1em] \Rightarrow x = \frac{594 \times 20}{33} \\[1em] \Rightarrow x = 18 \times 20 \quad \text{[Dividing 594 and 33 by 33]} \\[1em] \Rightarrow x = 360\end{aligned}$$

∴ Manufacturing price = ₹ 360

Hence, option 1 is the correct option.

Given:

Initial S.P. = ₹ 720

Initial Loss percentage = 25%

Desired Gain percentage = 25%

Let us find the Cost Price (C.P.):

We have the formula,

$$\begin{aligned}\text {C.P.} = \Big( \frac{100}{100 - \text{Loss percentage}} \times \text{S.P.} \Big) \\[1em] = ₹ \Big(\frac{100}{100 - 25} \times 720\Big) \\[1em] = ₹ \Big(\frac{100}{75} \times 720\Big) \\[1em] = ₹ \Big(\frac{4}{3} \times 720\Big) \quad \text{[Dividing 100 and 75 by 25]} \\[1em] = ₹ \Big(\frac{4}{1} \times 240\Big) \quad \text{[Dividing 720 and 3 by 3]} \\[1em] = ₹ 960\end{aligned}$$

C.P. = ₹ 960

Now, let us find the New Selling Price for 25% Gain:

We have the formula,

$$\begin{aligned}\text {S.P.} = \Big( \frac{100 + \text{Gain percentage}}{100} \Big) \times \text{C.P.} \\[1em] = ₹ \Big(\frac{100 + 25}{100} \times 960\Big) \\[1em] = ₹ \Big(\frac{125}{100} \times 960\Big) \\[1em] = ₹ \Big(\frac{5}{4} \times 960\Big) \quad \text{[Dividing 125 and 100 by 25]} \\[1em] = ₹ \Big(\frac{5}{1} \times 240\Big) \quad \text{[Dividing 960 and 4 by 4]} \\[1em] = ₹ 1200\end{aligned}$$

Hence, option 4 is the correct option.