Profit & Loss - Exercise 10(A)

Amit bought a calculator for ₹ 960 and sold it for ₹ 1104. Find his gain and gain per cent.

Answer

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

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

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

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

= 15%

Gain = ₹ 144, Gain % = 15%

Ankita bought a mobile phone for ₹ 2350 and sold it for ₹ 2538. Find her gain and gain per cent.

Answer

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

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

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

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

= 8%

Gain = ₹ 188, Gain % = 8%

Ayush bought a bicycle for ₹ 6250 and had to sell it for ₹ 5875. Find his loss and loss per cent.

Answer

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

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

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

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

= 6%

Loss = ₹ 375, Loss % = 6%

Aman bought a computer for ₹ 24000 and its accessories pack worth for ₹ 1750. He sold it all for ₹ 26780. Find his gain and gain per cent.

Answer

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

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

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

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

= 4%

Gain = ₹ 1030, Gain % = 4%

A man bought a refrigerator for ₹ 35615 and paid ₹ 125 on its transportation. He sold it for ₹ 33953. Find his gain or loss per cent.

Answer

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

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

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

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

= 5%

Loss % = 5%

By selling a bicycle for ₹ 5670 a trader gains ₹ 270. Find his gain per cent.

Answer

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

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

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

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

= 5%

Gain % = 5%

By selling a chair for ₹ 1410 a carpenter suffers a loss of ₹ 90. Find his loss per cent.

Answer

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

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

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

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

= 6%

Loss % = 6%

A fruit-seller bought bananas at the rate of 3 for ₹ 8 and sold them at the rate of 2 for ₹ 7. Find his gain or loss per cent.

Answer

Given:

C.P. → 3 bananas = ₹ 8

C.P. of 1 banana = ₹ $\dfrac{8}{3}$

S.P. → 2 bananas = ₹ 7

S.P. of 1 banana = ₹ $\dfrac{7}{2}$

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

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

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

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

Gain = S.P. - C.P.

Gain = ₹ 21 - ₹ 16 = ₹ 5

And

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

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

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

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

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

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

Lemons are bought at the rate of 3 for ₹ 4. At what rate must they be sold to gain 20%?

Answer

Given:

C.P. of 3 lemons = ₹ 4

C.P. of 1 lemon = ₹ $\dfrac{4}{3}$

Gain % = 20%

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

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

S.P. of 1 lemon = ₹ $\dfrac{8}{5}$

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

Rate = 5 for ₹ 8

The selling price of 12 pens is equal to the cost price of 14 pens. Find the gain per cent.

Answer

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

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

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

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

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

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

The cost price of 12 oranges is equal to the selling price of 15 oranges. Find the loss per cent.

Answer

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

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

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

= 20%

Loss % = 20%

Vinay sold a plot of land for ₹ 143000, gaining 4%. For how much did he purchase the plot?

Answer

Given:

S.P. of plot of land = ₹ 143000

Gain percentage = 4%

C.P. = ?

We have the formula,

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

Hence, Vinay purchased the plot for ₹ 137500.

John sold his T.V. set for ₹ 14100, losing 6%. For how much did he purchase it?

Answer

Given:

S.P. of the T.V. = ₹ 14100

Loss percentage = 6%

C.P. = ?

We have the formula,

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

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

On selling a bed for ₹ 10800, a carpenter loses 10%. For what amount should he sell it to gain 5%?

Answer

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,

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

C.P. = ₹ 12000

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

We have the formula:

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

∴ New S.P. = ₹ 12600

Hence, he should sell the bed for ₹ 12600.

On selling an almirah for ₹ 20350, a man gains 10%. What per cent does he gain on selling the same for ₹ 19610?

Answer

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,

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

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

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

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

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

= 6%

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

On selling a fan for ₹ 4700, a shopkeeper loses 6%. At what price must he sell it to gain 6%?

Answer

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,

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

C.P. = ₹ 5000

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

We have the formula,

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

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

Kamal sold two scooters for ₹ 19800 each, gaining 10% on the one and losing 10% on the other. Find his gain or loss per cent on the whole transaction.

Answer

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) :

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

C.P.₁ = ₹ 18000

For second scooter (10% loss) :

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

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

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

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

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

= 1%

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

A buys an article for ₹ 650 and sells it to B at a profit of 20%. B sells it to C at a loss of 20%. What does C pay for it?

Answer

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:

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

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

∴ 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 :

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

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

∴ S.P._B ​= ₹ 624

Hence, C pays ₹ 624 for the article.