Profit and Loss

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

$\text {Gain}$

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

$\text {Gain}$

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

$\text {Loss}$

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

$\text {Gain}$

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

$\text {Loss}$

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

$\text {Gain}$

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

$\text {Loss}$

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

$\text {Gain}$

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

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

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

$\text {Gain}$

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

$\text {Loss}$

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,

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

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,

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

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,

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

C.P. = ₹ 12000

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

We have the formula:

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

∴ 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,

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

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

$\text {Gain}$

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,

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

C.P. = ₹ 5000

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

We have the formula,

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

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) :

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

C.P.₁ = ₹ 18000

For second scooter (10% loss) :

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

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,

$\text {Loss}$

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:

$\text {S.P.}_\text A ​= ₹ 650 + 20$

∴ 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 :

$\text {S.P.}_\text B ​= ₹ 780 - 20$

∴ S.P._B ​= ₹ 624

Hence, C pays ₹ 624 for the article.

There is a gain if

1. C.P. > S.P.
2. C.P. = S.P.
3. C.P. < S.P.
4. C.P. + S.P. = 0

Answer

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

Hence, option 3 is the correct option.

Loss % is equal to

1. $\Big(\dfrac{C.P. - S.P.}{C.P.} \times 100\Big)$%

2. $\Big(\dfrac{S.P. - C.P.}{C.P.} \times 100\Big)$%

3. $\Big(\dfrac{C.P. - S.P.}{S.P.} \times 100\Big)$%

4. $\Big(\dfrac{S.P. - C.P.}{S.P.} \times 100\Big)$%

Answer

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.

Gain or loss is always reckoned on

1. S.P.
2. C.P.
3. S.P. - C.P.
4. S.P. + C.P.

Answer

Profit or loss is always calculated on the cost price.

Hence, option 2 is the correct option.

A book is bought for ₹80 and sold for ₹100 by a vendor. His gain per cent is

1. 20%

2. $22\dfrac{1}{2}$%

3. 25%

4. $33\dfrac{1}{3}$%

Answer

Given:

C.P. = ₹ 80

S.P. = ₹ 100

Gain = S.P. - C.P.

Gain = 100 - 80 = ₹ 20

And

$\text {Gain}$

Hence, option 3 is the correct option.

On selling a chocolate for ₹105, the shopkeeper loses ₹15. His loss per cent is

1. 10%

2. $12\dfrac{1}{2}$%

3. 15%

4. $14\dfrac{2}{7}$%

Answer

Given:

S.P. = ₹ 105

Loss = ₹ 15

Loss = C.P. - S.P.

⇒ C.P. = S.P. + Loss

⇒ C.P. = ₹ 105 + ₹ 15 = ₹ 120

And

$\text {Loss}$

Hence, option 2 is the correct option.

On selling a pair of shoes for ₹720, the shopkeeper gains 20%. The cost price of the shoes, is

1. ₹ 600
2. ₹ 640
3. ₹ 650
4. ₹ 690

Answer

Given:

S.P. = ₹ 720

Gain = 20%

Then

$\text {C.P.} = \Big( \dfrac{100}{100 + \text{Gain }\%} \times \text{S.P.} \Big) \\[1em] = ₹ \Big(\dfrac{100}{100 + 20} \times 720\Big) \\[1em] = ₹ \Big(\dfrac{100}{120} \times 720\Big) \\[1em] = ₹ 100 \times 6 \\[1em] = ₹ 600$

Hence, option 1 is the correct option.

If the cost price of 15 chairs be equal to the selling price of 20 chairs, the loss per cent is

1. 20%
2. 25%
3. 35%
4. 37.5%

Answer

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 = ₹ $\dfrac{15}{20}$ = ₹ $\dfrac{3}{4}$

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

Loss = ₹ 1 - ₹ $\dfrac{3}{4}$

Loss = ₹ $\dfrac{1}{4}$

And

$\text {Loss}$

Hence, option 2 is the correct option.

If the cost price of 15 pens is equal to the selling price of 12 pens, the gain per cent is

1. $12\dfrac{1}{2}$%

2. 15%

3. 20%

4. 25%

Answer

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 = ₹ $\dfrac{15}{12}$ = ₹ $\dfrac{5}{4}$

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

Gain = ₹ $\dfrac{5}{4}$ - ₹ 1

Gain = ₹ $\dfrac{1}{4}$

And

$\text {Gain}$

Hence, option 4 is the correct option.

By selling a bag for ₹465, a man loses 7%. To gain 7%, it must be sold for

1. ₹ 511
2. ₹ 525
3. ₹ 531
4. ₹ 535

Answer

Given:

Initial S.P. = ₹ 465

Initial Loss percentage = 7%

Desired Gain percentage = 7%

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

We have,

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

C.P. = ₹ 500

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

We have:

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

New S.P. = ₹ 535

Hence, option 4 is the correct option.

On selling a photo frame for ₹ 144, shopkeeper loses $\dfrac{1}{7}$ of his outlay. If it is sold for ₹ 189, the gain per cent will be

1. 12.5%
2. 25%
3. 30%
4. 36%

Answer

Given:

Initial (S.P.) = ₹ 144

Loss = $\dfrac{1}{7}$ 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 $\dfrac{1}{7}$ of the C.P., then the Selling Price is what is left after subtracting that fraction.

S.P. = C.P. - Loss

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

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

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

⇒ C.P. = ₹ $\dfrac{144 \times 7}{6}$

⇒ 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,

$\text {Gain}$

Hence, option 1 is the correct option.

Fill in the blanks :

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

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

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

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

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

Answer

(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:

$85$

∴ 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

$80$

He had bought the scooter for ₹ 48,000.

Write true (T) or false (F) :

(i) Profit % is always calculated on the cost price.

(ii) Net C.P. of an article = Actual C.P. - Overhead expenses.

(iii) There is a gain if C.P. > S.P.

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

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

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

Answer

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

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

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 — $\text{C.P.} = \dfrac{100}{100 + \text{Gain}\%} \times S.P.$

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

Birju is a fruitseller. Today he bought pears to sell. He purchased them at the rate of 8 for ₹ 75 from the wholesale market.

(1) How many pears should he sell for ₹ 90 if he wishes to gain 20% ?

1. 6
2. 7
3. 8
4. 9

(2) He found that another fruitseller Ghanshyam was selling pears at 9 for ₹ 90. Find the gain per cent of Ghanshyam. (Assume that the wholesale rate is the same for all fruitsellers.)

1. $6\dfrac{2}{3}$%

2. $7\dfrac{1}{2}$%

3. $8\dfrac{1}{3}$%

4. $9\dfrac{3}{3}$%

(3) He decides to sell pears at the rate of 8 for ₹ 90. Find his gain per cent :

1. 15%

2. $17\dfrac{1}{2}$%

3. 20%

4. $22\dfrac{1}{2}$%

(4) In a box of 120 pears, he found that 24 were rotten and he had to throw them away. He sold the remaining pears at 8 for ₹ 90. Find his gain or less per cent on this box :

1. 2%, gain
2. 4%, loss
3. 6%, gain
4. 8%, loss

Answer

(1)

Given:

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

Desired Gain: 20%

Total Selling Price (S.P.): ₹ 90

C.P. of 1 pear = ₹ $\dfrac{75}{8}$

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

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

S.P. of 1 pear = ₹ 11.25

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

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

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

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 = ₹ $\dfrac{90}{9} = ₹ 10$

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

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

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

And

$\text {Gain}$

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

$\text {Gain}$

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 = ₹ $\dfrac{75}{8}$

Selling rate : 8 for ₹ 90

⇒ S.P. of 1 pear = ₹ $\dfrac{90}{8}$

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. = $\dfrac{75}{8} \times 120$

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. = $\dfrac{90}{8} \times 96$

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

$\text {Loss}$

Hence, option 2 is the correct option.

Assertion: A shopkeeper sold a coat for ₹3320 at a gain of ₹320. For earning a gain of 10%, he should have sold the coat for ₹3300.

Reason: SP = $\dfrac{(100 + \text{gain\%})}{100} \times CP$.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. Assertion (A) is true but Reason (R) is false.
4. Assertion (A) is false but Reason (R) is true.

Answer

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 = $\dfrac{110}{100} \times 3000 = ₹ 3300$

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

Reason:

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

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

Hence, option 1 is the correct option.

Assertion: A fruit seller purchased 20 kg onions at ₹ 50 per kg. Out of these, 5% of the onions were found to be rotten. If he sells the remaining onions at ₹ 60 per kg, then his profit is 14%.

Reason: Gain% = $\dfrac{\text{CP}}{\text{gain}}\times 100$.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. Assertion (A) is true but Reason (R) is false.
4. Assertion (A) is false but Reason (R) is true.

Answer

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

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

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

$\text {Gain}$

The Assertion is correct. So, it is True.

Reason:

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

This is incorrect. Correct formula is:

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

Hence, option 3 is the correct option.

Assertion: By selling a chair for ₹ 1440, a shopkeeper loses 10%. The CP of the chair was ₹ 1600.

Reason: Profit or loss percentage are always calculated on CP.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. Assertion (A) is true but Reason (R) is false.
4. Assertion (A) is false but Reason (R) is true.

Answer

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

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

⇒ C.P. = $\dfrac{1440 \times 100}{90}$

⇒ C.P. = $\dfrac{16 \times 100}{1}$

⇒ 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.