Profit & Loss - Exercise 10(B)

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

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

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

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

= 25%

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

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

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

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

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

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

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

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

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

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

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

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

= 25%

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

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

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

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

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

= 25%

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,

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

C.P. = ₹ 500

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

We have:

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

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,

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

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

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

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

= 12.5%

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% of x = ₹ 4590

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

∴ 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

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

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

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

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

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

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

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

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%:

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

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

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

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

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

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

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

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

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

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

= $\Big(\dfrac{1}{1} \times 20\Big)$% $\quad$ [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 = ₹ $\dfrac{75}{8}$

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

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

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

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

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

= 4%

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 = $\dfrac{(100 + \text{gain percentage})}{100} \times CP$.

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

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

Hence, option 1 is the correct option.

Assertion: A 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

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

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

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

= 14%

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.

11 oranges are bought for ₹ 10 and 10 oranges are sold for ₹ 11. The gain/loss per cent is:

1. 21% loss
2. 11% gain
3. 21% gain
4. 11% loss

Answer

Given:

C.P. of 11 oranges = ₹ 10

C.P. of 1 orange = ₹ $\dfrac{10}{11}$

S.P. of 10 oranges = ₹ 11

S.P. of 1 orange = ₹ $\dfrac{11}{10}$

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

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

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

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

Gain = S.P. - C.P.

Gain = ₹ 121 - ₹ 100 = ₹ 21

And

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

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

= 21%

Hence, option 3 is the correct option.

A bookseller bought 400 textbooks for ₹ 18,000. He wanted to sell them at a profit so that he gets 40 books free. At what profit per cent should he sell them?

1. 10%
2. 12%
3. 15%
4. 18%

Answer

Given:

C.P. of 400 textbooks = ₹ 18000

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

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

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

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

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

= 10%

Hence, option 1 is the correct option.

A man sells two goats for ₹ 4,000 each, neither losing nor gaining in the deal. If he sold one goat at a gain of 25%, then the other goat is sold at a loss of:

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

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

3. 50%

4. 47%

Answer

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) :

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

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

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

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

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

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

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

Hence, option 2 is the correct option.

Avantika bought 80 pears for ₹ 40. Out of them, 25 pears were spoiled and thrown away. She sold the remaining pears at a profit of 10%. The selling price of 1 pear is:

1. ₹ 0.25
2. ₹ 0.80
3. ₹ 1.25
4. ₹ 2.50

Answer

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:

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

Total S.P. of 55 pears = ₹ 44

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

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

Hence, option 2 is the correct option.

Select the incorrect match.

Answer

We will use the formula:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Hence, option 3 is the correct option.

Garima purchased a dozen pens for ₹ 60 and sold them for ₹ 84 whereas Kajal purchased a dozen pens for ₹ 90 and sold them for ₹ 150. Whose profit per cent is more and by how much?

1. Garima, 23.4%
2. Kajal, 25.4%
3. Kajal, 26.6%
4. Garima, 31.6%

Answer

For Garima :

C.P. = ₹ 60

S.P. = ₹ 84

Gain = S.P. - C.P.

Gain = ₹ 84 - ₹ 60 = ₹ 24

And

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

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

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

= $\Big(\dfrac{2}{1} \times 20\Big)$% $\quad$ [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% = $\Big(\dfrac{\text{Gain}}{\text{C.P.}} \times 100\Big)$%

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

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

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

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

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

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

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

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

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

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

Hence, option 3 is the correct option.

On selling a cycle for ₹ 12,000, a dealer loses 4%. For how much should he sell it to gain 10%?

1. ₹ 12,750
2. ₹ 11,750
3. ₹ 13,750
4. ₹ 14,750

Answer

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,

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

C.P. = ₹ 12500

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

We have the formula,

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

Hence, option 3 is the correct option.

By selling 48 apples, a salesman suffers a loss equal to the selling price of 6 apples. Find his loss per cent.

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

2. $9\dfrac{1}{9}$%

3. $11\dfrac{2}{9}$%

4. $11\dfrac{1}{9}$%

Answer

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 = $\dfrac{54s}{48} = \dfrac{9s}{8}$

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

And

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

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

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

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

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

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

Hence, option 4 is the correct option.

A manufacturer sells an item to an agency at a profit of 25%. The agency sells the item to a shopkeeper at 10% profit and shopkeeper sells the item at a profit of 20%. If the selling price of the item is ₹ 594, the manufacturing price is:

1. ₹ 360
2. ₹ 400
3. ₹ 420
4. ₹ 425

Answer

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) :

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

So, Agency's C.P. = ₹ $\dfrac{5x}{4}$

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

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

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

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

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

Final S.P. = ₹ $\dfrac{33x}{20}$

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

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

∴ Manufacturing price = ₹ 360

Hence, option 1 is the correct option.

If a man were to sell his chair for ₹720, he would lose 25%. To gain 25%, SP of the chair should be:

1. ₹ 1000
2. ₹ 1050
3. ₹ 1160
4. ₹ 1200

Answer

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,

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

C.P. = ₹ 960

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

We have the formula,

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

Hence, option 4 is the correct option.