Profit, Loss and Discount — Multiple Choice Questions

An old bicycle is bought for ₹ 675 and ₹ 125 is spent on its repairs. If the repaired bicycle is sold for ₹ 880, the profit or loss as percent is:

1. 10% profit

2. 10% loss

3. 20% profit

4. 20% loss

Answer

Total C.P. = 675 + 125 = ₹ 800.

S.P. = ₹ 880.

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

Profit = 880 − 800 = ₹ 80.

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

= $\left(\dfrac{80}{800} \times 100\right)$%

= $\dfrac{8,000}{800}$%

= 10%

Hence, option 1 is the correct option.

The cost price of 20 pens is equal to the selling price of 16 pens; the profit or loss as percent is:

1. 20% loss

2. 20% profit

3. 25% loss

4. 25% profit

Answer

Let the C.P. of each pen be ₹ x.

C.P. of 20 pens = ₹ 20x = S.P. of 16 pens.

S.P. of 1 pen = $\dfrac{20x}{16}$ = ₹ $\dfrac{5x}{4}$.

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

Profit on 1 pen = $\dfrac{5x}{4} - x$ = ₹ $\dfrac{x}{4}$.

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

= $\left(\dfrac{x/4}{x} \times 100\right)$%

= 25%

Hence, option 4 is the correct option.

The C.P. of 16 pens is equal to the S.P. of 20 pens; the profit or loss as percent is:

1. 20% loss

2. 20% profit

3. 25% loss

4. 25% profit

Answer

Let the C.P. of each pen be ₹ x.

C.P. of 16 pens = ₹ 16x = S.P. of 20 pens.

S.P. of 1 pen = $\dfrac{16x}{20} = ₹ \dfrac{4x}{5}$.

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

Loss on 1 pen = $x - \dfrac{4x}{5} = ₹ \dfrac{x}{5}$.

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

= $\left(\dfrac{\dfrac{x}{5}}{x} \times 100\right)$%

= 20%

Hence, option 1 is the correct option.

An article is bought for ₹ 15,000 and ₹ 1,000 is spent on its repairs. If the article is sold at 20% profit, the selling price is:

1. ₹ 12,800

2. ₹ 18,000

3. ₹ 3,200

4. ₹ 19,200

Answer

Total C.P. = 15,000 + 1,000 = ₹ 16,000.

S.P. = C.P. $\times \dfrac{100 + 20}{100}$

$= 16,000 \times \dfrac{120}{100}\\[1em] = \dfrac{19,20,000}{100}\\[1em] = ₹\ 19,200$

Hence, option 4 is the correct option.

Rasheed buys a certain number of bananas at 2 for ₹ 1 and sold all of them at ₹ 1 each. The profit or loss made is:

1. 100% profit

2. 100% loss

3. 50% profit

4. 50% loss

Answer

C.P. of 1 banana = $\dfrac{1}{2}$ = ₹ 0.50.

S.P. of 1 banana = ₹ 1.

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

Profit = 1 − 0.50 = ₹ 0.50.

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

= $\left(\dfrac{0.50}{0.50} \times 100\right)$%

= 100%

Hence, option 1 is the correct option.

Two identical articles are bought at ₹ 300 each. If one is sold at 25% profit and the other at 25% loss. The profit or loss made on the whole is:

1. ₹ 50 loss

2. neither profit nor loss

3. ₹ 50 profit

4. ₹ 20 loss

Answer

Total C.P. = 300 + 300 = ₹ 600.

S.P. of first (25% profit) = $300 \times \dfrac{125}{100}$ = ₹ 375.

S.P. of second (25% loss) = $300 \times \dfrac{75}{100}$ = ₹ 225.

Total S.P. = 375 + 225 = ₹ 600.

Since total S.P. = total C.P., there is neither profit nor loss.

Hence, option 2 is the correct option.

Two articles are sold for ₹ 300 each. If on one article, a profit of 25% is made and on the other a loss of 25% is made. The profit or the loss made on the whole is:

1. ₹ 40 profit

2. ₹ 40 loss

3. no profit no loss

4. none of these

Answer

S.P. of each article = ₹ 300.

C.P. of first (25% profit) = $\dfrac{\text{S.P.} \times 100}{100 + \text{profit percentage}}$

= $\dfrac{300 \times 100}{125}$

= ₹ 240

C.P. of second (25% loss) = $\dfrac{\text{S.P.} \times 100}{100 - \text{loss percentage}}$

= $\dfrac{300 \times 100}{75}$

= ₹ 400

Total C.P. = 240 + 400 = ₹ 640.

Total S.P. = 300 + 300 = ₹ 600.

Since C.P. > S.P., loss = 640 − 600 = ₹ 40.

Hence, option 2 is the correct option.

Mohit purchased an article for ₹ 1,000 and sold for ₹ 3,000. The profit percent made is:

1. 100%

2. $166\dfrac{2}{3}$%

3. 200%

4. 300%

Answer

C.P. = ₹ 1,000 and S.P. = ₹ 3,000.

Profit = 3,000 − 1,000 = ₹ 2,000.

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

= $\left(\dfrac{2,000}{1,000} \times 100\right)$%

= 200%

Hence, option 3 is the correct option.

The S.P. of an article is $\dfrac{4}{5}$ of its C.P. The profit or loss as percent is:

1. 20% loss

2. 20% profit

3. 25% loss

4. 25% profit

Answer

Let the C.P. be ₹ 5.

S.P. = $\dfrac{4}{5}$ of 5 = ₹ 4.

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

Loss = 5 − 4 = ₹ 1.

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

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

= 20%

Hence, option 1 is the correct option.

The C.P. of an article is $\dfrac{4}{5}$ of its S.P. The profit or loss as percent is:

1. 20% loss

2. 20% profit

3. 25% loss

4. 25% profit

Answer

Let the S.P. be ₹ 5.

C.P. = $\dfrac{4}{5}$ of 5 = ₹ 4.

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

Profit = 5 − 4 = ₹ 1.

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

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

= 25%

Hence, option 4 is the correct option.

The marked price of a T.V. is ₹ 60,000 which is available at a discount of 25%. For this T.V., a customer will pay:

1. ₹ 75,000

2. ₹ 45,000

3. ₹ 72,000

4. ₹ 48,000

Answer

Marked price = ₹ 60,000 and discount = 25%.

S.P. = M.P. $\times \left(1 - \dfrac{\text{discount percentage}}{100}\right)$

$= 60,000 \times \left(1 - \dfrac{25}{100}\right)\\[1em] = 60,000 \times \dfrac{75}{100}\\[1em] = \dfrac{45,00,000}{100}\\[1em] = ₹\ 45,000$

Hence, option 2 is the correct option.

A calculator is marked at ₹ 600 and is available at a discount of ₹ 100. If on selling, a profit of ₹ 100 is made, its cost price is:

1. ₹ 600

2. ₹ 400

3. ₹ 500

4. ₹ 700

Answer

Marked price = ₹ 600 and discount = ₹ 100.

S.P. = M.P. − discount = 600 − 100 = ₹ 500.

C.P. = S.P. − profit = 500 − 100 = ₹ 400.

Hence, option 2 is the correct option.

The single discount equivalent to two successive discounts of 20% and 20% is:

1. 40%

2. 36%

3. 4%

4. 64%

Answer

Let the marked price be ₹ 100.

After the first discount of 20%: price = 100 − 20 = ₹ 80.

After the second discount of 20% on ₹ 80: price = 80 − $\dfrac{20}{100} \times 80$ = 80 − 16 = ₹ 64.

Total discount = 100 − 64 = ₹ 36.

So, the single equivalent discount = 36%.

Hence, option 2 is the correct option.

By selling an article for ₹ 800, a loss of ₹ 200 is made. The loss percent is:

1. 20%

2. 25%

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

4. none of these

Answer

S.P. = ₹ 800 and loss = ₹ 200.

C.P. = S.P. + loss = 800 + 200 = ₹ 1,000.

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

= $\left(\dfrac{200}{1,000} \times 100\right)$%

= 20%

Hence, option 1 is the correct option.

By selling an article for ₹ 800, a gain of ₹ 200 is made. The gain percent is:

1. 20%

2. 25%

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

4. none of these

Answer

S.P. = ₹ 800 and gain = ₹ 200.

C.P. = S.P. − gain = 800 − 200 = ₹ 600.

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

= $\left(\dfrac{200}{600} \times 100\right)$%

= $\dfrac{20,000}{600}$%

= $\dfrac{100}{3}$%

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

Hence, option 3 is the correct option.