Profit, Loss and Discount — Exercise 10(A)

Find the gain or loss percent, if:

C.P. = ₹ 200 and S.P. = ₹ 224

Answer

C.P. = ₹ 200 and S.P. = ₹ 224

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

Gain = S.P. − C.P. = 224 − 200 = ₹ 24.

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

= $\left(\dfrac{24}{200} \times 100\right)$%

= $\dfrac{2,400}{200}$%

= 12%

Hence, the gain percent is 12%.

Find the gain or loss percent, if:

C.P. = ₹ 450 and S.P. = ₹ 400

Answer

C.P. = ₹ 450 and S.P. = ₹ 400

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

Loss = C.P. − S.P. = 450 − 400 = ₹ 50.

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

= $\left(\dfrac{50}{450} \times 100\right)$%

= $\dfrac{5,000}{450}$%

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

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

Hence, the loss percent is $11\dfrac{1}{9}$%.

Find the gain or loss percent, if:

C.P. = ₹ 550 and gain = ₹ 22

Answer

C.P. = ₹ 550 and gain = ₹ 22

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

= $\left(\dfrac{22}{550} \times 100\right)$%

= $\dfrac{2,200}{550}$%

= 4%

Hence, the gain percent is 4%.

Find the gain or loss percent, if:

C.P. = ₹ 216 and loss = ₹ 72

Answer

C.P. = ₹ 216 and loss = ₹ 72

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

= $\left(\dfrac{72}{216} \times 100\right)$%

= $\dfrac{7,200}{216}$%

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

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

Hence, the loss percent is $33\dfrac{1}{3}$%.

Find the gain or loss percent, if:

S.P. = ₹ 500 and loss = ₹ 100

Answer

S.P. = ₹ 500 and loss = ₹ 100

C.P. = S.P. + loss = 500 + 100 = ₹ 600.

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

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

= $\dfrac{10,000}{600}$%

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

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

Hence, the loss percent is $16\dfrac{2}{3}$%.

Find the selling price, if:

C.P. = ₹ 500 and gain = 25%

Answer

C.P. = ₹ 500 and gain = 25%

S.P. = C.P. $\times \left(1 + \dfrac{\text{gain percentage}}{100}\right)$

$= 500 \times \left(1 + \dfrac{25}{100}\right)\\[1em] = 500 \times \dfrac{125}{100}\\[1em] = ₹\ 625$

Hence, the selling price of the article is ₹ 625.

Find the selling price, if:

C.P. = ₹ 60 and loss = $12\dfrac{1}{2}$%

Answer

C.P. = ₹ 60 and loss = $12\dfrac{1}{2}$%

As, $12\dfrac{1}{2}$% $= \dfrac{25}{2}$%

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

$= 60 \times \left(1 - \dfrac{25}{200}\right)\\[1em] = 60 \times \dfrac{175}{200}\\[1em] = ₹\ 52.50$

Hence, the selling price of the article is ₹ 52.50.

Rohit bought a tape recorder for ₹ 1,500 and sold it for ₹ 1,800. Calculate his profit or loss percent.

Answer

C.P. = ₹ 1,500 and S.P. = ₹ 1,800.

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

Profit = 1,800 − 1,500 = ₹ 300.

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

= $\left(\dfrac{300}{1,500} \times 100\right)$%

= $\dfrac{30,000}{1,500}$%

= 20%

Hence, Rohit made a profit of 20%.

An article bought for ₹ 350 is sold at a profit of 20%. Find its selling price.

Answer

C.P. = ₹ 350 and profit = 20%.

S.P. = C.P. $\times \left(1 + \dfrac{\text{profit percentage}}{100}\right)$

$= 350 \times \dfrac{120}{100}\\[1em] = \dfrac{42,000}{100}\\[1em] = ₹\ 420$

Hence, the selling price of the article is ₹ 420.

An old machine is bought for ₹ 1,400 and is sold at a loss of 15%. Find its selling price.

Answer

C.P. = ₹ 1,400 and loss = 15%.

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

$= 1,400 \times \dfrac{85}{100}\\[1em] = \dfrac{1,19,000}{100}\\[1em] = ₹\ 1,190$

Hence, the selling price of the machine is ₹ 1,190.

Oranges are bought at 5 for ₹ 10 and sold at 6 for ₹ 15. Find profit or loss as percent.

Answer

C.P. of 1 orange = $\dfrac{10}{5}$ = ₹ 2.

S.P. of 1 orange = $\dfrac{15}{6}$ = ₹ 2.50.

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

Profit on 1 orange = 2.50 − 2 = ₹ 0.50.

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

= $\left(\dfrac{0.50}{2} \times 100\right)$%

= $\dfrac{50}{2}$%

= 25%

Hence, the profit percent is 25%.

A certain number of articles are bought at 3 for ₹ 150 and all of them are sold at 4 for ₹ 180. Find the loss or gain as percent.

Answer

C.P. of 1 article = $\dfrac{150}{3}$ = ₹ 50.

S.P. of 1 article = $\dfrac{180}{4}$ = ₹ 45.

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

Loss on 1 article = 50 − 45 = ₹ 5.

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

= $\left(\dfrac{5}{50} \times 100\right)$%

= $\dfrac{500}{50}$%

= 10%

Hence, the loss percent is 10%.

A vendor bought 120 sweets at 20 p each. In his house, 18 were consumed and he sold the remaining at 30 p each. Find his profit or loss as percent.

Answer

Total C.P. = 120 × 20 p = 2,400 p = ₹ 24.

Number of sweets sold = 120 − 18 = 102.

Total S.P. = 102 × 30 p = 3,060 p = ₹ 30.60.

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

Profit = 30.60 − 24 = ₹ 6.60.

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

= $\left(\dfrac{6.60}{24} \times 100\right)$%

= $\dfrac{660}{24}$%

= 27.5%

Hence, the profit percent is 27.5%.

The cost price of an article is ₹ 1,200 and selling price is $\dfrac{5}{4}$ times of its cost price. Find:

(i) selling price of the article,

(ii) profit or loss as percent.

Answer

C.P. = ₹ 1,200 and S.P. = $\dfrac{5}{4}$ times of C.P.

(i) S.P. = $\dfrac{5}{4} \times 1,200$

= $\dfrac{6,000}{4}$

= ₹ 1,500

Hence, the selling price of the article is ₹ 1,500.

(ii) Since S.P. > C.P., there is a profit.

Profit = 1,500 − 1,200 = ₹ 300.

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

= $\left(\dfrac{300}{1,200} \times 100\right)$%

= $\dfrac{30,000}{1,200}$%

= 25%

Hence, the profit percent is 25%.

The selling price of an article is ₹ 1,200 and cost price is $\dfrac{5}{4}$ times of its selling price. Find:

(i) cost price of the article,

(ii) profit or loss as percent.

Answer

S.P. = ₹ 1,200 and C.P. = $\dfrac{5}{4}$ times of S.P.

(i) C.P. = $\dfrac{5}{4} \times 1,200$

= $\dfrac{6,000}{4}$

= ₹ 1,500

Hence, the cost price of the article is ₹ 1,500.

(ii) Since C.P. > S.P., there is a loss.

Loss = 1,500 − 1,200 = ₹ 300.

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

= $\left(\dfrac{300}{1,500} \times 100\right)$%

= $\dfrac{30,000}{1,500}$%

= 20%

Hence, the loss percent is 20%.