Profit, Loss and Discount — Exercise 10(B)

Find the cost price, if:

S.P. = ₹ 21 and gain = 5%

Answer

S.P. = ₹ 21 and gain = 5%

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

$= \dfrac{21 \times 100}{100 + 5}\\[1em] = \dfrac{2,100}{105}\\[1em] = ₹\ 20$

Hence, the cost price of the article is ₹ 20.

Find the cost price, if:

S.P. = ₹ 22 and loss = 12%

Answer

S.P. = ₹ 22 and loss = 12%

C.P. = $\dfrac{\text{S.P.} \times 100}{100 - \text{loss percentage}}$

$= \dfrac{22 \times 100}{100 - 12}\\[1em] = \dfrac{2,200}{88}\\[1em] = ₹\ 25$

Hence, the cost price of the article is ₹ 25.

Find the cost price, if:

S.P. = ₹ 340 and gain = ₹ 20

Answer

S.P. = ₹ 340 and gain = ₹ 20

C.P. = S.P. − gain

= 340 − 20

= ₹ 320

Hence, the cost price of the article is ₹ 320.

Find the cost price, if:

S.P. = ₹ 200 and loss = ₹ 50

Answer

S.P. = ₹ 200 and loss = ₹ 50

C.P. = S.P. + loss

= 200 + 50

= ₹ 250

Hence, the cost price of the article is ₹ 250.

Find the cost price, if:

S.P. = ₹ 1 and loss = 5 p

Answer

S.P. = ₹ 1 = 100 p and loss = 5 p

C.P. = S.P. + loss

= 100 + 5

= 105 p

= ₹ $\dfrac{105}{100}$

= ₹ 1.05

Hence, the cost price of the article is ₹ 1.05.

By selling an article for ₹ 810, a loss of 10 percent is suffered. Find its cost price.

Answer

S.P. = ₹ 810 and loss = 10%.

C.P. = $\dfrac{\text{S.P.} \times 100}{100 - \text{loss percentage}}$

$= \dfrac{810 \times 100}{100 - 10}\\[1em] = \dfrac{81,000}{90}\\[1em] = ₹\ 900$

Hence, the cost price of the article is ₹ 900.

By selling a scooter for ₹ 9,200, a man gains 15%. Find the cost price of the scooter.

Answer

S.P. = ₹ 9,200 and gain = 15%.

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

$= \dfrac{9,200 \times 100}{100 + 15}\\[1em] = \dfrac{9,20,000}{115}\\[1em] = ₹\ 8,000$

Hence, the cost price of the scooter is ₹ 8,000.

On selling an article for ₹ 2,640, a profit of 10 percent is made. Find:

(i) cost price of the article.

(ii) new selling price of it, in order to gain 15%.

Answer

S.P. = ₹ 2,640 and profit = 10%.

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

$= \dfrac{2,640 \times 100}{110}\\[1em] = \dfrac{2,64,000}{110}\\[1em] = ₹\ 2,400$

Hence, the cost price of the article is ₹ 2,400.

(ii) New S.P. = C.P. $\times \dfrac{100 + 15}{100}$

$= 2,400 \times \dfrac{115}{100}\\[1em] = \dfrac{2,76,000}{100}\\[1em] = ₹\ 2,760$

Hence, the new selling price of the article is ₹ 2,760.

A T.V. set is sold for ₹ 6,800 at a loss of 15%. Find:

(i) cost price of the T.V. set.

(ii) new selling price of it, in order to gain 12%.

Answer

S.P. = ₹ 6,800 and loss = 15%.

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

$= \dfrac{6,800 \times 100}{85}\\[1em] = \dfrac{6,80,000}{85}\\[1em] = ₹\ 8,000$

Hence, the cost price of the T.V. set is ₹ 8,000.

(ii) New S.P. = C.P. $\times \dfrac{100 + 12}{100}$

$= 8,000 \times \dfrac{112}{100}\\[1em] = \dfrac{8,96,000}{100}\\[1em] = ₹\ 8,960$

Hence, the new selling price of the T.V. set is ₹ 8,960.

A fruit seller bought mangoes at ₹ 90 per dozen and sold them at a loss of 8 percent. How much will a customer pay for:

(i) one mango

(ii) 40 mangoes

Answer

C.P. of 1 dozen (12) mangoes = ₹ 90 and loss = 8%.

S.P. of 12 mangoes = C.P. $\times \dfrac{100 - 8}{100}$

$= 90 \times \dfrac{92}{100}\\[1em] = \dfrac{8,280}{100}\\[1em] = ₹\ 82.80$

So, the S.P. of 12 mangoes = ₹ 82.80.

(i) S.P. of 1 mango = $\dfrac{\text{S.P. of 12 mangoes}}{12} = \dfrac{82.80}{12}$ = ₹ 6.90.

Hence, a customer will pay ₹ 6.90 for one mango.

(ii) S.P. of 40 mangoes = 40 × 6.90 = ₹ 276.

Hence, a customer will pay ₹ 276 for 40 mangoes.

By selling two transistors for ₹ 600 each, a shopkeeper gains 20 percent on one transistor and loses 20 percent on the other. Find:

(i) C.P. of each transistor.

(ii) total C.P. and total S.P. of both the transistors.

(iii) profit or loss percent on the whole.

Answer

(i) For the first transistor (gain 20%), S.P. = ₹ 600.

C.P. of first = $\dfrac{\text{S.P.} \times 100}{100 + \text{gain percentage}}$

= $\dfrac{600 \times 100}{100 + 20}$

= $\dfrac{60,000}{120}$

= ₹ 500

For the second transistor (loss 20%), S.P. = ₹ 600.

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

= $\dfrac{600 \times 100}{100 - 20}$

= $\dfrac{60,000}{80}$

= ₹ 750

Hence, the cost prices of the two transistors are ₹ 500 and ₹ 750 respectively.

(ii) Total C.P. = 500 + 750 = ₹ 1,250.

Total S.P. = 600 + 600 = ₹ 1,200.

Hence, the total cost price is ₹ 1,250 and the total selling price is ₹ 1,200.

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

Loss = 1,250 − 1,200 = ₹ 50.

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

= $\left(\dfrac{50}{1,250} \times 100\right)$%

= $\dfrac{5,000}{1,250}$%

= 4%

Hence, the loss percent on the whole is 4%.

Mangoes are bought at 20 for ₹ 60. If they are sold at a profit of $33\dfrac{1}{3}$ percent, find:

(i) selling price of each mango.

(ii) S.P. of 8 mangoes.

Answer

C.P. of 1 mango = $\dfrac{60}{20}$ = ₹ 3 and profit = $33\dfrac{1}{3}$% $= \dfrac{100}{3}$%.

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

$= 3 \times \left(1 + \dfrac{100}{3 \times 100}\right)\\[1em] = 3 \times \left(1 + \dfrac{1}{3}\right)\\[1em] = 3 \times \dfrac{4}{3}\\[1em] = ₹\ 4$

Hence, the selling price of each mango is ₹ 4.

(ii) S.P. of 8 mangoes = 8 × 4 = ₹ 32.

Hence, the selling price of 8 mangoes is ₹ 32.

Find the cost price of an article, which is sold for ₹ 4,050 at a loss of 10%. Also, find the new selling price of the article which must give a profit of 8%.

Answer

S.P. = ₹ 4,050 and loss = 10%.

C.P. = $\dfrac{\text{S.P.} \times 100}{100 - \text{loss percentage}}$

$= \dfrac{4,050 \times 100}{90}\\[1em] = \dfrac{4,05,000}{90}\\[1em] = ₹\ 4,500$

Hence, the cost price of the article is ₹ 4,500.

New S.P. = C.P. $\times \dfrac{100 + 8}{100}$

$= 4,500 \times \dfrac{108}{100}\\[1em] = \dfrac{4,86,000}{100}\\[1em] = ₹\ 4,860$

Hence, the new selling price of the article is ₹ 4,860.

By selling an article for ₹ 825, a man loses an amount equal to $\dfrac{1}{3}$ of its selling price. Find:

(i) the cost price of the article.

(ii) the profit percent or the loss percent made, if the same article is sold for ₹ 1,265.

Answer

S.P. = ₹ 825.

(i) Loss = $\dfrac{1}{3}$ of S.P. = $\dfrac{1}{3} \times 825$ = ₹ 275.

C.P. = S.P. + loss = 825 + 275 = ₹ 1,100.

Hence, the cost price of the article is ₹ 1,100.

(ii) When the article is sold for ₹ 1,265:

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

Profit = 1,265 − 1,100 = ₹ 165.

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

= $\left(\dfrac{165}{1,100} \times 100\right)$%

= $\dfrac{16,500}{1,100}$%

= 15%

Hence, the profit percent made is 15%.

Find the loss or gain as percent, if the C.P. of 10 articles, all of the same kind, is equal to S.P. of 8 articles.

Answer

Let the C.P. of each article be ₹ x.

C.P. of 10 articles = ₹ 10x.

Given, C.P. of 10 articles = S.P. of 8 articles.

So, S.P. of 8 articles = ₹ 10x.

S.P. of 1 article = $\dfrac{10x}{8}$ = ₹ $\dfrac{5x}{4}$.

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

Gain on 1 article = $\dfrac{5x}{4} - x$ = ₹ $\dfrac{x}{4}$.

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

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

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

= 25%

Hence, the gain percent is 25%.

Find the loss or gain as percent, if the C.P. of 8 articles, all of the same kind, is equal to S.P. of 10 articles.

Answer

Let the C.P. of each article be ₹ x.

C.P. of 8 articles = ₹ 8x.

Given, C.P. of 8 articles = S.P. of 10 articles.

So, S.P. of 10 articles = ₹ 8x.

S.P. of 1 article = $\dfrac{8x}{10}$ = ₹ $\dfrac{4x}{5}$.

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

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

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

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

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

= 20%

Hence, the loss percent is 20%.

The cost price of an article is 96% of its selling price. Find the loss or the gain as percent on the whole.

Answer

Let the S.P. of the article be ₹ 100.

C.P. = 96% of S.P. = $\dfrac{96}{100} \times 100$ = ₹ 96.

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

Gain = 100 − 96 = ₹ 4.

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

= $\left(\dfrac{4}{96} \times 100\right)$%

= $\dfrac{400}{96}$%

= $\dfrac{25}{6}$%

= $4\dfrac{1}{6}$%

Hence, the gain percent is $4\dfrac{1}{6}$%.

The selling price of an article is 96% of its cost price. Find the loss or the gain as percent on the whole.

Answer

Let the C.P. of the article be ₹ 100.

S.P. = 96% of C.P. = $\dfrac{96}{100} \times 100$ = ₹ 96.

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

Loss = 100 − 96 = ₹ 4.

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

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

= 4%

Hence, the loss percent is 4%.

Hundred oranges are bought for ₹ 350 and all of them are sold at the rate of ₹ 48 per dozen. Find the profit percent or loss percent made.

Answer

C.P. of 100 oranges = ₹ 350.

S.P. of 1 orange = $\dfrac{48}{12}$ = ₹ 4.

S.P. of 100 oranges = 100 × 4 = ₹ 400.

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

Profit = 400 − 350 = ₹ 50.

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

= $\left(\dfrac{50}{350} \times 100\right)$%

= $\dfrac{5,000}{350}$%

= $\dfrac{100}{7}$%

= $14\dfrac{2}{7}$%

Hence, the profit percent is $14\dfrac{2}{7}$%.

Oranges are bought at 100 for ₹ 80 and all of them are sold at 80 for ₹ 100. Find the loss or gain as percent in this transaction.

Answer

Let the number of oranges be 100.

C.P. of 100 oranges = ₹ 80.

S.P. of 1 orange = $\dfrac{100}{80}$ = ₹ 1.25.

S.P. of 100 oranges = 100 × 1.25 = ₹ 125.

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

Gain = 125 − 80 = ₹ 45.

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

= $\left(\dfrac{45}{80} \times 100\right)$%

= $\dfrac{4,500}{80}$%

= $\dfrac{225}{4}$%

= 56.25%

Hence, the gain percent is 56.25%.

An article is bought for ₹ 5,700 and ₹ 1,300 is spent on its repairing, transportation, etc. For how much should this article be sold in order to gain 20% on the whole?

Answer

Total C.P. = cost + expenses = 5,700 + 1,300 = ₹ 7,000.

Gain = 20%.

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

$= 7,000 \times \dfrac{120}{100}\\[1em] = \dfrac{8,40,000}{100}\\[1em] = ₹\ 8,400$

Hence, the article should be sold for ₹ 8,400 in order to gain 20% on the whole.

Rani bought an old machine for ₹ 4,800 and spent ₹ 1,200 on its repairs. If she sold the repaired machine for ₹ 5,400, find her profit or loss, as percent, on this transaction.

Answer

Total C.P. = cost + repairs = 4,800 + 1,200 = ₹ 6,000.

S.P. = ₹ 5,400.

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

Loss = 6,000 − 5,400 = ₹ 600.

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

= $\left(\dfrac{600}{6,000} \times 100\right)$%

= $\dfrac{60,000}{6,000}$%

= 10%

Hence, Rani made a loss of 10%.