Profit, Loss and Discount — Exercise 10(C)

A machine is marked at ₹ 5,000 and is sold at a discount of 10%. Find the selling price of the machine.

Answer

Marked price = ₹ 5,000 and discount = 10%.

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

$= 5,000 \times \dfrac{90}{100}\\[1em] = \dfrac{4,50,000}{100}\\[1em] = ₹\ 4,500$

Hence, the selling price of the machine is ₹ 4,500.

A shopkeeper marked a dinner set for ₹ 1,000. He sold it at ₹ 900. What percent discount did he give?

Answer

Marked price = ₹ 1,000 and S.P. = ₹ 900.

Discount = M.P. − S.P. = 1,000 − 900 = ₹ 100.

Discount% = $\left(\dfrac{\text{discount}}{\text{M.P.}} \times 100\right)$%

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

= $\dfrac{10,000}{1,000}$%

= 10%

Hence, the shopkeeper gave a discount of 10%.

A pair of shoes, marked at ₹ 320, are sold at a discount of 15 percent. Find:

(i) the discount,

(ii) the selling price of the shoes.

Answer

Marked price = ₹ 320 and discount = 15%.

(i) Discount = $\dfrac{\text{discount percentage}}{100} \times$ M.P.

= $\dfrac{15}{100} \times 320$

= $\dfrac{4,800}{100}$

= ₹ 48

Hence, the discount is ₹ 48.

(ii) S.P. = M.P. − discount = 320 − 48 = ₹ 272.

Hence, the selling price of the shoes is ₹ 272.

The list price of an article is ₹ 450 and it is sold for ₹ 360. Find:

(i) the discount,

(ii) the discount percent.

Answer

List (marked) price = ₹ 450 and S.P. = ₹ 360.

(i) Discount = M.P. − S.P. = 450 − 360 = ₹ 90.

Hence, the discount is ₹ 90.

(ii) Discount% = $\left(\dfrac{\text{discount}}{\text{M.P.}} \times 100\right)$%

= $\left(\dfrac{90}{450} \times 100\right)$%

= $\dfrac{9,000}{450}$%

= 20%

Hence, the discount percent is 20%.

A shopkeeper buys an article for ₹ 300. He increases its price by 20% and then gives 10% discount on the new price. Find:

(i) the new price (marked price) of the article.

(ii) the discount given by the shopkeeper.

(iii) the selling price.

(iv) the profit percent made by the shopkeeper.

Answer

C.P. = ₹ 300.

(i) Marked price = C.P. increased by 20% = $300 \times \dfrac{120}{100}$

= $\dfrac{36,000}{100}$

= ₹ 360

Hence, the marked price of the article is ₹ 360.

(ii) Discount = 10% of 360 = $\dfrac{10}{100} \times 360$ = ₹ 36.

Hence, the discount given by the shopkeeper is ₹ 36.

(iii) S.P. = M.P. − discount = 360 − 36 = ₹ 324.

Hence, the selling price of the article is ₹ 324.

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

Profit = 324 − 300 = ₹ 24.

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

= $\left(\dfrac{24}{300} \times 100\right)$%

= $\dfrac{2,400}{300}$%

= 8%

Hence, the profit percent made by the shopkeeper is 8%.

A car is marked at ₹ 50,000. The dealer gives 5% discount on first ₹ 20,000 and 2% discount on the remaining ₹ 30,000. Find:

(i) the total discount.

(ii) the price charged by the dealer.

Answer

Marked price = ₹ 50,000.

(i) Discount on first ₹ 20,000 = 5% of 20,000 = $\dfrac{5}{100} \times 20,000$ = ₹ 1,000.

Discount on remaining ₹ 30,000 = 2% of 30,000 = $\dfrac{2}{100} \times 30,000$ = ₹ 600.

Total discount = 1,000 + 600 = ₹ 1,600.

Hence, the total discount is ₹ 1,600.

(ii) Price charged = M.P. − total discount = 50,000 − 1,600 = ₹ 48,400.

Hence, the price charged by the dealer is ₹ 48,400.

A dealer buys a T.V. set for ₹ 2,500. He marks it at ₹ 3,200 and then gives a discount of 10% on it. Find:

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

(ii) the profit percent made by the dealer.

Answer

C.P. = ₹ 2,500 and marked price = ₹ 3,200.

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

$= 3,200 \times \left(1 - \dfrac{10}{100}\right)\\[1em] = 3,200 \times \dfrac{90}{100}\\[1em] = \dfrac{2,88,000}{100}\\[1em] = ₹\ 2,880$

Hence, the selling price of the T.V. set is ₹ 2,880.

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

Profit = 2,880 − 2,500 = ₹ 380.

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

= $\left(\dfrac{380}{2,500} \times 100\right)$%

= $\dfrac{38,000}{2,500}$%

= 15.2%

Hence, the profit percent made by the dealer is 15.2%.

A sells his goods at 15% discount. Find the marked price of an article which is sold for ₹ 680.

Answer

S.P. = ₹ 680 and discount = 15%.

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

$\Rightarrow 680 = \text{M.P.} \times \left(1 - \dfrac{15}{100}\right)\\[1em] \Rightarrow 680 = \text{M.P.} \times \dfrac{85}{100}\\[1em] \Rightarrow \text{M.P.} = \dfrac{680 \times 100}{85}\\[1em] \Rightarrow \text{M.P.} = ₹\ 800$

Hence, the marked price of the article is ₹ 800.

A shopkeeper allows 20% discount on the marked price of his articles. Find the marked price of an article for which he charges ₹ 560.

Answer

S.P. = ₹ 560 and discount = 20%.

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

$\Rightarrow 560 = \text{M.P.} \times \left(1 - \dfrac{20}{100}\right)\\[1em] \Rightarrow 560 = \text{M.P.} \times \dfrac{80}{100}\\[1em] \Rightarrow \text{M.P.} = \dfrac{560 \times 100}{80}\\[1em] \Rightarrow \text{M.P.} = ₹\ 700$

Hence, the marked price of the article is ₹ 700.

An article is bought for ₹ 1,200 and ₹ 100 is spent on its transportation, etc. Find:

(i) the total C.P. of the article.

(ii) the selling price of it in order to gain 20% on the whole.

Answer

(i) Total C.P. = cost + transportation = 1,200 + 100 = ₹ 1,300.

Hence, the total cost price of the article is ₹ 1,300.

(ii) Gain = 20%.

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

$= 1,300 \times \dfrac{120}{100}\\[1em] = \dfrac{1,56,000}{100}\\[1em] = ₹\ 1,560$

Hence, the selling price of the article is ₹ 1,560.

40 pens are bought at 4 for ₹ 50 and all of them are sold at 5 for ₹ 80. Find:

(i) C.P. of one pen.

(ii) S.P. of one pen.

(iii) Profit made by selling one pen.

(iv) Profit percent made by selling one pen.

(v) C.P. of 40 pens.

(vi) S.P. of 40 pens.

(vii) Profit made by selling 40 pens.

(viii) Profit percent made by selling 40 pens.

Are the results of parts (iv) and (viii) same?

What conclusion do you draw from the above result?

Answer

(i) C.P. of one pen = $\dfrac{50}{4}$ = ₹ 12.50.

Hence, the C.P. of one pen is ₹ 12.50.

(ii) S.P. of one pen = $\dfrac{80}{5}$ = ₹ 16.

Hence, the S.P. of one pen is ₹ 16.

(iii) Profit on one pen = 16 − 12.50 = ₹ 3.50.

Hence, the profit made by selling one pen is ₹ 3.50.

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

= $\left(\dfrac{3.50}{12.50} \times 100\right)$%

= $\dfrac{350}{12.50}$%

= 28%

Hence, the profit percent made by selling one pen is 28%.

(v) C.P. of 40 pens = 40 × 12.50 = ₹ 500.

Hence, the C.P. of 40 pens is ₹ 500.

(vi) S.P. of 40 pens = 40 × 16 = ₹ 640.

Hence, the S.P. of 40 pens is ₹ 640.

(vii) Profit on 40 pens = 640 − 500 = ₹ 140.

Hence, the profit made by selling 40 pens is ₹ 140.

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

= $\left(\dfrac{140}{500} \times 100\right)$%

= $\dfrac{14,000}{500}$%

= 28%

Hence, the profit percent made by selling 40 pens is 28%.

Yes, the results of parts (iv) and (viii) are the same, i.e. 28%.

Hence, the profit percent does not depend on the number of articles bought and sold; it remains the same whether it is calculated for one pen, 40 pens or 100 pens.

The C.P. of 5 identical articles is equal to S.P. of 4 articles. Calculate the profit percent or loss percent made if all the articles bought have been sold.

Answer

Let the C.P. of each article be ₹ x.

C.P. of 5 articles = ₹ 5x.

Given, C.P. of 5 articles = S.P. of 4 articles.

So, S.P. of 4 articles = ₹ 5x.

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

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

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

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

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

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

= 25%

Hence, the profit percent is 25%.

The C.P. of 12 pens is the same as the S.P. of 15 pens. Calculate the profit or loss percent made, if all the pens bought are considered to be sold.

Answer

Let the C.P. of each pen be ₹ x.

C.P. of 12 pens = ₹ 12x.

Given, C.P. of 12 pens = S.P. of 15 pens.

So, S.P. of 15 pens = ₹ 12x.

S.P. of 1 pen = $\dfrac{12x}{15}$ = ₹ $\dfrac{4x}{5}$.

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

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

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

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

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

= 20%

Hence, the loss percent is 20%.

A certain number of articles are bought at ₹ 450 per dozen and all of them are sold at a profit of 20%. Find the S.P. of:

(i) one article

(ii) seven articles.

Answer

C.P. of 1 dozen (12) articles = ₹ 450.

C.P. of 1 article = $\dfrac{450}{12}$ = ₹ 37.50 and profit = 20%.

(i) S.P. of 1 article = C.P. $\times \dfrac{100 + 20}{100}$

$= 37.50 \times \dfrac{120}{100}\\[1em] = \dfrac{4,500}{100}\\[1em] = ₹\ 45$

Hence, the selling price of one article is ₹ 45.

(ii) S.P. of 7 articles = 7 × 45 = ₹ 315.

Hence, the selling price of seven articles is ₹ 315.

An article is marked 60% above the cost price and sold at 20% discount. Find the profit percent made.

Answer

Let the C.P. of the article be ₹ 100.

Marked price = C.P. increased by 60% = $100 \times \dfrac{160}{100}$ = ₹ 160.

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

$= 160 \times \left(1 - \dfrac{20}{100}\right)\\[1em] = 160 \times \dfrac{80}{100}\\[1em] = \dfrac{12,800}{100}\\[1em] = ₹\ 128$

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

Profit = 128 − 100 = ₹ 28.

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

= $\left(\dfrac{28}{100} \times 100\right)$%

= 28%

Hence, the profit percent is 28%.