Profit, Loss and Discount

10 articles are bought for ₹ 40 and are sold at ₹ 5 per article. The profit / loss made is:

1. 25% loss

2. 25% profit

3. 20% loss

4. 20% profit

Answer

C.P. of 10 articles = ₹ 40

C.P. of 1 article = ₹ $\dfrac{40}{10}$ = ₹ 4

S.P. of 1 article = ₹ 5

(∵ S.P. is greater than C.P., means article is sold at a profit.)

Profit = S.P. - C.P.

= ₹ 5 - ₹ 4 = ₹ 1

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

$= \dfrac{1}{4} \times 100$ %

$= \dfrac{100}{4}$ %

$= 25$ %

Hence, option 2 is the correct option.

A table is sold at 80% of its cost price. The profit or loss as percent is :

1. 20% loss

2. 20% profit

3. 25% loss

4. 25% profit

Answer

Lets take the C.P. of table to be ₹ $100$.

S.P. of table = ₹ $80$ of cost price.

$\text{S.P.}= ₹\Big(\dfrac{80}{100} \times 100\Big) \\[1em] = ₹\Big(\dfrac{80}{\cancel{100}} \times \cancel{100}\Big) \\[1em] = ₹ 80$

(∵ C.P. is greater than S.P., means table is sold at a loss.)

Loss = C.P. - S.P.

= ₹ 100 - ₹ 80 = ₹ 20

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

$= \dfrac{20}{100} \times 100$%

$= \dfrac{20}{\cancel{100}} \times \cancel{100}$%

$= 20$%

Hence, option 1 is the correct option.

C.P. = ₹ 150 and loss = ₹ 50 ⇒ the S.P. is:

1. ₹ 200

2. ₹ 100

3. ₹ 225

4. ₹ 75

Answer

Given:

C.P. = ₹ 150

Loss = ₹ 50

Loss = C.P. - S.P.

Putting the values, we get

₹ 50 = ₹ 150 - S.P.

S.P. = ₹ 150 - ₹ 50

= ₹ 100

Hence, option 2 is the correct option.

C.P. = ₹ 150 and loss = 50% ⇒ the S.P. is:

1. ₹ 200

2. ₹ 100

3. ₹ 225

4. ₹ 75

Answer

Given:

C.P. = ₹ 150

Loss % = 50%

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

Putting the values, we get

$\Rightarrow\text{50} = \dfrac{\text{Loss}}{150} \times 100\\[1em] \Rightarrow\text{Loss} = \dfrac{50 \times 150}{100} \\[1em] = \dfrac{7500}{100} \\[1em] = 75$

As we know:

$\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow 75 = 150 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 150 - 75\\[1em] \Rightarrow \text{S.P.} = 75$

Hence, option 4 is the correct option.

S.P. = ₹ 250 and profit = 25% ⇒ the C.P. is:

1. ₹ 225

2. ₹ 275

3. ₹ 200

4. ₹ none of these

Answer

Given:

S.P. = ₹ 250

Profit % = 25%

Let C.P. = $₹x$.

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

Putting the values, we get

$\Rightarrow 25 = \dfrac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{25 \times x}{100}\\[1em] = \dfrac{x}{4}$

As we know:

$\text{Profit} = \text{S.P. - C.P.}\\[1em] \Rightarrow \dfrac{x}{4} = 250 - x\\[1em] \Rightarrow 250 = \dfrac{x}{4} + x\\[1em] \Rightarrow 250 = \dfrac{x}{4} + \dfrac{4x}{4}\\[1em] \Rightarrow 250 = \dfrac{(x + 4x)}{4} \\[1em] \Rightarrow 250 = \dfrac{5x}{4}\\[1em] \Rightarrow x = \dfrac{4 \times 250}{5}\\[1em] \Rightarrow x = \dfrac{1000}{5}\\[1em] \Rightarrow x = 200$

Hence, option 3 is the correct option.

C.P. = ₹ 400 and overheads = ₹ 100. If loss = 10%; the S.P. is :

1. ₹ 360

2. ₹ 440

3. ₹ 450

4. ₹ 550

Answer

Given:

C.P. = ₹ 400

Overheads = ₹ 100

Hence, total C.P. = C.P. + overheads

= ₹ 400 + ₹ 100 = ₹ 500

Loss % = 10%

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

Putting the values, we get

$\Rightarrow10 = \dfrac{\text{Loss}}{500} \times 100\\[1em] \Rightarrow\text{Loss} = \dfrac{10 \times 500}{100} \\[1em] = \dfrac{5000}{100} \\[1em] = 50$

As we know:

$\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow 50 = 500 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 500 - 50\\[1em] = 450$

Hence, option 3 is the correct option.

A fruit-seller buys oranges at 4 for ₹ 8 and sells them at 3 for ₹ 9. Find his profit percent.

Answer

C.P. of 4 oranges = ₹ 8

C.P. of 1 orange = ₹ $\dfrac{8}{4}$ = ₹ 2

S.P. of 3 oranges = ₹ 9

S.P. of 1 orange = ₹ $\dfrac{9}{3}$ = ₹ 3

(∵ S.P. is greater than C.P., means oranges are sold at a profit.)

Profit = S.P. - C.P.

= ₹ 3 - ₹ 2 = ₹ 1

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

$= \dfrac{1}{2} \times 100$ %

$= \dfrac{100}{2}$ %

$= 50$ %

Hence, the profit percent = $50$.

A man buys a certain number of articles at 15 for ₹ 112.50 and sells them at 12 for ₹ 108. Find :

(i) his gain as percent;

(ii) the number of articles sold to make a profit of ₹ 75.

Answer

(i) C.P. of 15 articles = ₹ 112.50

C.P. of 1 article = ₹ $\dfrac{112.50}{15}$ = ₹ 7.5

S.P. of 12 articles = ₹ 108

S.P. of 1 article = ₹ $\dfrac{108}{12}$ = ₹ 9

(∵ S.P. is greater than C.P., means article is sold at a profit.)

Profit = S.P. - C.P.

= ₹ 9 - ₹ 7.5 = ₹ 1.5

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

$= \dfrac{1.5}{7.5} \times 100$ %

$= \dfrac{150}{7.5}$ %

$= \dfrac{1500}{75}$ %

$= 20$ %

Hence, the profit percent = $20$.

(ii) Profit on 1 article = ₹ 1.5

Lets suppose $x$ articles are sold to make the profit of ₹ 75.

Profit on $x$ articles = ₹ 75

No. of articles x Profit on 1 article = Total Profit

$⇒ x \times 1.5 = 75\\[1em] ⇒ x = \dfrac{75}{1.5}\\[1em] ⇒ x = \dfrac{750}{15}\\[1em] ⇒ x = 50$

Hence, 50 articles need to be sold to make a profit of ₹ 75.

A boy buys an old bicycle for ₹ 162 and spends ₹ 18 on its repairs before selling the bicycle for ₹ 207. Find his gain or loss as percent.

Answer

C.P. of bicycle = ₹ 162

Amount spent on its repair = ₹ 18

Final C.P. = ₹ 162 + ₹ 18 = ₹ 180

S.P. of bicycle = ₹ 207

(∵ S.P. is greater than C.P., means bicycle is sold at a gain.)

Gain = S.P. - C.P.

= ₹ 207 - ₹ 180

= ₹ 27

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

$= \dfrac{27}{180} \times 100$%

$= \dfrac{2700}{180}$%

$= 15$%

Hence, bicycle is sold at a gain of 15%.

An article is bought from Jaipur for ₹ 4,800 and is sold in Delhi for ₹ 5,820. If ₹ 1,200 is spent on its transportation, etc., find the loss or the gain as percent.

Answer

Given:

C.P. of an article = ₹ 4,800

Cost spent on transportation, etc. = ₹ 1,200

Total C.P. = ₹ 4,800 + ₹ 1,200

= ₹ 6,000

S.P. of the article = ₹ 5,820

(∵ C.P. is greater than S.P., means article is sold at loss.)

Loss = C.P. - S.P.

= ₹ 6,000 - ₹ 5,820

= ₹ 180

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

$= \dfrac{180}{6000} \times 100$%

$= \dfrac{18,000}{6000}$%

$= 3$%

Hence, article is sold at a loss of 3%.

Mohit sold a T.V. for ₹ 3,600, gaining one-sixth of its selling price. Find :

(i) the gain.

(ii) the cost price of the T.V.

(iii) the gain percent.

Answer

(i) Given:

S.P. of T.V. = ₹ 3,600

Gain = one-sixth of its selling price

$\text{Gain}= ₹\Big(\dfrac{1}{6} \times 3,600\Big) \\[1em] = ₹ \dfrac{3,600}{6}\\[1em] = ₹ 600$

Gain = ₹600

(ii) As we know that,

Gain = S.P. - C.P.

Putting the values, we get

₹ 600 = ₹ 3,600 - C.P.

C.P. = ₹ 3,600 - ₹ 600

= ₹ 3,000

The cost price of the T.V. = ₹ 3,000.

(iii)

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

$= \dfrac{600}{3000} \times 100$%

$= \dfrac{1}{5} \times 100$%

$= \dfrac{100}{5}$%

$= 20$%

Hence, T.V. is sold at a gain of 20%.

By selling a certain number of goods for ₹ 5,500, a shopkeeper loses equal to one-tenth of their selling price. Find :

(i) the loss incurred

(ii) the cost price of the goods

(iii) the loss as percent.

Answer

(i) Given:

S.P. of a certain number of goods = ₹ 5,500

Loss = one-tenth of its selling price

$= ₹ \dfrac{1}{10} \times 5,500\\[1em] = ₹ \dfrac{5,500}{10}\\[1em] = ₹ 550$

Loss = ₹ 550

(ii) As we know that,

Loss = C.P. - S.P.

Putting the values, we get

₹ 550 = C.P. - ₹ 5,500

C.P. = ₹ 5,500 + ₹ 550

= ₹ 6,050

The cost price of the goods = ₹ 6,050.

(iii)

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

$= \dfrac{550}{6050} \times 100$%

$= \dfrac{55,000}{6050}$%

$= \dfrac{100}{11}$%

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

Hence, T.V. is sold at a loss of $9\dfrac{1}{11}$.

The selling price of a sofa set is $\dfrac{4}{5}$ times of its cost price. Find the gain or the loss as percent.

Answer

Given:

The S.P. of a sofa set = $\dfrac{4}{5}$ times of its C.P.

Let the cost price of sofa set is ₹$100$.

S.P. = ₹$\dfrac{4}{5} \times 100$

= ₹$\dfrac{400}{5}$

= ₹80

(∵ C.P. is greater than S.P., means sofa is sold at a loss.)

Loss = C.P. - S.P.

= ₹100 - ₹80

= ₹20

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

$= \dfrac{20}{100} \times 100$%

$= \dfrac{20}{\cancel{100}} \times \cancel{100}$%

$= 20$%

Hence, Sofa is sold at a loss of 20%.

The cost price of an article is $\dfrac{4}{5}$ times of its selling price. Find the loss or the gain as percent.

Answer

Given:

The C.P. of an article = $\dfrac{4}{5}$ times of its S.P.

Let the S.P. be ₹ $100$.

$\text{C.P.} = ₹ \dfrac{4}{5} \times 100\\[1em] = ₹ \dfrac{400}{5}\\[1em] = ₹ 80$

(∵ S.P. is greater than C.P., means article is sold at gain.)

Gain = S.P. - C.P.

= ₹ 100 - ₹ 80

= ₹ 20

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

$= \dfrac{20}{80} \times 100$%

$= \dfrac{1}{4} \times 100$%

$= \dfrac{100}{4}$%

$= 25$%

Hence, Gain% = 25%

The cost price of an article is 90% of its selling price. What is the profit or the loss as percent ?

Answer

Given:

The C.P. of an article = 90% of its S.P.

Let the S.P. be ₹ 100.

$\text{C.P.} = ₹ \dfrac{90}{100} \times 100\\[1em] = ₹ \dfrac{90}{\cancel{100}}\times\cancel{100}\\[1em] = ₹ 90$

(∵ S.P. is greater than C.P., means article is sold at profit.)

Profit = S.P. - C.P.

= ₹ 100 - ₹ 90

= ₹ 10

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

$= \dfrac{10}{90} \times 100$%

$= \dfrac{1}{9} \times 100$%

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

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

Hence, Profit% = $11\dfrac{1}{9}$%

The cost price of an article is 30 percent less than its selling price. Find the profit or the loss as percent.

Answer

Given:

The C.P. of an article = 30% less than its S.P.

Let the S.P. be ₹ 100.

$\text{C.P.} = \text{S.P.} - \dfrac{30}{100} \times \text{S.P.}\\[1em] \text{C.P.} = ₹100 - \dfrac{30}{100} \times 100\\[1em] = ₹ 100 - \dfrac{30}{\cancel{100}}\times\cancel{100}\\[1em] = ₹ 100 - 30\\[1em] = ₹ 70$

(∵ S.P. is greater than C.P., means article is sold at profit.)

Profit = S.P. - C.P.

= ₹ 100 - ₹ 70

= ₹ 30

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

$= \dfrac{30}{70} \times 100$%

$= \dfrac{3,000}{70}$%

$= \dfrac{300}{7}$%

$= 42\dfrac{6}{7}$%

Hence, Profit% = $42\dfrac{6}{7}$%

A shopkeeper bought 300 eggs at 80 paisa each. 30 eggs were broken in transit and then he sold the remaining eggs at one rupee each. Find his gain or loss as percent.

Answer

C.P. of 1 egg = 80 paisa

C.P. of 300 eggs = 300 x $\dfrac{80}{100}$

= 300 x $\dfrac{4}{5}$

= $\dfrac{1,200}{5}$

= ₹ 240

S.P. of 1 egg = ₹ 1

Total number of eggs = 300

Broken eggs = 30

Remaining eggs = 300 - 30 = 270

S.P. of 270 egg = 270 x ₹ 1 = ₹ 270

(∵ S.P. is greater than C.P.,means eggs are sold at gain.)

Gain = S.P. - C.P.

= ₹ 270 - ₹ 240

= ₹ 30

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

$= \dfrac{30}{240} \times 100$%

$= \dfrac{1}{8} \times 100$%

$= \dfrac{100}{8}$%

$= 12.5$%

Hence, Gain% = 12.5%

By selling an article for ₹ 900, a man gains 20%. Find his cost price and the gain.

Answer

Given:

S.P. = ₹ 900

Gain % = 20%

Let C.P. = $₹x$.

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

Putting the values, we get

$\Rightarrow 20 = \dfrac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{20 \times x}{100}\\[1em] = \dfrac{x}{5}$

As we know:

$\text{Profit} = \text{S.P. - C.P.}\\[1em] \Rightarrow \dfrac{x}{5} = 900 - x\\[1em] \Rightarrow 900 = \dfrac{x}{5} + x\\[1em] \Rightarrow 900 = \dfrac{x}{5} + \dfrac{5x}{5}\\[1em] \Rightarrow 900 = \dfrac{(x + 5x)}{5} \\[1em] \Rightarrow 900 = \dfrac{6x}{5}\\[1em] \Rightarrow x = \dfrac{5 \times 900}{6}\\[1em] \Rightarrow x = \dfrac{4500}{6}\\[1em] \Rightarrow x = 750$

Gain = $\dfrac{x}{5}$

Gain = $\dfrac{750}{5}$ = 150

Hence, C.P. = ₹ 750 and gain = ₹ 150.

By selling an article for ₹ 704, a person loses 12%. Find his cost price and the loss.

Answer

Given:

S.P. = ₹ 704

Loss % = 12%

Let C.P. = $₹x$.

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

Putting the values, we get

$\Rightarrow 12 = \dfrac{\text{Loss}}{x} \times 100\\[1em] \Rightarrow \text{Loss} = \dfrac{12 \times x}{100}\\[1em] = \dfrac{3x}{25}$

As we know:

$\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow \dfrac{3x}{25} = x - 704\\[1em] \Rightarrow 704 = x - \dfrac{3x}{25}\\[1em] \Rightarrow 704 = \dfrac{25x}{25} - \dfrac{3x}{25}\\[1em] \Rightarrow 704 = \dfrac{(25x - 3x)}{25} \\[1em] \Rightarrow 704 = \dfrac{22x}{25}\\[1em] \Rightarrow x = \dfrac{25 \times 704}{22}\\[1em] \Rightarrow x = \dfrac{17,600}{22}\\[1em] \Rightarrow x = ₹ 800$

Loss = $\dfrac{3x}{25}$

Gain = $\dfrac{3 \times 800}{25}$

Gain = $\dfrac{2400}{25}$ = $96$

Hence, C.P. = ₹ 800 and loss = ₹ 96.

Find the selling price :

(i) C.P. = ₹ 352, overheads = ₹ 28 and profit = 20%.

(ii) C.P. = ₹ 576, overheads = ₹ 44 and loss = 16%.

Answer

(i) Given:

C.P. = ₹ 352

Overheads = ₹ 28

Hence, total C.P. = C.P. + overheads

= ₹ 352 + ₹ 28 = ₹ 380

Profit % = 20%

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

Putting the values, we get

$\Rightarrow20 = \dfrac{\text{Profit}}{380} \times 100\\[1em] \Rightarrow\text{Profit} = \dfrac{20 \times 380}{100} \\[1em] = \dfrac{7600}{100} \\[1em] = 76$

As we know:

$\text{Profit} = \text{S.P. - C.P.}\\[1em] \Rightarrow 76 = \text{S.P.} - 380\\[1em] = 380 + 76\\[1em] = 456$

Hence, S.P. = ₹ 456.

(ii) Given:

C.P. = ₹ 576

Overheads = ₹ 44

Hence, total C.P. = C.P. + overheads

= ₹ 576 + ₹ 44 = ₹ 620

Loss % = 16%

Let the C.P. be ₹ $x$.

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

Putting the values, we get

$\Rightarrow16 = \dfrac{\text{Loss}}{620} \times 100\\[1em] \Rightarrow\text{Loss} = \dfrac{16 \times 620}{100} \\[1em] = \dfrac{9,920}{100} \\[1em] = 99.2$

As we know:

$\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow 99.2 = 620 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 620 - 99.2\\[1em] = 520.80$

Hence, S.P. = ₹ 520.80.

If John sells his bicycle for ₹ 637, he will suffer a loss of 9%. For how much should it be sold if he desires a profit of 5% ?

Answer

Given:

S.P. of bicycle = ₹ 637

Loss % = 9%

Let C.P. = $₹x$.

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

Putting the values, we get

$\Rightarrow 9 = \dfrac{\text{Loss}}{x} \times 100\\[1em] \Rightarrow \text{Loss} = \dfrac{9 \times x}{100}\\[1em] = \dfrac{9x}{100}$

As we know:

$\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow \dfrac{9x}{100} = x - 637\\[1em] \Rightarrow 637 = x - \dfrac{9x}{100}\\[1em] \Rightarrow 637 = \dfrac{100x}{100} - \dfrac{9x}{100}\\[1em] \Rightarrow 637 = \dfrac{(100x - 9x)}{100} \\[1em] \Rightarrow 637 = \dfrac{91x}{100}\\[1em] \Rightarrow x = \dfrac{100 \times 637}{91}\\[1em] \Rightarrow x = \dfrac{63,700}{91}\\[1em] \Rightarrow x = 700$

Hence, C.P. = ₹ 700

Profit % = 5 %

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

Putting the values, we get

$\Rightarrow 5 = \dfrac{\text{Profit}}{700} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{5 \times 700}{100}\\[1em] = \dfrac{3500}{100}\\[1em] = 35$

And,

$\text{Profit} = \text{S.P. - C.P.}$

Putting all the values, we get

$\Rightarrow 35 = \text{S.P.} - 700\\[1em] \Rightarrow \text{S.P.} = 35 + 700\\[1em] = 735$

John should sell his bicycle for ₹ 735 to make a profit of 5%.

A man sells a radio set for ₹ 605 and gains 10%. At what price should he sell another radio of the same kind in order to gain 16% ?

Answer

Given:

S.P. of radio set = ₹ 605

Gain % = 10 %

Let C.P. = $₹x$.

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

Putting the values, we get

$\Rightarrow 10 = \dfrac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{10 \times x}{100}\\[1em] = \dfrac{10x}{100}\\[1em] = \dfrac{x}{10}$

As we know:

$\text{Profit} = \text{S.P. - C.P.}\\[1em] \Rightarrow \dfrac{x}{10} = 605 - x\\[1em] \Rightarrow 605 = \dfrac{x}{10} + x\\[1em] \Rightarrow 605 = \dfrac{10x}{10} + \dfrac{x}{10}\\[1em] \Rightarrow 605 = \dfrac{(10x + x)}{10} \\[1em] \Rightarrow 605 = \dfrac{11x}{10}\\[1em] \Rightarrow x = \dfrac{10 \times 605}{11}\\[1em] \Rightarrow x = \dfrac{6,050}{11}\\[1em] \Rightarrow x = 550$

Hence, C.P. = ₹ 550

Profit % = 16 %

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

Putting the values, we get

$\Rightarrow 16 = \dfrac{\text{Profit}}{550} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{16 \times 550}{100}\\[1em] = \dfrac{8800}{100}\\[1em] = 88$

And,

$\text{Profit} = \text{S.P. - C.P.}$

Putting all the values, we get

$\Rightarrow 88 = \text{S.P.} - 550\\[1em] \Rightarrow \text{S.P.} = 88 + 550\\[1em] = 638$

The man should sell the other radio for ₹ 638 in order to make a profit of 16%.

By selling a sofa set for ₹ 2,500, the shopkeeper loses 20%. Find his loss percent or profit percent, if he sells the same sofa set for ₹ 3,150.

Answer

Given:

S.P. of sofa set = ₹ 2,500

Loss % = 20 %

Let C.P. = $₹x$.

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

Putting the values, we get

$\Rightarrow 20 = \dfrac{\text{Loss}}{x} \times 100\\[1em] \Rightarrow \text{Loss} = \dfrac{20 \times x}{100}\\[1em] = \dfrac{x}{5}$

As we know:

$\text{Loss} = \text{C.P. - S.P.}\\[1em] \Rightarrow \dfrac{x}{5} = x - 2,500\\[1em] \Rightarrow 2,500 = x - \dfrac{x}{5}\\[1em] \Rightarrow 2,500 = \dfrac{5x}{5} - \dfrac{x}{5}\\[1em] \Rightarrow 2,500 = \dfrac{(5x - x)}{5} \\[1em] \Rightarrow 2,500 = \dfrac{4x}{5}\\[1em] \Rightarrow x = \dfrac{2,500 \times 5}{4}\\[1em] \Rightarrow x = \dfrac{12,500}{4}\\[1em] \Rightarrow x = 3,125$

When C.P. = ₹ 3,125

New S.P. = ₹ 3,150

(∵ When S.P. is greater than C.P., means sofa set will be sold at a profit.)

Profit = S.P. - C.P.

= ₹ 3,150 - ₹ 3,125

= ₹ 25

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

$= \dfrac{25}{3125} \times 100$%

$= \dfrac{1}{125} \times 100$%

$= \dfrac{100}{125}$%

$= 0.8$%

If the man sells the same sofa set for ₹ 3,150, profit % = 0.8%.

Identical pens are bought at 10 for ₹ 80. If these pens are sold at 25% profit; the S.P. per pen is :

1. ₹ 6

2. ₹ 10

3. ₹ 12

4. ₹ 8

Answer

C.P. of 10 pens = ₹ 80

C.P. of 1 pen = ₹ $\dfrac{80}{10}$ = ₹ 8

Profit = 25%

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

$\Rightarrow 25 = \dfrac{\text{Profit}}{8} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{25 \times 8}{100}\\[1em] = \dfrac{200}{100}\\[1em] = 2$

As we know,

$\text{Profit} = \text{S.P. - C.P.}$

Putting the values, we get

$\Rightarrow 2 = \text{S.P.} - 8\\[1em] \Rightarrow \text{S.P.} = 2 + 8\\[1em] \Rightarrow \text{S.P.} = 10\\[1em]$

Hence,option 2 is the correct option.

If C.P. of 20 identical articles is same as S.P. of 25 articles. The profit or the loss as percent is :

1. 25% loss

2. 25% profit

3. 20% loss

4. 20% profit

Answer

C.P. of 20 articles = S.P. of 25 articles

Let the C.P. of 20 articles be ₹ 100.

The C.P. of 1 article = ₹ $\dfrac{100}{20}$ = ₹ 5

The S.P. of 25 articles = The C.P. of 20 articles = ₹ 100

The S.P. of 1 article = ₹ $\dfrac{100}{25}$ = ₹ 4

(∵ C.P. is greater than S.P., means articles are sold at a loss.)

Loss = C.P. - S.P.

= ₹ (5 - 4) = ₹ 1

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

$= \dfrac{1}{5} \times 100$%

$= \dfrac{100}{5}$%

$= 20$%

Hence,option 3 is the correct option.

The marked price of an article is ₹ 500 and is sold for ₹ 400; the discount given is :

1. 10%

2. 20%

3. 25%

4. none of these

Answer

Given:

M.P. of an article = ₹ 500

S.P. of article = ₹ 400

Discount = M.P. - S.P.

= ₹ 500 - ₹ 400

= ₹ 100

$\text{Discount}$% $= \dfrac{\text{Discount}}{\text{M.P.}}\times 100$%

$= \dfrac{100}{500}\times 100$%

$= \dfrac{1}{5}\times 100$%

$= \dfrac{100}{5}$%

$= 20$%

Hence,option 2 is the correct option.

An article is marked at ₹ 800 and is sold at 20% discount. Its S.P. is :

1. ₹ 160

2. ₹ 960

3. ₹ 640

4. ₹ 780

Answer

Given:

M.P. = ₹ 800

Discount % = 20%

$\text{Discount}$% $= \dfrac{\text{Discount}}{\text{M.P.}} \times 100$

Putting the values, we get

$\Rightarrow\ 20 = \dfrac{\text{Discount}}{800} \times 100\\[1em] \Rightarrow\ \text{Discount} = \dfrac{20 \times 800}{100}\\[1em] = \dfrac{16000}{100}\\[1em] = 160$

And we know,

$\text{Discount} = \text{M.P. - S.P}$

Putting the values,we get

$160 = 800 - \text{S.P}\\[1em] \Rightarrow \text{S.P.} = 800 - 160\\[1em] \Rightarrow \text{S.P.} = 640$

Hence, option 3 is the correct option.

By selling 10 articles, a man gains equal to cost price of 2 articles, the profit made is :

1. 40%

2. 20%

3. 25%

4. 50%

Answer

Let the C.P. of 1 article be ₹ 100.

So, the C.P. of 2 article = ₹ 100 x 2 = ₹ 200

Similarly, the C.P. of 10 article = ₹ 100 x 10 = ₹ 1000

Gain = Cost price of 2 articles = ₹ 200

As we know,

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

$= \dfrac{200}{1000} \times 100$%

$= \dfrac{1}{5} \times 100$%

$= \dfrac{100}{5}$%

$= 20$%

Hence,option 2 is the correct option.

A fruit-seller sells 4 oranges for ₹ 3, gaining 50%. Find :

(i) C.P. of 4 oranges.

(ii) C.P. of one orange.

(iii) S.P. of one orange

(iv) profit made by selling one orange

(v) number of oranges need to be bought and sold in order to gain ₹ 24.

Answer

(i) Given:

S.P. of 4 oranges = ₹ 3

S.P. of 1 orange = ₹ $\dfrac{3}{4}$

Gain = 50%

Let C.P. = $₹x$.

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

Putting the values, we get

$\Rightarrow 50 = \dfrac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{50 \times x}{100}\\[1em] = \dfrac{x}{2}$

As we know:

$\text{Profit} = \text{S.P. - C.P.}\\[1em] \Rightarrow \dfrac{x}{2} = \dfrac{3}{4} - x\\[1em] \Rightarrow \dfrac{3}{4} = \dfrac{x}{2} + x\\[1em] \Rightarrow \dfrac{3}{4} = \dfrac{x}{2} + \dfrac{2x}{2}\\[1em] \Rightarrow \dfrac{3}{4} = \dfrac{(x + 2x)}{2} \\[1em] \Rightarrow \dfrac{3}{4} = \dfrac{3x}{2}\\[1em] \Rightarrow x = \dfrac{3 \times 2}{4 \times 3}\\[1em] \Rightarrow x = \dfrac{6}{12}\\[1em] \Rightarrow x = \dfrac{1}{2}$

C.P. of 1 orange = ₹ $\dfrac{1}{2}$

C.P. of 4 oranges = ₹ $4\times\dfrac{1}{2}$

= ₹ $\dfrac{4}{2}$

= ₹ 2

Hence, C.P. of 4 oranges = ₹ 2.

(ii) C.P. of 1 orange = ₹ $\dfrac{1}{2}$ = ₹ 0.5

(iii) S.P. of 1 orange = ₹ $\dfrac{3}{4}$ = ₹ 0.75

(iv) Profit = S.P. - C.P.

= ₹ 0.75 - ₹ 0.50

= ₹ 0.25

Hence, Profit = ₹ 0.25.

(v) Gain on 1 orange = ₹ 0.25

Let number of oranges needed to gain ₹ 24 be $x$

Gain on $x$ orange = ₹ 0.25 x $x$ = ₹ 24

⇒ $x = \dfrac{24}{0.25}$

⇒ $x = \dfrac{2400}{25}$

⇒ $x = 96$

Hence, 96 oranges need to be bought and sold in order to gain ₹ 24.

A man sells 12 articles for ₹ 80 gaining $33\dfrac{1}{3}$. Find the number of articles bought by the man for ₹ 90.

Answer

Given:

S.P. of 12 articles = ₹ 80

S.P. of 1 article = ₹ $\dfrac{80}{12}$ = ₹ $\dfrac{20}{3}$

Gain = $33\dfrac{1}{3}$ = $\dfrac{100}{3}$

Let C.P. of 1 article = $₹x$.

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

Putting the values, we get

$\Rightarrow \dfrac{100}{3} = \dfrac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{100 \times x}{3 \times 100}\\[1em] = \dfrac{\cancel{100} \times x}{3 \times \cancel{100}}\\[1em] = \dfrac{x}{3}$

As we know:

$\text{Profit} = \text{S.P. - C.P.}\\[1em] \Rightarrow \dfrac{x}{3} = \dfrac{20}{3} - x\\[1em] \Rightarrow \dfrac{20}{3} = \dfrac{x}{3} + x\\[1em] \Rightarrow \dfrac{20}{3} = \dfrac{x}{3} + \dfrac{3x}{3}\\[1em] \Rightarrow \dfrac{20}{3} = \dfrac{(x + 3x)}{3} \\[1em] \Rightarrow \dfrac{20}{3} = \dfrac{4x}{3}\\[1em] \Rightarrow x = \dfrac{20 \times 3}{4 \times 3}\\[1em] \Rightarrow x = \dfrac{60}{12}\\[1em] \Rightarrow x = 5$

C.P. of 1 article = ₹ 5

Let number of articles bought by the man for ₹ 90 be $y$

C.P. of $y$ articles = ₹ 5 x $y$ = ₹ 90

⇒ $y = \dfrac{90}{5}$

⇒ $y = 18$

Hence, 18 articles are bought by the man for ₹ 90.

The selling price of 15 articles is equal to the cost price of 12 articles. Find the gain or loss as percent.

Answer

Let the C.P. of 1 article be ₹ 100.

The C.P. of 12 articles = ₹ 100 x 12 = ₹ 1200

The S.P. of 15 articles = the C.P. of 12 articles

The S.P. of 15 articles = ₹ 1200

The S.P. of 1 article = ₹ $\dfrac{1200}{15}$ = ₹ 80

(∵ C.P. is greater than S.P., means article is sold at a loss.)

Loss = C.P. - S.P.

= ₹ 100 - ₹ 80

= ₹ 20

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

$= \dfrac{20}{100} \times 100$%

$= \dfrac{20}{\cancel{100}} \times \cancel{100}$%

$= 20$%

Hence, loss % = 20%.

A shopkeeper bought rice worth ₹ 4,500. He sold one-third of it at 10% profit. If he desires a profit of 12% on the whole, find :

(i) the selling price of the rest of the rice.

(ii) the percentage profit on the rest of the rice.

Answer

(i) Given:

C.P. of whole rice = ₹ 4,500

Profit desired on the whole = 12 %

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

Putting the values, we get

$12 = \dfrac{\text{Profit}}{4,500} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{12 \times 4,500}{100}\\[1em] = \dfrac{54,000}{100}\\[1em] = 540$

As we know,

$\text{Profit} = \text{S.P. - C.P.}$

Putting the values, we get

$540 = \text{S.P.} - 4,500\\[1em] \Rightarrow \text{S.P.} = 540 + 4,500\\[1em] = 5,040$

C.P. of $\dfrac{1}{3}$rice = ₹ $\dfrac{1}{3} \times 4,500$

= ₹ $\dfrac{4,500}{3}$

= ₹ $1,500$

Gain on it = 10%

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

Putting the values, we get

$10 = \dfrac{\text{Profit}}{1,500} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{10 \times 1,500}{100}\\[1em] = \dfrac{15,000}{100}\\[1em] = 150$

As we know,

$\text{Profit} = \text{S.P. - C.P.}$

Putting the values, we get

$150 = \text{S.P.} - 1,500\\[1em] \Rightarrow \text{S.P.} = 150 + 1,500\\[1em] = 1,650$

The S.P. of the rest of the rice = ₹ 5,040 - ₹ 1,650 = ₹ 3,390

The selling price of the rest of the rice = ₹ 3,390.

(ii) C.P. of the rest of the rice = ₹ 4,500 - ₹ 1,500 = ₹ 3,000

Profit on the rest of the rice = Remaining S.P. - Remaining C.P.

= ₹ 3,390 - ₹ 3,000

= ₹ 390

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

$= \dfrac{390}{3000}\times 100$%

$= \dfrac{13}{100}\times 100$%

$= \dfrac{1300}{100}$%

$= 13$%

The profit percentage of rest of the rice = 13%.

Mohan bought a certain number of notebooks for ₹ 600. He sold $\dfrac{1}{4}$ of them at 5 percent loss. At what price should he sell the remaining notebooks so as to gain 10% on the whole ?

Answer

Given:

C.P. of notebooks = ₹ 600

Gain desired on the whole = 10 %

$\text{Profit}$% $= \dfrac{\text{profit}}{\text{C.P}}\times 100$%

Putting the values, we get

$10 = \dfrac{\text{Profit}}{600} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{10 \times 600}{100}\\[1em] = \dfrac{6000}{100}\\[1em] = 60$

As we know,

$\text{Profit} = \text{S.P. - C.P.}$

Putting the values, we get

$60 = \text{S.P.} - 600\\[1em] \Rightarrow \text{S.P.} = 60 + 600\\[1em] = 660$

C.P. of $\dfrac{1}{4}$number of notebooks = ₹ $\dfrac{1}{4} \times 600$

= ₹ $\dfrac{600}{4}$

= ₹ $150$

Loss of $\dfrac{1}{4}$number of notebooks = 5%

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

Putting the values, we get

$5 = \dfrac{\text{Loss}}{150} \times 100\\[1em] \Rightarrow \text{Loss} = \dfrac{5 \times 150}{100}\\[1em] = \dfrac{750}{100}\\[1em] = 7.5$

As we know,

$\text{Loss} = \text{C.P. - S.P.}$

Putting the values, we get

$7.5 = 150 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 150 - 7.5\\[1em] = 142.5$

The S.P. of rest of notebooks = ₹ 660 - ₹ 142.5 = ₹ 517.5

The selling price of the rest of the notebooks = ₹ 517.50.

Raju sells a watch at 5% profit. Had he sold it for ₹ 24 more he would have gained 11%. Find the cost price of the watch.

Answer

Let C.P. of the watch be ₹ $x$.

Profit % = 5 %

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

Putting the values, we get

$5 = \dfrac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{5 \times x}{100}\\[1em] = \dfrac{x}{20}$

As we know,

$\text{Profit} = \text{S.P. - C.P.}$

Putting the values, we get

$\dfrac{x}{20} = \text{S.P.} - x\\[1em] \Rightarrow \text{S.P.} = \dfrac{x}{20} + x\\[1em] = \dfrac{x}{20} + \dfrac{20x}{20}\\[1em] = \dfrac{(x + 20x)}{20}\\[1em] = \dfrac{21x}{20}$

Given,

If S.P. was 24 more gain would have been 11%

New S.P. = $\dfrac{21x}{20} + 24$

New Profit = New S.P. - C.P.

$= \dfrac{21x}{20} + 24 - x \\[1em] = \dfrac{21x + 480 - 20x}{20} \\[1em] = \dfrac{x + 480}{20}$

New Profit % = 11 %

$\text{Profit}$% $= \dfrac{\text{Profit}}{\text{C.P}}\times 100 \\[1em]$

$\Rightarrow 11 = \dfrac{\dfrac{x + 480}{20}}{x} \times 100 \\[1em] \Rightarrow 11 = \dfrac{x + 480}{20x} \times 100 \\[1em] \Rightarrow 11 = \dfrac{x + 480}{x} \times 5 \\[1em] \Rightarrow 11x = 5x + 2400 \\[1em] \Rightarrow 11x - 5x = 2400 \\[1em] \Rightarrow 6x = 2400 \\[1em] \Rightarrow x = \dfrac{2400}{6} \\[1em] \Rightarrow x = 400$

Hence, cost price of watch = ₹ 400.

A wrist watch is available at a discount of 9%. If the list price of the watch is ₹ 1,400, find the discount given and the selling price of the watch.

Answer

Given:

M.P. of the watch = ₹ 1,400

Discount = 9%

$\text{Discount}$% $= \dfrac{\text{Discount}}{\text{M.P.}}\times 100\\[1em]$

$\Rightarrow 9 = \dfrac{\text{Discount}}{1400}\times 100\\[1em] \Rightarrow \text{Discount} = \dfrac{9 \times 1,400}{100}\\[1em] = \dfrac{12,600}{100}\\[1em] = ₹ 126\\[1em]$

As we know,

$\text{Discount} = \text{M.P. - S.P}\\[1em] \Rightarrow 126 = 1,400 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 1,400 - 126\\[1em] = ₹ 1,274\\[1em]$

Hence, discount = ₹ 126 and S.P. = ₹ 1,274

A shopkeeper sells an article for ₹ 248.50 after allowing a discount of 10% on its list price. Find the list price of the article.

Answer

Given:

S.P. of an article = ₹ 248.50

Discount = 10%

Let the M.P. of the article be ₹ $x$.

As we know,

$\text{Discount }$% $= \dfrac{\text{Discount}}{\text{M.P.}} \times 100$

$\Rightarrow 10 = \dfrac{\text{Discount}}{x} \times 100\\[1em] \Rightarrow \text{Discount} = \dfrac{10 \times x}{100}\\[1em] = \dfrac{10x}{100}\\[1em] = \dfrac{x}{10}$

And

$\text{Discount = M.P. - S.P}\\[1em] \Rightarrow\dfrac{x}{10} = x - 248.50\\[1em] \Rightarrow 248.50 = x - \dfrac{x}{10}\\[1em] \Rightarrow 248.50 = \dfrac{10x}{10} - \dfrac{x}{10}\\[1em] \Rightarrow 248.50 = \dfrac{(10x - x)}{10} \\[1em] \Rightarrow 248.50 = \dfrac{9x}{10} \\[1em] \Rightarrow x = \dfrac{10 \times 248.50}{9} \\[1em] \Rightarrow x = \dfrac{2485}{9} \\[1em] \Rightarrow x = ₹ 276.11 \\[1em]$

Hence, the list price = ₹ 276.11

A shopkeeper buys an article for ₹ 450. He marks it at 20% above the cost price. Find :

(i) the marked price of the article.

(ii) the selling price, if he sells the article at 10 percent discount.

(iii) the percentage discount given by him, if he sells the article for ₹ 496.80.

Answer

(i) Given:

C.P. of an article = ₹ 450.

M.P. of the article = 20% above the C.P.

= C.P. + 20% of C.P.

= ₹ $450 + \dfrac{20}{100} \times 450$

= ₹ $450 + \dfrac{1}{5} \times 450$

= ₹ $450 + \dfrac{450}{5}$

= ₹ $450 + 90$

= ₹ $540$

Hence, M.P. of the article = ₹ $540$.

(ii) M.P. of the article = ₹ $540$

Discount = 10 %

As we know,

$\text{Discount }$% $= \dfrac{\text{Discount}}{\text{M.P.}} \times 100\\[1em]$

$\Rightarrow 10 = \dfrac{\text{Discount}}{540} \times 100\\[1em] \Rightarrow \text{Discount} = \dfrac{10 \times 540}{100}\\[1em] = \dfrac{5400}{100}\\[1em] = 54$

And

$\text{Discount = M.P. - S.P}\\[1em] \Rightarrow 54 = 540 - \text{S.P}\\[1em] \Rightarrow \text{S.P} = 540 - 54\\[1em] \Rightarrow \text{S.P} = ₹ 486$

Hence, S.P. of the article = ₹ 486.

(iii) When M.P. of the article = ₹ 540

S.P. of the article = ₹ 496.80

As we know ,

$\text{Discount = M.P. - S.P.}\\[1em] \text{Discount} = 540 - 496.80\\[1em] \text{Discount} = ₹ 43.2$

And,

$\text{Discount}$% $= \dfrac{\text{Discount}}{\text{M.P.}} \times 100$

$\Rightarrow\text{Discount}$% $= \dfrac{43.2}{540} \times 100$

$= \dfrac{4320}{540}$%

$= 8$%

If S.P. of the article is ₹ 496.80, then the percentage discount is 8%.

The list price of an article is ₹ 800 and is available at a discount of 15 percent. Find :

(i) the selling price of the article;

(ii) the cost price of the article if a profit of $13\dfrac{1}{3}$ is made on selling it.

Answer

(i) Given:

M.P. of an article = ₹ 800

Discount of the article = 15%

$\text{Discount}$% $= \dfrac{\text{Discount}}{\text{M.P.}} \times 100$

$\Rightarrow 15 = \dfrac{\text{Discount}}{800} \times 100\\[1em] \Rightarrow \text{Discount} = \dfrac{15 \times 800}{100}\\[1em] = \dfrac{12000}{100}\\[1em] = 120$

And,

$\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow 120 = 800 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 800 - 120\\[1em] \Rightarrow \text{S.P.} = 680$ Hence, S.P. of the article = ₹ 680.

(ii) S.P. of the article = ₹ 680

Profit = $13\dfrac{1}{3}$ = $\dfrac{40}{3}$

Let the C.P. be ₹ $x$.

As we know,

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

$\Rightarrow \dfrac{40}{3} = \dfrac{\text{Profit}}{x} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{40 \times x}{3 \times 100}\\[1em] = \dfrac{40x}{300}\\[1em] = \dfrac{2x}{15}\\[1em]$

And,

$\text{Profit = S.P. - C.P.}\\[1em] \Rightarrow \dfrac{2x}{15} = 680 - x\\[1em] \Rightarrow \dfrac{2x}{15} + x = 680\\[1em] \Rightarrow \dfrac{2x}{15} + \dfrac{15x}{15} = 680\\[1em] \Rightarrow \dfrac{(2x + 15x)}{15} = 680\\[1em] \Rightarrow \dfrac{17x}{15} = 680\\[1em] \Rightarrow x = \dfrac{680 \times 15}{17}\\[1em] \Rightarrow x = \dfrac{10,200}{17}\\[1em] \Rightarrow x = 600\\[1em]$

Hence, C.P. of the article = ₹ 600.

An article is marked at ₹ 2,250. By selling it at a discount of 12%, the dealer makes a profit of 10%. Find :

(i) the selling price of the article.

(ii) the cost price of the article for the dealer.

Answer

(i) Given:

M.P. of an article = ₹ 2,250

Discount % = 12 %

$\text{Discount}$% $= \dfrac{\text{Discount}}{\text{M.P.}} \times 100$

$\Rightarrow 12 = \dfrac{\text{Discount}}{2250} \times 100\\[1em] \Rightarrow \text{Discount} = \dfrac{12 \times 2250}{100}\\[1em] = \dfrac{27,000}{100}\\[1em] = 270$

$\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow 270 = 2,250 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 2,250 - 270\\[1em] \Rightarrow \text{S.P.} = 1,980$

The S.P. of the article = ₹ 1,980.

(ii) S.P. of the article = ₹ 1,980

Profit of the article = 10%

Let the C.P. of the article be ₹ $x$.

$\text{Profit}$% $= \dfrac{\text{Profit}}{\text{C.P.}}\times 100\\[1em]$

$\Rightarrow 10 = \dfrac{\text{Profit}}{x}\times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{10 \times x}{100}\\[1em] = \dfrac{10x}{100}\\[1em] = \dfrac{x}{10}$

and,

$\text{Profit = S.P. - C.P.}\\[1em] \Rightarrow \dfrac{x}{10} = 1980 - x\\[1em] \Rightarrow \dfrac{x}{10} + x = 1980 \\[1em] \Rightarrow \dfrac{x}{10} + \dfrac{10x}{10} = 1980 \\[1em] \Rightarrow \dfrac{(x + 10x)}{10} = 1980 \\[1em] \Rightarrow \dfrac{11x}{10} = 1980 \\[1em] \Rightarrow x = \dfrac{1980 \times 10}{11} \\[1em] \Rightarrow x = \dfrac{19800}{11} \\[1em] \Rightarrow x = 1800$

The cost price of the article = ₹ 1,800

By selling an article at 20% discount, a shopkeeper gains 25%. If the selling price of the article is ₹ 1,440, find :

(i) the marked price of the article.

(ii) the cost price of the article.

Answer

(i) Given:

Discount on the article = 20%

S.P. of the article = ₹ 1,440

Let the M.P. of the article be ₹$x$.

As we know,

$\text{Discount}$% $= \dfrac{\text{Discount}}{\text{M.P.}} \times 100$

$\Rightarrow 20 = \dfrac{\text{Discount}}{x} \times 100\\[1em] \Rightarrow \text{Discount} = \dfrac{20 \times x}{100}\\[1em] \Rightarrow \text{Discount} = \dfrac{20x}{100}\\[1em] \Rightarrow \text{Discount} = \dfrac{x}{5}\\[1em]$

And,

$\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow \dfrac{x}{5} = x - 1440\\[1em] \Rightarrow 1440 = x - \dfrac{x}{5}\\[1em] \Rightarrow 1440 = \dfrac{5x}{5} - \dfrac{x}{5}\\[1em] \Rightarrow 1440 = \dfrac{(5x - x)}{5} \\[1em] \Rightarrow 1440 = \dfrac{4x}{5} \\[1em] \Rightarrow x = \dfrac{5 \times 1,440}{4} \\[1em] \Rightarrow x = \dfrac{7,200}{4} \\[1em] \Rightarrow x = 1,800$

Hence, M.P. of the article = ₹ 1,800

(ii) S.P. of the article = ₹ 1,440

Gain% of the article = 25%

Let the C.P. be ₹ $y$.

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

$\Rightarrow 25 = \dfrac{\text{Gain}}{y}\times 100\\[1em] \Rightarrow \text{Gain} = \dfrac{25 \times y}{100}\\[1em] \Rightarrow \text{Gain} = \dfrac{25y}{100}\\[1em] \Rightarrow \text{Gain} = \dfrac{y}{4}$

And,

$\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow \dfrac{y}{4} = 1,440 - y\\[1em] \Rightarrow \dfrac{y}{4} + y = 1,440 \\[1em] \Rightarrow \dfrac{y}{4} + \dfrac{4y}{4} = 1,440 \\[1em] \Rightarrow \dfrac{(y + 4y)}{4} = 1,440 \\[1em] \Rightarrow \dfrac{5y}{4} = 1,440 \\[1em] \Rightarrow y = \dfrac{1,440 \times 4}{5} \\[1em] \Rightarrow y = \dfrac{5,760}{5} \\[1em] \Rightarrow y = 1,152$

Hence, C.P. of the article = ₹ 1,152

A shopkeeper marks his goods at 30 percent above the cost price and then gives a discount of 10 percent. Find his gain percent.

Answer

Given:

M.P. of the goods = 30% above the C.P.

Let the C.P. be ₹ $100$.

M.P. = C.P. + 30% of C.P.

= $100 + \dfrac{30}{100} \times 100$

= $100 + \dfrac{30}{\cancel{100}} \times \cancel{100}$

= $100 + 30$

= $130$

So, M.P. of the goods = ₹ $130$

Discount % = 10%

$\text{Discount}$% $= \dfrac{\text{Discount}}{\text{M.P.}} \times 100$

$\Rightarrow 10 = \dfrac{\text{Discount}}{130} \times 100 \\[1em] \Rightarrow \text{Discount} = \dfrac{10 \times 130}{100}\\[1em] = \dfrac{1300}{100}\\[1em] = 13$

Now,

$\text{Discount = M.P. - S.P.} \\[1em] \Rightarrow 13 = 130 - \text{S.P.} \\[1em] \Rightarrow \text{S.P.} = 130 - 13 \\[1em] = 117$

Hence, S.P. of the goods = ₹ $117$

C.P. of the goods = ₹ 100

($\because$ S.P. is greater than C.P., means goods are sold at a gain.)

$\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow \text{Gain} = 117 - 100 \\[1em] \Rightarrow \text{Gain} = 17$

And

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

$\Rightarrow\text{Gain}$% $= \dfrac{17}{100} \times 100$%

$= \dfrac{17}{\cancel{100}} \times \cancel{100}$%

$= 17$%

Hence, Gain percent = 17%

A ready-made garments shop in Delhi allows 20 percent discount on its garments and still makes a profit of 20 percent. Find the marked price of a dress which is bought by the shopkeeper for ₹ 400.

Answer

Given:

C.P. of a dress = ₹ 400

Profit of the dress = 20%

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

$\Rightarrow 20 = \dfrac{\text{Profit}}{400} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{20 \times 400}{100}\\[1em] = \dfrac{8000}{100}\\[1em] = 80\\[1em]$

And,

$\text{Profit = S.P. - C.P.}\\[1em] \Rightarrow 80 = \text{S.P.} - 400\\[1em] \Rightarrow \text{S.P.} = 80 + 400\\[1em] = 480$

S.P. of the dress = ₹ 480

Discount on the dress = 20%

Let the M.P. of the dress = ₹ $x$.

$\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow \text{Discount} = x - 480$

And,

$\text{Discount}$% $= \dfrac{\text{Discount}}{\text{M.P.}} \times 100$

$\Rightarrow 20 = \dfrac{(x - 480)}{x} \times 100\\[1em] \Rightarrow 20 \times x = (x - 480) \times 100\\[1em] \Rightarrow 20x = 100x - 48000\\[1em] \Rightarrow 48000 = 100x - 20x \\[1em] \Rightarrow 48000 = 80x \\[1em] \Rightarrow x = \dfrac{48000}{80} \\[1em] \Rightarrow x = 600$

Hence, M.P. of the dress = ₹ 600.

At 12% discount, the selling price of a pen is ₹ 13.20. Find its marked price. Also find the new selling price of the pen, if it is sold at 5% discount.

Answer

Given:

S.P. of the pen = ₹ 13.20

Discount % = 12%

Let the M.P. of the pen = ₹ $x$.

$\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow \text{Discount} = x - 13.20$

And,

$\text{Discount}$% $= \dfrac{\text{Discount}}{\text{M.P.}} \times 100$

$\Rightarrow 12 = \dfrac{(x - 13.20)}{x} \times 100\\[1em] \Rightarrow 12 \times x = (x - 13.20) \times 100\\[1em] \Rightarrow 12x = 100x - 1320\\[1em] \Rightarrow 1320 = 100x - 12x \\[1em] \Rightarrow 1320 = 88x \\[1em] \Rightarrow x = \dfrac{1320}{88} \\[1em] \Rightarrow x = 15$

Now, M.P. of the pen = ₹ 15

Discount% = 5 %

$\text{Discount}$% $= \dfrac{\text{Discount}}{\text{M.P.}} \times 100$

$\Rightarrow 5 = \dfrac{\text{Discount}}{15}\times 100\\[1em] \Rightarrow \text{Discount} = \dfrac{5 \times 15}{100}\\[1em] = \dfrac{75}{100}\\[1em] = 0.75$

And,

$\text{Discount = M.P. - S.P.}\\[1em] \Rightarrow 0.75 = 15 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 15 - 0.75\\[1em] \Rightarrow \text{S.P.} = 14.25$

Hence, M.P. of pen = ₹ 15 and new S.P. = ₹ 14.25

The cost price of an article is ₹ 2,400 and it is marked at 25% above the cost price. Find the profit and the profit percent, if the article is sold at 15% discount.

Answer

Given:

M.P. of the article = 25% above the C.P.

The C.P. of the article = ₹ 2,400.