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# Profit and Loss Discount Questions for SSC CHSL and MTS

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Question 1: A single discount equivalent to three simple discounts of 10%, 12%, and 15% is:

a) 32.68%

b) 34.17%

c) 37%

d) 35.36%

Solution:

The successive discounts are 10%,12% and 15%

Let the Initial value be 100.

According to question, $100\times\ \frac{\left(100-10\right)}{100}\times\ \frac{\left(100-12\right)}{100}\times\ \frac{\left(100-15\right)}{100}$

i.e; $100\times\ \frac{90}{100}\times\ \frac{88}{100}\times\ \frac{85}{100}$

Discounted value = 67.32 %

Equivalent discount = initial value – discounted value

= 100 – 67.32 = 32.68 .

Hence option A is correct.

Another method :

Discount is also called successive decrease

if x and y are two successive discounts then ,

$x\ +\ y\ -\frac{\left(x\times\ y\right)}{100}$

first we take first two discount 10% and 12%

$\therefore\ 10\ +\ 12\ -\frac{10\times\ 12}{100}=\ 20.8\ \%$

Now we take,

20.8% and 15% ,

$\therefore\ 20.8\ +\ 15\ -\frac{20.8\times\ 15}{100}=\ 32.68\ \%$

Question 2: A shopkeeper sold an article for ₹455 at a loss (in ₹). If he sells it for ₹490, then he would gain an amount four times the loss. At what price (in ₹) should he sell the article to gain 25%?

a) 575

b) 577.50

c) 570.50

d) 115.50

Solution:

Let the loss when the shopkeeper sold the article for ₹455 = L

and the Cost price of the article = C

$\Rightarrow$ C – 455 = L

$\Rightarrow$ C = L + 455……(1)

According to the problem, when the shopkeeper sells it for ₹490, then he would gain an amount four times the loss.

$\Rightarrow$ 490 – C = 4L

$\Rightarrow$ 490 – (L + 455) = 4L

$\Rightarrow$ 35 = 5L

$\Rightarrow$ L = 7

From (1),

C = L + 455 = 7 + 455 = ₹462

Cost price of the article = ₹462

Selling price of the article when the shopkeeper sells at 25% gain = $\frac{125}{100}\times$C

= $\frac{125}{100}\times$462

= ₹577.50

Hence, the correct answer is Option B

Question 3: A shopkeeper marks an article at a price such that after giving a discount of x%, he gains 20%. If the cost price and the marked price of the article are ₹920 and ₹1472 respectively, then what is the value of x?

a) 18

b) 30

c) 20

d) 25

Solution:

Cost price of the article = ₹920

Gain = 20%

Selling price of the article = $\frac{120}{100}\times$920

= ₹1104

Marked price of the article = ₹1472

Discount = x%

Selling price of the article = $\frac{100-x}{100}\times$1472

1104 = $\frac{100-x}{100}\times$1472

69 = $\frac{100-x}{100}\times$92

6900 = 9200 – 92x

92x = 2300

x = 25

Hence, the correct answer is Option D

Question 4: In festival season, a shopkeeper allows a discount of 10% on every item. Even after giving the discount, he makes a profit of 20%. If he does not give any discount, then what will be his profit percent? (correct to 2 decimal places)

a) 33

b) 25

c) 33.33

d) 33.43

Solution:

Let the cost price of the article = 100C

Profit = 20%

Selling price of the article = $\frac{120}{100}\times$100C = 120C

Discount = 10%

$\frac{90}{100}\times$Marked price = 120C

Marked price of the article = $\frac{400}{3}$C

When no discount is provided,

Selling price = $\frac{400}{3}$C

Profit% = $\frac{\frac{400}{3}C-100C}{100C}\times100$

= 33.33%

Hence, the correct answer is Option C

Question 5: A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?

a) 128

b) 132

c) 154

d) 256

Solution:

Using mixture and alligation method, Ratio of the quantity of rice sold at 20% profit and 5% loss = 20 : 5

= 4 : 1

Quantity of rice sold at 5% loss = $\frac{1}{4+1}\times$640

= 128 kg

Hence, the correct answer is Option A

Question 6: The cost price of an article is ₹280. A shopkeeper sells it by allowing 16% discount on its marked price and still gains 20%. What is the marked price(in ₹) of the article?

a) 400

b) 360

c) 420

d) 350

Solution:

The cost price of article = ₹280

Gain = 20%

Selling price of the article = $\frac{120}{100}\times$280

= ₹336

Let the marked price of the article = M

Discount = 16%

Selling price of the article = $\frac{84}{100}$M

$\Rightarrow$  336 = $\frac{84}{100}$M

$\Rightarrow$  M = 400

Marked price of the article = ₹400

Hence, the correct answer is Option A

Question 7: A shop keeper sold an article at four-fifth of the marked price and suffered a loss of $3 \frac{1}{3}\%$. Find the profit percent, if he sold the article at the marked price. (correct to nearest integer)

a) 22

b) 18

c) 21

d) 20

Solution:

Let the cost price of the article = 100C

Loss = $3 \frac{1}{3}\%$ = $\frac{10}{3}\%$

Selling price of the article = 100C – $\frac{\frac{10}{3}}{100}\times$100C

= $\frac{290}{3}$C

Shop keeper sold the article at four-fifth of the marked price.

$\frac{290}{3}$C = $\frac{4}{5}\times$Marked price of the article

Marked price of the article = $\frac{725}{6}$C

Profit percentage when article is sold at marked price = $\frac{\frac{725}{6}C-100C}{100C}\times100$

= $\frac{125C}{6\times100C}\times100$

= 20.833%

= 21% (approximately)

Hence, the correct answer is Option C

Question 8: Trader A gives a single discount of 25% and Trader B gives two successive discounts of 20% and 5% on an identical item. If the discount given by A is ₹320 more than the discount given by B, then what is the marked price (in ₹) of the item?

a) 3200

b) 32000

c) 30000

d) 25000

Solution:

Let the marked price of the item = M

i) Trader A gives a single discount of 25%.

Discount = $\frac{25}{100}$M = $\frac{1}{4}$M

ii) Trader B gives two successive discounts of 20% and 5%.

Price of the item after 20% discount = $\frac{80}{100}\times$M

Price of the item after 5% discount = $\frac{95}{100}\times\frac{80}{100}\times$M = $\frac{19}{25}$M

Total discount given trader B = M – $\frac{19}{25}$M = $\frac{6}{25}$M

According to the problem, discount given by A is ₹320 more than the discount given by B.

$\frac{1}{4}$M = $\frac{6}{25}$M + 320

$\frac{25M-24M}{100}=320$

M = ₹32000

Hence, the correct answer is Option B

Question 9: A customer wanted to purchase an item marked for ₹10000. Shopkeeper offered two types of discounts, 25% flat discount or successive discounts of 14% and 12%. Which is the better offer for the customers and by how much?

a) first offer by ₹68

b) second offer by ₹68

c) first offer by ₹32

d) second offer by ₹100

Solution:

25% flat discount

Selling price of the item = $\frac{75}{100}\times10000$ = ₹7500

Successive discounts of 14% and 12%

Price of the item after 14% discount = $\frac{86}{100}\times10000$ = ₹8600

Price of the item after 12% discount = $\frac{88}{100}\times8600$ = ₹7568

Difference between selling prices = 7568 – 7500 = ₹68

First offer is better by ₹68.

Hence, the correct answer is Option A

Question 10: If selling price of 75 articles is equal to cost price of 60 articles, then the approximate loss or gain percent is:

a) Profit of 25%

b) No profit no loss

c) Loss of 30%

d) Loss of 20%

Solution:

Let the cost price of 60 articles = C

Cost price of 1 article = $\frac{C}{60}$

Selling price of 75 articles = C

Selling price of 1 article = $\frac{C}{75}$

Loss% = $\frac{\frac{C}{60}-\frac{C}{75}}{\frac{C}{60}}\times100$

= $\frac{\frac{5C-4C}{300}}{\frac{C}{60}}\times100$

= $\frac{60}{300}\times100$

= 20%

Hence, the correct answer is Option D

Question 11: The marked price of an article is ₹180. Renu sells it after 20% discount on its marked price and still gains 25%, The cost price (in ₹) of the article is:

a) 120.80

b) 110.80

c) 115.20

d) 125.50

Solution:

Marked price of an article is ₹180.

Discount = 20%

Selling price of the article = $\frac{80}{100}\times$180 = ₹144

Let the cost price of the article = C

Profit = 25%

Selling price of the article = $\frac{125}{100}$C

$\frac{125}{100}$C = 144

C = $\frac{576}{5}$

C = 115.2

Cost price of the article = ₹115.20

Hence, the correct answer is Option C

Question 12: The cost price of an article is ₹250. A shopkeeper gains 20% by selling it at a discount of 36% on its marked price. What is the marked price (in ₹) of the article?

a) 450

b) 380.50

c) 475

d) 468.75

Solution:

Cost price of the article is ₹250.

Profit = 20%

Selling price of the article = $\frac{120}{100}\times$250 = ₹300

Let the marked price of the article = M

Discount = 36%

$\frac{64}{100}\times$M = 300

M = 468.75

Marked price of the article = ₹468.75

Hence, the correct answer is Option D

Question 13: Radha bought a fridge and a washing machine together for ₹57300. She sold the fridge at a profit of 15% and washing machine at a loss of 24% and both are sold at the same price. The cost price of washing machine(in ₹) is:

a) 28650

b) 34500

c) 24500

d) 22800

Solution:

Let the cost price of fridge = x

Profit = 15%

Selling price of fridge = $\frac{115}{100}$x

Cost price of washing machine = 57300 – x

Loss = 24%

Selling price of washing machine = $\frac{76}{100}\left(57300-\text{x}\right)$

According to the problem, both are sold at same price.

$\frac{115}{100}$x = $\frac{76}{100}\left(57300-\text{x}\right)$

115x + 76x = 76$\times$57300

191x = 76$\times$57300

x = 76$\times$300

x = 22800

Cost price of fridge = ₹22800

Cost price of washing machine = 57300 – x

= 57300 – 22800

= ₹34500

Hence, the correct answer is Option B

Question 14: The marked price of an article is ₹5320. It is subject to two successive discounts, the first being 15%, and the second at a rate of 20% of the first. What is the selling price (to nearest ₹) of the article?

a) ₹4522

b) ₹4127

c) ₹4000

d) ₹4386

Solution:

The marked price of an article is ₹5320.

First discount = 15%

Price of the article after 15% discount = $\frac{85}{100}\times5320$ = ₹4522

Second discount = 20% of 15% = $\frac{20}{100}\times$15% = 3%

Selling price of the article after 3% discount = $\frac{97}{100}\times4522$ = ₹4386.34

= ₹4386 (approximately)

Hence, the correct answer is Option D

Question 15: Hari suffered a loss of 8% by selling an article. If he had sold it for ₹300 more, he would have made a profit of 4%. Find his CP (in ₹).

a) 2400

b) 2250

c) 2575

d) 2500

Solution:

Let the cost price of article = 100C

Hari suffered a loss of 8% by selling an article.

Selling price of the article = $\frac{92}{100}\times$100C = 92C

If he had sold it for ₹300 more, he would have made a profit of 4%.

92C + 300 = $\frac{104}{100}\times$100C

92C + 300 = 104C

12C = 300

C = 25

The cost price of article = ₹2500

Hence, the correct answer is Option D

Question 16: What price (in ₹) should Radha mark on a bag which costs ₹1680 so as to earn a profit of 25% after allowing a discount of 16% on the marked price?

a) 2800

b) 2000

c) 2100

d) 2500

Solution:

Cost price of the bag = ₹1680

Profit = 25%

Selling price of the bag = $\frac{125}{100}\times1680$

Let the marked price of the bag = M

Discount = 16%

Selling price of the bag = $\frac{84}{100}\times$M

$\Rightarrow$  $\frac{84}{100}\times$M = $\frac{125}{100}\times1680$

$\Rightarrow$  M = 2500

Marked price of the bag = M = ₹2500

Hence, the correct answer is Option D

Question 17: A shopkeeper sold two items. The selling price of the first item equals the cost price of the second item. He sold the first item at a profit of 20% and the second item at a loss of 10%. What is his overall profit’ loss percent?

a) Profit, $3\frac{7}{11}\%$

b) Loss, $4\frac{6}{11}\%$

c) Profit, $4\frac{7}{11}\%$

d) Loss, $8\frac{1}{3}\%$

Solution:

Let the cost price of first item = 100C

Profit on first item = 20%

Selling price of first item = $\frac{120}{100}\times$100C = 120C

The selling price of the first item equals the cost price of the second item.

Cost price of the second item = 120C

Loss on second item = 10%

Selling price of second item = $\frac{90}{100}\times$120C = 108C

Total cost price = 100C + 120C = 220C

Total selling price = 120C + 108C = 228C

Overall profit percentage = $\frac{228C-220C}{220C}\times100$

= $\frac{8C}{220C}\times100$

= $\frac{40}{11}$

= $3\frac{7}{11}\%$

Hence, the correct answer is Option A

Question 18: A sold an article to B at a profit of 25%. B sold it to C at a profit of 15%. The profit made by B is ₹40 less than the profit made by A. What is the cost price (in ₹) of the article for A?

a) 240

b) 640

c) 546

d) 400

Solution:

Let the cost price of A = 100C

Profit percentage of A = 25%

Profit of A = $\frac{25}{100}\times$100C = 25C

Selling price of A = Cost price of B = 100C + 25C = 125C

Profit percentage of B = 15%

Profit of B = $\frac{15}{100}\times$125C = $\frac{75}{4}$C

The profit made by B is ₹40 less than the profit made by A.

$\frac{75}{4}$C = 25C – 40

25C – $\frac{75}{4}$C = 40

$\frac{25}{4}$C = 40

C = $\frac{32}{5}$

Cost price of the article for A = 100C = $100\times\frac{32}{5}$ = ₹640

Hence, the correct answer is Option B

Question 19: An article is marked 27% above its cost price. If x % discount is allowed on the marked price and still there is a profit of 6.68%, then what is the value of x ?

a) 15

b) 20

c) 16

d) 12.5

Solution:

Let the cost price of the article = 100C

Profit = 6.68%

Selling price of the article = 106.68C

Article is marked 27% above its cost price.

Marked price of the article = 127C

Discount = x%

Selling price of the article = $\frac{100-x}{100}\times$127C

$\Rightarrow$  $\frac{100-x}{100}\times$127C = 106.68C

$\Rightarrow$  100 – x = $\frac{10668}{127}$

$\Rightarrow$  100 – x = 84

$\Rightarrow$  x = 16

Hence, the correct answer is Option C

Question 20: A shopkeeper bought a machine for ₹4600 and spent ₹500 on its repairs and transport. He marked the machine at 8% above the over all cost price. If he sold the machine for ₹4681.80 after giving x% discount, then the value of x is:

a) 15

b) 20

c) 12

d) 18

Solution:

Total cost price = 4600 + 500 = ₹5100

Marked price = $\frac{108}{100}\times5100$ = ₹5508

Discount = x%

Selling price = ₹4681.80

$\frac{100-x}{100}\times5508=4681.80$

100 – x = $\frac{468180}{5508}$

100 – x = 85

x = 15

Hence, the correct answer is Option A

Question 21: If the price of an eraser is reduced by 25%, a person can buy three more erasers for ₹ 2. How many erasers can be bought for ₹ 2 as the original price?

a) 10

b) 8

c) 9

d) 12

Solution:

Let the original price of 1 eraser = $a$

Number of erasers that can be bought for ₹2 = $\frac{2}{a}$

Price of 1 eraser when reduced by 25% = $\frac{75}{100}a$ = $\frac{3}{4}a$

Number of erasers that can be bought for ₹2 after reduction in price = $\frac{2}{\frac{3}{4}a}$ = $\frac{8}{3a}$

According to the problem,

$\frac{2}{a}+3=\frac{8}{3a}$

$\Rightarrow$  $\frac{8}{3a}-\frac{2}{a}=3$

$\Rightarrow$  $\frac{2}{3a}=3$

$\Rightarrow$  $a=\frac{2}{9}$

$\therefore\$Number of erasers that be bought for ₹2 with original price = $\frac{2}{a}$ = $\frac{2}{\frac{2}{9}}$ = 9

Hence, the correct answer is Option C

Question 22: The marked price of an article is 25% more than its cost price. If 10% discount is given on the marked price, then what is the profit percentage?

a) 12.5%

b) 11.5%

c) 12%

d) 10%

Solution:

Let the cost price of the article = C

Given, Marked price of the article is 25% more than its cost price

$\Rightarrow$  Marked price of the article = $\frac{125}{100}$C = $\frac{5}{4}$C

Discount% = 10%

Selling price of the article = $\frac{90}{100}\times\frac{5}{4}$C = $\frac{9}{8}$C

$\therefore\$Profit Percentage = $\frac{\frac{9}{8}C-C}{C}\times100=\frac{1}{8}\times100=$ 12.5%

Hence, the correct answer is Option A

Question 23: On selling 26 balls for ₹ 1,350, there is a loss equal to the cost price of eight balls. The cost price of a ball is:

a) ₹ 60

b) ₹ 65

c) ₹ 75

d) ₹ 70

Solution:

Let the cost price of 1 ball = c

Cost price of 26 balls = 26c

Given, Selling price of 26 balls = ₹ 1350

Loss = 8c

$\Rightarrow$  26c – 1350 = 8c

$\Rightarrow$  18c = 1350

$\Rightarrow$  c = 75

$\therefore\$Cost price of a ball = ₹ 75

Hence, the correct answer is Option C

Question 24: A man sold his bike for ₹ 25,000 at 25% profit. At what price would it he have sold if he had incurred a loss of 15%?

a) ₹ 19,000

b) ₹ 17,000

c) ₹ 16,000

d) ₹ 18,000

Solution:

Let the cost price of bike = C

Profit% = 25%

$\Rightarrow$ Selling price of the bike = $\frac{125}{100}$C

Given, Selling price of the bike = ₹ 25,000

$\Rightarrow$ $\frac{125}{100}$C = 25000

$\Rightarrow$  C = 20000

Cost price of the bike = ₹ 20,000

Selling price of the bike at 15% loss = $\frac{85}{100}\times20000$ = ₹ 17,000

Hence, the correct answer is Option B

Question 25: The printed price on a book is ₹ 150. If it is sold after two successive discounts of 30% and 40%, then find its selling price.

a) ₹ 63

b) ₹ 64

c) ₹ 66

d) ₹ 65

Price of the book after 30% discount = $\frac{70}{100}\times150$ = ₹ 105
Selling price of the book after 40% discount = $\frac{60}{100}\times105$ = ₹ 63