# Profit and Loss Discount Questions for SSC CHSL and MTS

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

a)Â 32.68%

b)Â 34.17%

c)Â 37%

d)Â 35.36%

**1)Â AnswerÂ (A)**

**Solution:**

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

Let the Initial value be 100.

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

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

Discounted valueÂ = 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:Â **A shopkeeper sold an article for â‚¹455 at a loss (in â‚¹). If he sells it for â‚¹490, then he would gain an amount four times the loss. At what price (in â‚¹) should he sell the article to gain 25%?

a)Â 575

b)Â 577.50

c)Â 570.50

d)Â 115.50

**2)Â AnswerÂ (B)**

**Solution:**

Let the loss when the shopkeeper sold the article forÂ â‚¹455 = L

and the Cost price of the article = C

$\Rightarrow$ C – 455 = L

$\Rightarrow$ C = L + 455……(1)

According to the problem, when the shopkeeperÂ sells it for â‚¹490, 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 = â‚¹462

Cost price of the article =Â â‚¹462

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

=Â $\frac{125}{100}\times$462

=Â â‚¹577.50

Hence, the correct answer is Option B

**Question 3:Â **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 â‚¹920 and â‚¹1472 respectively, then what is the value of x?

a)Â 18

b)Â 30

c)Â 20

d)Â 25

**3)Â AnswerÂ (D)**

**Solution:**

Cost price of the article =Â â‚¹920

Gain = 20%

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

=Â â‚¹1104

Marked price of the article = â‚¹1472

Discount = x%

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

1104 =Â $\frac{100-x}{100}\times$1472

69Â = $\frac{100-x}{100}\times$92

6900 = 9200 – 92x

92x = 2300

x = 25

Hence, the correct answer is Option D

**Question 4:Â **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)Â 33

b)Â 25

c)Â 33.33

d)Â 33.43

**4)Â AnswerÂ (C)**

**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 =Â $\frac{400}{3}$C

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

= 33.33%

Hence, the correct answer is Option C

**Question 5:Â **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)Â 128

b)Â 132

c)Â 154

d)Â 256

**5)Â AnswerÂ (A)**

**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

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**Question 6:Â **The cost price of an article is â‚¹280. A shopkeeper sells it by allowing 16% discount on its marked price and still gains 20%. What is the marked price(in â‚¹) of the article?

a)Â 400

b)Â 360

c)Â 420

d)Â 350

**6)Â AnswerÂ (A)**

**Solution:**

The cost price of article = â‚¹280

Gain = 20%

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

=Â â‚¹336

Let the marked price of the article = M

Discount = 16%

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

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

$\Rightarrow$Â M = 400

Marked price of the article =Â â‚¹400

Hence, the correct answer is Option A

**Question 7:Â **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)Â 22

b)Â 18

c)Â 21

d)Â 20

**7)Â AnswerÂ (C)**

**Solution:**

Let the cost price of the article = 100C

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

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

=Â $\frac{290}{3}$C

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

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

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

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

=Â $\frac{125C}{6\times100C}\times100$

= 20.833%

= 21% (approximately)

Hence, the correct answer is Option C

**Question 8:Â **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 â‚¹320 more than the discount given by B, then what is the marked price (in â‚¹) of the item?

a)Â 3200

b)Â 32000

c)Â 30000

d)Â 25000

**8)Â AnswerÂ (B)**

**Solution:**

Let the marked price of the item = M

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

Discount = $\frac{25}{100}$M =Â $\frac{1}{4}$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 =Â $\frac{95}{100}\times\frac{80}{100}\times$M =Â $\frac{19}{25}$M

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

According to the problem,Â discount given by A is â‚¹320 more than the discount given by B.

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

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

M = â‚¹32000

Hence, the correct answer is Option B

**Question 9:Â **A customer wanted to purchase an item marked for â‚¹10000. 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)Â first offer by â‚¹68

b)Â second offer by â‚¹68

c)Â first offer by â‚¹32

d)Â second offer by â‚¹100

**9)Â AnswerÂ (A)**

**Solution:**

**25% flat discount**

Selling price of the item =Â $\frac{75}{100}\times10000$ =Â â‚¹7500

**Successive discounts of 14% and 12%**

Price of the item after 14% discount =Â $\frac{86}{100}\times10000$ =Â â‚¹8600

Price of the item after 12% discount =Â $\frac{88}{100}\times8600$ =Â â‚¹7568

Difference between selling prices =Â 7568 – 7500 =Â â‚¹68

First offer is betterÂ by â‚¹68.

Hence, the correct answer is Option A

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

a)Â Profit of 25%

b)Â No profit no loss

c)Â Loss of 30%

d)Â Loss of 20%

**10)Â AnswerÂ (D)**

**Solution:**

Let the cost price of 60 articles = C

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

Selling price of 75 articles = C

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

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

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

=Â $\frac{60}{300}\times100$

= 20%

Hence, the correct answer is Option D

**Question 11:Â **The marked price of an article is â‚¹180. Renu sells it after 20% discount on its marked price and still gains 25%, The cost price (in â‚¹) of the article is:

a)Â 120.80

b)Â 110.80

c)Â 115.20

d)Â 125.50

**11)Â AnswerÂ (C)**

**Solution:**

Marked price of an article is â‚¹180.

Discount = 20%

Selling price of the article = $\frac{80}{100}\times$180 =Â â‚¹144

Let the cost price of the article =Â C

Profit = 25%

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

$\frac{125}{100}$C =Â 144

C =Â $\frac{576}{5}$

C = 115.2

Cost price of the article =Â â‚¹115.20

Hence, the correct answer is Option C

**Question 12:Â **The cost price of an article is â‚¹250. A shopkeeper gains 20% by selling it at a discount of 36% on its marked price. What is the marked price (in â‚¹) of the article?

a)Â 450

b)Â 380.50

c)Â 475

d)Â 468.75

**12)Â AnswerÂ (D)**

**Solution:**

Cost price of the article is â‚¹250.

Profit = 20%

Selling price of the article = $\frac{120}{100}\times$250 =Â â‚¹300

Let the marked price of the article = M

Discount = 36%

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

M = 468.75

Marked price of the article =Â â‚¹468.75

Hence, the correct answer is Option D

**Question 13:Â **Radha bought a fridge and a washing machine together for â‚¹57300. 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 â‚¹) is:

a)Â 28650

b)Â 34500

c)Â 24500

d)Â 22800

**13)Â AnswerÂ (B)**

**Solution:**

Let the cost price of fridge = x

Profit = 15%

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

Cost price ofÂ washing machine =Â 57300 – x

Loss = 24%

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

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

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

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

191x =Â 76$\times$57300

x =Â 76$\times$300

x =Â 22800

Cost price of fridge =Â â‚¹22800

Cost price of washing machine = 57300 – x

=Â 57300 – 22800

=Â â‚¹34500

Hence, the correct answer is Option B

**Question 14:Â **The marked price of an article is â‚¹5320. 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 â‚¹) of the article?

a)Â â‚¹4522

b)Â â‚¹4127

c)Â â‚¹4000

d)Â â‚¹4386

**14)Â AnswerÂ (D)**

**Solution:**

The marked price of an article is â‚¹5320.

First discount = 15%

Price of the article after 15% discount =Â $\frac{85}{100}\times5320$ =Â â‚¹4522

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

Selling price of the article after 3% discount =Â $\frac{97}{100}\times4522$ =Â â‚¹4386.34

=Â â‚¹4386 (approximately)

Hence, the correct answer is Option D

**Question 15:Â **Hari suffered a loss of 8% by selling an article. If he had sold it for â‚¹300 more, he would have made a profit of 4%. Find his CP (in â‚¹).

a)Â 2400

b)Â 2250

c)Â 2575

d)Â 2500

**15)Â AnswerÂ (D)**

**Solution:**

Let the cost price of article = 100C

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

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

If he had sold it for â‚¹300 more, he would have made a profit of 4%.

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

92C + 300 = 104C

12C = 300

C = 25

The cost price of article =Â â‚¹2500

Hence, the correct answer is Option D

**Question 16:Â **What price (in â‚¹) should Radha mark on a bag which costs â‚¹1680 so as to earn a profit of 25% after allowing a discount of 16% on the marked price?

a)Â 2800

b)Â 2000

c)Â 2100

d)Â 2500

**16)Â AnswerÂ (D)**

**Solution:**

Cost price of the bag =Â â‚¹1680

Profit = 25%

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

Let the marked price of the bag = M

Discount = 16%

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

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

$\Rightarrow$Â M = 2500

Marked price of the bag = M =Â â‚¹2500

Hence, the correct answer is Option D

**Question 17:Â **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 profitâ€™ loss percent?

a)Â Profit, $3\frac{7}{11}\%$

b)Â Loss, $4\frac{6}{11}\%$

c)Â Profit, $4\frac{7}{11}\%$

d)Â Loss, $8\frac{1}{3}\%$

**17)Â AnswerÂ (A)**

**Solution:**

Let the cost price of first item = 100C

Profit on first item = 20%

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

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

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

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

=Â $\frac{8C}{220C}\times100$

=Â $\frac{40}{11}$

=Â $3\frac{7}{11}\%$

Hence, the correct answer is Option A

**Question 18:Â **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 â‚¹40 less than the profit made by A. What is the cost price (in â‚¹) of the article for A?

a)Â 240

b)Â 640

c)Â 546

d)Â 400

**18)Â AnswerÂ (B)**

**Solution:**

Let the cost price of A = 100C

Profit percentage of AÂ = 25%

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

The profit made by B is â‚¹40 less than the profit made by A.

$\frac{75}{4}$C = 25C – 40

25C –Â $\frac{75}{4}$C = 40

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

C =Â $\frac{32}{5}$

Cost price of the article for A =Â 100C =Â $100\times\frac{32}{5}$ =Â â‚¹640

Hence, the correct answer is Option B

**Question 19:Â **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)Â 15

b)Â 20

c)Â 16

d)Â 12.5

**19)Â AnswerÂ (C)**

**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 =Â $\frac{100-x}{100}\times$127C

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

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

$\Rightarrow$Â 100 – x = 84

$\Rightarrow$Â x = 16

Hence, the correct answer is Option C

**Question 20:Â **A shopkeeper bought a machine for â‚¹4600 and spent â‚¹500 on its repairs and transport. He marked the machine at 8% above the over all cost price. If he sold the machine for â‚¹4681.80 after giving x% discount, then the value of x is:

a)Â 15

b)Â 20

c)Â 12

d)Â 18

**20)Â AnswerÂ (A)**

**Solution:**

Total cost price =Â 4600 + 500 = â‚¹5100

Marked price =Â $\frac{108}{100}\times5100$ =Â â‚¹5508

Discount = x%

Selling price =Â â‚¹4681.80

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

100 – x = $\frac{468180}{5508}$

100 – x = 85

x = 15

Hence, the correct answer is Option A

**Question 21:Â **If the price of an eraser is reduced by 25%, a person can buy three more erasers for â‚¹ 2. How many erasers can be bought for â‚¹ 2 as the original price?

a)Â 10

b)Â 8

c)Â 9

d)Â 12

**21)Â AnswerÂ (C)**

**Solution:**

Let the original price of 1 eraser = $a$

Number of erasers that can be bought forÂ â‚¹2 =Â $\frac{2}{a}$

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

Number of erasers that can be bought for â‚¹2 after reduction in price =Â $\frac{2}{\frac{3}{4}a}$ =Â $\frac{8}{3a}$

According to the problem,

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

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

$\Rightarrow$ Â $\frac{2}{3a}=3$

$\Rightarrow$ Â $a=\frac{2}{9}$

$\therefore\ $Number of erasers that be bought forÂ â‚¹2 with original price =Â $\frac{2}{a}$ = $\frac{2}{\frac{2}{9}}$Â = 9

Hence, the correct answer is Option C

**Question 22:Â **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)Â 12.5%

b)Â 11.5%

c)Â 12%

d)Â 10%

**22)Â AnswerÂ (A)**

**Solution:**

Let the cost price of the article = C

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

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

Discount% = 10%

Selling price of the article =Â $\frac{90}{100}\times\frac{5}{4}$C =Â $\frac{9}{8}$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:Â **On selling 26 balls for â‚¹ 1,350, there is a loss equal to the cost price of eight balls. The cost price of a ball is:

a)Â â‚¹ 60

b)Â â‚¹ 65

c)Â â‚¹ 75

d)Â â‚¹ 70

**23)Â AnswerÂ (C)**

**Solution:**

Let the cost price of 1 ball = c

Cost price of 26 balls = 26c

Given, Selling price of 26 balls = â‚¹ 1350

Loss = 8c

$\Rightarrow$Â 26c – 1350 = 8c

$\Rightarrow$Â 18c = 1350

$\Rightarrow$Â c = 75

$\therefore\ $Cost price of a ball = â‚¹ 75

Hence, the correct answer is Option C

**Question 24:Â **A man sold his bike for â‚¹ 25,000 at 25% profit. At what price would it he have sold if he had incurred a loss of 15%?

a)Â â‚¹ 19,000

b)Â â‚¹ 17,000

c)Â â‚¹ 16,000

d)Â â‚¹ 18,000

**24)Â AnswerÂ (B)**

**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 = â‚¹ 25,000

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

$\Rightarrow$Â C = 20000

Cost price of the bike = â‚¹ 20,000

Selling price of the bike at 15% loss =Â $\frac{85}{100}\times20000$ = â‚¹ 17,000

Hence, the correct answer is Option B

**Question 25:Â **The printed price on a book is â‚¹ 150. If it is sold after two successive discounts of 30% and 40%, then find its selling price.

a)Â â‚¹ 63

b)Â â‚¹ 64

c)Â â‚¹ 66

d)Â â‚¹ 65

**25)Â AnswerÂ (A)**

**Solution:**

Given, printed price on the book =Â â‚¹ 150

Price of the book after 30% discount = $\frac{70}{100}\times150$ = â‚¹ 105

Selling price of the book after 40% discount =Â $\frac{60}{100}\times105$ =Â â‚¹ 63

Hence, the correct answer is Option A