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# Profit and Loss Discount Questions for SSC MTS

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Question 1: An article was sold at a loss of 12%. If it was sold for ₹ 630 more, then there would have been a gain of 6%. Find the cost price of the article.

a) ₹ 3,500

b) ₹ 2,800

c) ₹ 2,500

d) ₹ 3,000

1) Answer (A)

Solution:

Let the cost price of the article = C

Selling price of the article at 12% loss = $\frac{88}{100}$C

Selling price of the article at 6% gain = $\frac{106}{100}$C

According to the problem,

$\frac{88}{100}$C $+ 630 = \frac{106}{100}$C

$\Rightarrow$  $\frac{106}{100}$C $- \frac{88}{100}$C $=630$

$\Rightarrow$  $\frac{18}{100}$C $=630$

$\Rightarrow$  C = 3500

$\therefore\$Cost price of the article = ₹ 3,500

Hence, the correct answer is Option A

Question 2: The printed price of a cooker is ₹ 2,000, and discounts are 30%, 20% and 10%, respectively. Find the selling price of the cooker.

a) ₹ 1,002

b) ₹ 1,008

c) ₹ 1,004

d) ₹ 1,006

2) Answer (B)

Solution:

Given, Marked price(Printed price) of the cooker = ₹ 2,000

Price of the cooker after 30% discount = $\frac{70}{100}\times2000$ = ₹ 1,400

Price of the cooker after 20% discount = $\frac{80}{100}\times1400$ = ₹ 1,120

Price of the cooker after 10% discount = $\frac{90}{100}\times1120$ = ₹ 1,008

$\therefore\$Selling price of the cooker after successive discounts = ₹ 1,008

Hence, the correct answer is Option B

Question 3: Anil bought some articles at 6 for ₹ 8 and sold them at 10 for ₹ 12. His percentage loss orgain is:

a) 10% loss

b) 10% gain

c) 8% gain

d) 8% loss

3) Answer (A)

Solution:

Cost price of 6 articles = ₹ 8

$\Rightarrow$  Cost price of 1 article = $\frac{8}{6}$  = ₹ $\frac{4}{3}$

Selling price of 10 articles = ₹ 12

$\Rightarrow$  Selling price of 1 article = $\frac{12}{10}$ = ₹ $\frac{6}{5}$

Loss of 1 article = $\frac{4}{3}-\frac{6}{5}=\frac{20-18}{15}=$  ₹ $\frac{2}{15}$

Loss% $=\frac{\frac{2}{15}}{\frac{4}{3}}\times100=\frac{2}{15}\times\frac{3}{4}\times100=10\%$

Hence, the correct answer is Option A

Question 4: Marked price of an article is 20% more than it’s cost price. At what percent less should it be sold for no profit and no loss ?

a) $16 \frac{2}{3}$%

b) $16 \frac{1}{3}$%

c) $14 \frac{1}{3}$%

d) $14 \frac{2}{3}$%

4) Answer (A)

Solution:

Let the cost price of the article = C

$\Rightarrow$ Marked price of the article = $\frac{120}{100}$C = $\frac{6}{5}$C

For no profit and no loss, Selling price = Cost price = C

$\therefore\$Required percentage = $\frac{\frac{6}{5}C-C}{\frac{6}{5}C}\times100$ = $\frac{\frac{1}{5}C}{\frac{6}{5}C}\times100$ = $16 \frac{2}{3}$%

Hence, the correct answer is Option A

Question 5: Sohan purchased an old scooter, and sold it for ₹28,000 thus gaining a 12% profit on the cost price. The cost price of the scooter is:

a) ₹27,000

b) ₹30,000

c) ₹25,000

d) ₹26,000

5) Answer (C)

Solution:

Let the cost price of the scooter = C

Profit% = 12%

$\Rightarrow$ Selling price of the scooter = $\frac{112}{100}$C

Given, Selling price of the scooter = ₹28,000

$\Rightarrow$ $\frac{112}{100}$C = 28000

$\Rightarrow$  C = ₹25,000

$\therefore\$Cost price of the scooter = ₹25,000

Hence, the correct answer is Option C

Question 6: The marked price of a toy is ₹450. After a certain discount on the marked price, the selling price of the toy is ₹405. The rate of discount is:

a) 8%

b) 12%

c) 15%

d) 10%

6) Answer (D)

Solution:

Marked price of the toy = ₹450

Selling price of the toy = ₹405

Discount = 450 – 405 = 45

$\therefore\$Discount% = $\frac{45}{450}\times100=10\%$

Hence, the correct answer is Option D

Question 7: A trader marks his goods in such a way that even after allowing 15% discount on marked price he still gains 27.5%. If the cost price of the goods is ₹ 200, then its marked price is:

a) ₹ 300

b) ₹ 250

c) ₹ 350

d) ₹ 400

7) Answer (A)

Solution:

Given, cost price of the goods = ₹ 200

Gain% = 27.5%

$\Rightarrow$  Selling price of the goods = $\frac{127.5}{100}\times200=255$

Let the marked price of the goods = M

Discount = 15%

$\Rightarrow$  Selling price of the goods = $\frac{85}{100}$M

$\Rightarrow$  $\frac{85}{100}$M = 255

$\Rightarrow$  M = 300

$\therefore\$Marked price of the goods = ₹ 300

Hence, the correct answer is Option A

Question 8: Amit sold an article for ₹ 7,000 and incurred a loss. Had he sold it for ₹ 8,750, his gain would have been three-fourth of the amount of loss that he incurred. At what price should he sell the article to get 10% profit?

a) ₹ 8,800

b) ₹ 8,400

c) ₹ 8,000

d) ₹ 7,800

8) Answer (A)

Solution:

Let the cost price = C

Loss for selling price ₹ 7,000 = C – 7000

Profit for selling price ₹ 8,750 = 8750 – C

According to the problem,

$8750-\text{C}=\frac{3}{4}\left(\text{C}-7000\right)$

$\Rightarrow$  $8750-\text{C}=\frac{3}{4}\text{C}-5250$

$\Rightarrow$  $\frac{7}{4}\text{C}=14000$

$\Rightarrow$  C = 8000

$\therefore\$Selling price = $\frac{110}{100}\times8000$ = ₹ 8,800

Hence, the correct answer is Option A

Question 9: The selling price of a book, including the sales tax, is ₹ 956.34. The rate of sales tax is 10%. If the shopkeeper has made a profit of 15%, then the cost price of the book is:

a) ₹ 836

b) ₹ 797.34

c) ₹ 845.98

d) ₹ 756

9) Answer (D)

Solution:

Let the cost price of the book = C

Sales tax = 10%

Price of the book with sales tax = $\frac{110}{100}C$

Profit = 15%

Selling price of the book = ₹ 956.34

$\Rightarrow$  $\frac{115}{100}\times\frac{110}{100}C$ = 956.34

$\Rightarrow$  $C=\frac{956340}{115\times11}$

$\Rightarrow$  $C=\frac{86940}{115}$

$\Rightarrow$  $C=\frac{3780}{5}$

$\Rightarrow$  $C=756$

$\therefore\$Cost price of the book = ₹ 756

Hence, the correct answer is Option D

Question 10: A dozen pairs of gloves worth ₹ 600 are available at a discount of 10%. Find out how many pairs of gloves can be bought for ₹ 270.

a) Seven

b) Four

c) Six

d) Five

10) Answer (C)

Solution:

Marked price of dozen pair of gloves = ₹ 600

Discount = 10%

Selling price of the dozen pair of gloves by shopkeeper = $\frac{90}{100}\times600$ = ₹ 540

12 pair of gloves can be bought for ₹ 540

$\therefore\$6 pair of gloves can be bought for ₹ 270

Hence, the correct answer is Option C

Question 11: A person purchased 40 items at some price. He sold some items at a profit of 30% by selling them at a price equal to the cost price of 26 items. The remaining items are sold at 18% profit. The total profit percentage is:

a) 27%

b) 28%

c) 24%

d) 25%

11) Answer (C)

Solution:

Let the cost price = 40C

Number of items sold at 30% profit = a

Cost price of ‘a’ items = aC

Selling price of ‘a’ items = $\frac{130}{100}aC$

According to the problem,

Selling price of ‘a’ items = Cost price of 26 items

$=$>  $\frac{130}{100}aC=26C$

$=$>  $a=20$

$=$>  Number of items sold at 30% profit = a = 20

Remaining items sold at 18% profit = 40 – 20 = 20

Selling price of items sold at 30% profit = $\frac{130}{100}\times20C$ = $26C$

Selling price of items sold at 18% profit = $\frac{118}{100}\times20C$ = $23.6C$

$\therefore\$Total profit percentage = $\frac{26C+23.6C-40C}{40C}\times100=\frac{9.6}{40}\times100=24\%$

Hence, the correct answer is Option C

Question 12: By selling an article for $₹ 600$, a shopkeeper makes a profit of 20%. At what price should he sell the article to incur a loss of 20% ?

a) $₹ 500$

b) $₹ 400$

c) $₹ 300$

d) $₹ 600$

12) Answer (B)

Solution:

Let the cost price = C.P

Given,

Profit% = 20%

Selling price = $₹ 600$

$=$>  $\frac{120}{100}\text{C.P}=600$

$=$>  $\text{C.P}=500$

$\therefore\$Selling price when loss is 20% = $\frac{80}{100}\text{C.P}=\frac{80}{100}\times500=₹ 400$

Hence, the correct answer is Option B

Question 13: A product, whose MRP is $₹$ 978, is sold for $₹$ 925 by a wholesale shop owner. What is the percentage of discount given by him?

a) 9.2%

b) 6.5%

c) 5.4%

d) 7.8%

13) Answer (C)

Solution:

Given,

MRP of the product = $₹$ 978

Selling Price of the product = $₹$ 925

Discount = 978 – 925 = $₹$ 53

Discount% = $\frac{\text{Discount}}{\text{MRP}}\times100$

$=\frac{53}{978}\times100$

$=0.054\times100$

$=5.4$%

Hence, the correct answer is Option C

Question 14: A shopkeeper purchased pens in bulk for $₹ 28$ each. He sold each for $₹ 40$. What was his profit percentage?

a) 48.12%

b) 28.40%

c) 42.85%

d) 38.75%

14) Answer (C)

Solution:

Let the number of pens purchased by shopkeeper = n

Cost price of each pen = $₹ 28$

$=$>  Cost price of total pens = 28n

Selling price of each pen = $₹ 40$

$=$>  Selling price of total pens = 40n

$\therefore\$Profit percentage = $\frac{40n-28n}{28n}\times100$ = $\frac{12n}{28n}\times100$ = 42.85%

Hence, the correct answer is Option C

Question 15: A chair was purchased for $₹ 785$ and sold at a profit of 22%. What was the selling price?

a) $₹ 857.9$

b) $₹ 957.7$

c) $₹ 987.4$

d) $₹ 768.3$

15) Answer (B)

Solution:

Given,

Cost Price of the chair = $₹ 785$

Profit% = 22%

$=$>  Profit = $\frac{22}{100}\times785$

$\therefore\$Selling Price = Cost Price + Profit = $785+\frac{22}{100}\times785$ = $\frac{122}{100}\times785$ = $₹ 957.7$

Hence, the correct answer is Option B

Question 16: If the cost price of 25 articles is equal to the selling price of 35 articles find the profit/loss percentage.

a) Loss — 28.57%

b) Profit — 28.57%

c) Profit — 18.93%

d) Loss — 18.93%

16) Answer (A)

Solution:

Given, cost price of 25 articles is equal to the selling price of 35 articles

Let the cost price of 25 articles = C

$=$>  Cost price of 1 article = $\frac{C}{25}$

Selling price of 35 articles = C

$=$>  Selling price of 1 article = $\frac{C}{35}$

Loss = Cost price – Selling price = $\frac{C}{25}-\frac{C}{35}$ = $\frac{10C}{25\times35}$ = $\frac{2C}{175}$

$\therefore\$Loss% = $\frac{\frac{2C}{175}}{\frac{C}{25}}\times100$ = $\frac{2\times25}{175}\times100$ = $28.57\%$

Hence, the correct answer is Option A

Question 17: Sohan sold a plot for $₹ 2,55,000$ at a 15% loss. At what price should he sell the plot to gain a 10% profit?

a) $₹ 3,00,000$

b) $₹ 3,33,000$

c) $₹ 3,30,000$

d) $₹ 3,33,300$

17) Answer (C)

Solution:

Let the cost price of the plot = CP

Given, loss% = 15%

Selling price of the plot = $₹ 2,55,000$

$=$>  $\frac{85}{100}\text{CP}=255000$

$=$>  $\text{CP}=255000\times\frac{100}{85}$

$=$>  $\text{CP}=₹ 300000$

When gain is 10%,

Selling price of the article = $\frac{110}{100}\times300000=₹ 330000$

Hence, the correct answer is Option C

Question 18: A dealer marks his goods at 30% above the cost price. Then he allows 35% discount on it. What would be his loss percentage?

a) 15.5%

b) 16.5%

c) 17.5%

d) 18.5%

18) Answer (A)

Solution:

Let the Cost Price = C.P

Given, dealer marked his goods at 30% above cost price

$=$>  Marked Price (M.P) = $\frac{130}{100}$C.P = $\frac{13}{10}$C.P

Discount = 35%

$=$>  Selling Price (S.P) = $\frac{65}{100}$M.P = $\frac{65}{100}\times\frac{13}{10}$C.P = $\frac{845}{1000}$C.P

$\therefore\$Loss % = $\frac{\text{C.P}-\text{S.P}}{\text{C.P}}\times100\$

$=\frac{ \text{C.P}-\frac{845}{1000}\ \text{C.P}}{\text{C.P}}\times100\$

$=\frac{155}{1000}\times100\$

$=15.5$%

Hence, the correct answer is Option A

Question 19: The cost price of 33 books is the same as the selling price of ‘x’ books. If the profit is 10%, then the value of ‘x’ is :

a) 30

b) 20

c) 40

d) 10

19) Answer (A)

Solution:

Let the cost price of 33 books = C

Cost price of 1 book = $\frac{C}{33}$

Profit% = 10%

$=$>  Selling price of 1 book = $\frac{110}{100}\times\frac{C}{33}=\frac{C}{30}$

According to the problem,

Selling price of ‘$x$’ books = C

Selling price of 1 book = $\frac{C}{x}$

$=$>  $\frac{C}{x}=\frac{C}{30}$

$=$>  $x=30$

Hence, the correct answer is Option A

Question 20: In a 15% discount sale, the cost of a book is $₹ 2,150.$ What was the original price of the book? (Correct to two decimal places)

a) $₹ 1,527.00$

b) $₹ 2,500.00$

c) $₹ 2,529.41$

d) $₹ 2,250.50$

20) Answer (C)

Solution:

Given,

Cost Price of the book = $₹ 2,150$

Disount% = 15%

Let the Marked Price = MP

$=$>  $\frac{85}{100}\times \text{MP}=2150$

$=$>  $\text{MP}=₹ 2,529.41$

$\therefore\$Original Price of the book = $₹ 2,529.41$

Hence, the correct answer is Option C

Question 21: If the gain is one-fifth of the selling price, then the gain percentage is:

a) 16%

b) 20%

c) 80%

d) 25%

21) Answer (D)

Solution:

Let the Cost Price = CP

Selling Price = SP

Given, gain is one-fifth of the selling price

$=$>  Gain = $\frac{\text{SP}}{5}$

$=$>  $\text{SP}-\text{CP}=\frac{\text{SP}}{5}$

$=$>  $\text{CP}=\text{SP}-\frac{\text{SP}}{5}$

$=$>  $\text{CP}=\frac{4\text{SP}}{5}$

$\therefore\$Gain% = $\frac{\text{Gain}}{\text{CP}}\times100$

$=\frac{\frac{\text{SP}}{5}}{\frac{4\text{SP}}{5}}\times100$

$=\frac{1}{4}\times100$

$=25\%$

Hence, the correct answer is Option D

Question 22: A shopkeeper allows a discount of 20% on an article and still makes a profit of 25%. What does he pay for an article whose marked price is $₹800$?

a) $₹ 492$

b) $₹ 800$

c) $₹ 512$

d) $₹ 640$

22) Answer (C)

Solution:

Given, Marked Price (MP) = $₹800$

Discount% = 20%

$=$>  Selling Price (SP) = $\frac{80}{100}\times800=₹640$

Profi% = 25%

Let cost paid by the shopkeeper to purchase the article (Cost Price) = CP

$=$>  $\frac{125}{100}\text{CP}=640$

$=$>  $\text{CP}=₹512$

Hence, the correct answer is Option C

Question 23: Salma buys an article and then sells it for $₹ 810.$ If she loses 10%, then at what price should she sell it to gain 4%?

a) $₹ 900$

b) $₹ 936$

c) $₹ 864$

d) $₹ 729$

23) Answer (B)

Solution:

Given,

Selling Price of the article = $₹ 810$

Loss% = 10%

Let the Cost Price of the article = C.P

$=$>  $\frac{90}{100}\text{C.P}$ = $810$

$=$>  $\text{C.P}=₹ 900$

When gain is 4% then

Selling Price of the article = $\frac{104}{100}\text{C.P}=\frac{104}{100}\times900=₹ 936$

Hence, the correct answer is Option B

Question 24: A mobile phone was sold for ₹31,500 after giving two successive discounts of 30% and 10%, respectively. What was the marked price of the mobile?

a) ₹55,000

b) ₹50,000

c) ₹35,000

d) ₹52,500

24) Answer (B)

Solution:

Given,

Selling Price of the mobile phone = $₹31,500$

Let the Marked Price of the mobile phone = $\text{M.P}$

Price after 30% discount = $\frac{70}{100}\times \text{M.P}$

Selling Price after 10% discount = $\frac{90}{100}\times\frac{70}{100}\times \text{M.P}$

$=$>  $\frac{90}{100}\times\frac{70}{100}\times \text{M.P}=31500$

$=$>  $\text{M.P}=₹50000$

$\therefore\$Marked Price of the mobile phone = $₹50,000$

Hence, the correct answer is Option B

Question 25: If the marked price of a television set is $₹ 24,500,$ then its selling price after a 12% discount on it is:

a) $₹ 21,460$

b) $₹ 21,640$

c) $₹ 21,650$

d) $₹ 21,560$

25) Answer (D)

Solution:

Given,

Marked Price of the television set = $₹ 24,500$

Discount% = 12%

$=$> Discount = $\frac{12}{100}\times24500=2940$

$\therefore\$Selling Price = 24,500 – 2940 = $₹ 21,560$

Hence, the correct answer is Option D