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# Profit and Loss Discount Questions for SSC MTS

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

a)Â â‚¹ 3,500

b)Â â‚¹ 2,800

c)Â â‚¹ 2,500

d)Â â‚¹ 3,000

Solution:

Let the cost price of the article = C

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

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

According to the problem,

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

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

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

$\Rightarrow$Â  C = 3500

$\therefore\$Cost price of the article =Â â‚¹ 3,500

Hence, the correct answer is Option A

Question 2:Â The printed price of a cooker is â‚¹ 2,000, and discounts are 30%, 20% and 10%, respectively. Find the selling price of the cooker.

a)Â â‚¹ 1,002

b)Â â‚¹ 1,008

c)Â â‚¹ 1,004

d)Â â‚¹ 1,006

Solution:

Given, Marked price(Printed price) of the cooker =Â â‚¹ 2,000

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

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

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

$\therefore\$Selling price of the cooker after successive discounts =Â â‚¹ 1,008

Hence, the correct answer is Option B

Question 3:Â Anil bought some articles at 6 for â‚¹ 8 and sold them at 10 for â‚¹ 12. His percentage loss orgain is:

a)Â 10% loss

b)Â 10% gain

c)Â 8% gain

d)Â 8% loss

Solution:

Cost price of 6 articles =Â â‚¹ 8

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

Selling price of 10 articles =Â â‚¹ 12

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

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

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

a)Â $16 \frac{2}{3}$%

b)Â $16 \frac{1}{3}$%

c)Â $14 \frac{1}{3}$%

d)Â $14 \frac{2}{3}$%

Solution:

Let the cost price of the article = C

$\Rightarrow$ Marked price of the article =Â $\frac{120}{100}$C =Â $\frac{6}{5}$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:Â Sohan purchased an old scooter, and sold it for â‚¹28,000 thus gaining a 12% profit on the cost price. The cost price of the scooter is:

a)Â â‚¹27,000

b)Â â‚¹30,000

c)Â â‚¹25,000

d)Â â‚¹26,000

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 = â‚¹28,000

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

$\Rightarrow$Â  C =Â â‚¹25,000

$\therefore\$Cost price of the scooter =Â â‚¹25,000

Hence, the correct answer is Option C

Question 6:Â The marked price of a toy is â‚¹450. After a certain discount on the marked price, the selling price of the toy is â‚¹405. The rate of discount is:

a)Â 8%

b)Â 12%

c)Â 15%

d)Â 10%

Solution:

Marked price of the toy =Â â‚¹450

Selling price of the toy =Â â‚¹405

Discount = 450 – 405 = 45

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

Hence, the correct answer is Option D

Question 7:Â 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 â‚¹ 200, then its marked price is:

a)Â â‚¹ 300

b)Â â‚¹ 250

c)Â â‚¹ 350

d)Â â‚¹ 400

Solution:

Given, cost price of the goods =Â â‚¹ 200

Gain% = 27.5%

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

Let the marked price of the goods = M

Discount = 15%

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

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

$\Rightarrow$Â  M = 300

$\therefore\$Marked price of the goods = â‚¹ 300

Hence, the correct answer is Option A

Question 8:Â Amit sold an article for â‚¹ 7,000 and incurred a loss. Had he sold it for â‚¹ 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)Â â‚¹ 8,800

b)Â â‚¹ 8,400

c)Â â‚¹ 8,000

d)Â â‚¹ 7,800

Solution:

Let the cost price = C

Loss for selling priceÂ â‚¹ 7,000 = C – 7000

Profit for selling priceÂ â‚¹ 8,750 = 8750 – C

According to the problem,

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

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

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

$\Rightarrow$Â  C = 8000

$\therefore\$Selling price =Â $\frac{110}{100}\times8000$ = â‚¹ 8,800

Hence, the correct answer is Option A

Question 9:Â The selling price of a book, including the sales tax, is â‚¹ 956.34. 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)Â â‚¹ 836

b)Â â‚¹ 797.34

c)Â â‚¹ 845.98

d)Â â‚¹ 756

Solution:

Let the cost price of the book = C

Sales tax = 10%

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

Profit = 15%

Selling price of the book =Â â‚¹ 956.34

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

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

$\Rightarrow$ Â $C=\frac{86940}{115}$

$\Rightarrow$ Â $C=\frac{3780}{5}$

$\Rightarrow$ Â $C=756$

$\therefore\$Cost price of the book =Â â‚¹ 756

Hence, the correct answer is Option D

Question 10:Â A dozen pairs of gloves worth â‚¹ 600 are available at a discount of 10%. Find out how many pairs of gloves can be bought for â‚¹ 270.

a)Â Seven

b)Â Four

c)Â Six

d)Â Five

Solution:

Marked price of dozen pair of gloves =Â â‚¹ 600

Discount = 10%

Selling price of the dozen pair of gloves by shopkeeper =Â $\frac{90}{100}\times600$ = â‚¹ 540

12 pair of gloves can be bought forÂ â‚¹ 540

$\therefore\$6 pair of gloves can be bought forÂ â‚¹ 270

Hence, the correct answer is Option C

Question 11:Â 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)Â 27%

b)Â 28%

c)Â 24%

d)Â 25%

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 =Â $\frac{130}{100}aC$

According to the problem,

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

$=$> Â $\frac{130}{100}aC=26C$

$=$> Â $a=20$

$=$> Â 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 =Â $\frac{130}{100}\times20C$ =Â $26C$

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

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

Hence, the correct answer is Option C

Question 12:Â By selling an article for $â‚¹ 600$, a shopkeeper makes a profit of 20%. At what price should he sell the article to incur a loss of 20% ?

a)Â $â‚¹ 500$

b)Â $â‚¹ 400$

c)Â $â‚¹ 300$

d)Â $â‚¹ 600$

Solution:

Let the cost price = C.P

Given,

Profit% = 20%

Selling price = $â‚¹ 600$

$=$> Â $\frac{120}{100}\text{C.P}=600$

$=$> Â $\text{C.P}=500$

$\therefore\$Selling price when loss is 20% = $\frac{80}{100}\text{C.P}=\frac{80}{100}\times500=â‚¹ 400$

Hence, the correct answer is Option B

Question 13:Â A product, whose MRP is $â‚¹$ 978, is sold for $â‚¹$ 925 by a wholesale shop owner. What is the percentage of discount given by him?

a)Â 9.2%

b)Â 6.5%

c)Â 5.4%

d)Â 7.8%

Solution:

Given,

MRP of the product =Â $â‚¹$ 978

Selling Price of the product = $â‚¹$ 925

Discount = 978 – 925 =Â $â‚¹$ 53

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

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

$=0.054\times100$

$=5.4$%

Hence, the correct answer is Option C

Question 14:Â A shopkeeper purchased pens in bulk for $â‚¹ 28$ each. He sold each for $â‚¹ 40$. What was his profit percentage?

a)Â 48.12%

b)Â 28.40%

c)Â 42.85%

d)Â 38.75%

Solution:

Let the number of pens purchased by shopkeeper = n

Cost price of each pen =Â $â‚¹ 28$

$=$>Â  Cost price of total pens = 28n

Selling price of each pen = $â‚¹ 40$

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

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

Hence, the correct answer is Option C

Question 15:Â A chair was purchased for $â‚¹ 785$ and sold at a profit of 22%. What was the selling price?

a)Â $â‚¹ 857.9$

b)Â $â‚¹ 957.7$

c)Â $â‚¹ 987.4$

d)Â $â‚¹ 768.3$

Solution:

Given,

Cost Price of the chair =Â $â‚¹ 785$

Profit% = 22%

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

$\therefore\$Selling Price = Cost Price + Profit =Â $785+\frac{22}{100}\times785$ =Â $\frac{122}{100}\times785$ =Â $â‚¹ 957.7$

Hence, the correct answer is Option B

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

a)Â Loss â€” 28.57%

b)Â Profit â€” 28.57%

c)Â Profit â€” 18.93%

d)Â Loss â€” 18.93%

Solution:

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

Let the cost price of 25 articles = C

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

Selling price of 35 articles = C

$=$>Â  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:Â Sohan sold a plot for $â‚¹ 2,55,000$ at a 15% loss. At what price should he sell the plot to gain a 10% profit?

a)Â $â‚¹ 3,00,000$

b)Â $â‚¹ 3,33,000$

c)Â $â‚¹ 3,30,000$

d)Â $â‚¹ 3,33,300$

Solution:

Let the cost price of the plot =Â CP

Given, loss% = 15%

Selling price of the plot =Â $â‚¹ 2,55,000$

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

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

$=$> Â $\text{CP}=â‚¹ 300000$

When gain is 10%,

Selling price of the article =Â $\frac{110}{100}\times300000=â‚¹ 330000$

Hence, the correct answer is Option C

Question 18:Â 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)Â 15.5%

b)Â 16.5%

c)Â 17.5%

d)Â 18.5%

Solution:

Let the Cost Price = C.P

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

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

Discount = 35%

$=$>Â  Selling Price (S.P) =Â $\frac{65}{100}$M.P =Â $\frac{65}{100}\times\frac{13}{10}$C.P =Â $\frac{845}{1000}$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:Â The cost price of 33 books is the same as the selling price of â€˜xâ€™ books. If the profit is 10%, then the value of â€˜xâ€™ is :

a)Â 30

b)Â 20

c)Â 40

d)Â 10

Solution:

Let the cost price of 33 books = C

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

Profit% = 10%

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

According to the problem,

Selling price of ‘$x$’ books = C

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

$=$> Â $\frac{C}{x}=\frac{C}{30}$

$=$> Â $x=30$

Hence, the correct answer is Option A

Question 20:Â In a 15% discount sale, the cost of a book is $â‚¹ 2,150.$ What was the original price of the book? (Correct to two decimal places)

a)Â $â‚¹ 1,527.00$

b)Â $â‚¹ 2,500.00$

c)Â $â‚¹ 2,529.41$

d)Â $â‚¹ 2,250.50$

Solution:

Given,

Cost Price of the book =Â $â‚¹ 2,150$

Disount% = 15%

Let the Marked Price = MP

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

$=$> Â $\text{MP}=â‚¹ 2,529.41$

$\therefore\$Original Price of the book = $â‚¹ 2,529.41$

Hence, the correct answer is Option C

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

a)Â 16%

b)Â 20%

c)Â 80%

d)Â 25%

Solution:

Let the Cost Price = CP

Selling Price = SP

Given, gain is one-fifth of the selling price

$=$>Â  Gain = $\frac{\text{SP}}{5}$

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

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

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

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

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

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

$=25\%$

Hence, the correct answer is Option D

Question 22:Â 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 $â‚¹800$?

a)Â $â‚¹ 492$

b)Â $â‚¹ 800$

c)Â $â‚¹ 512$

d)Â $â‚¹ 640$

Solution:

Given, Marked Price (MP) =Â $â‚¹800$

Discount% = 20%

$=$> Â Selling Price (SP) =Â $\frac{80}{100}\times800=â‚¹640$

Profi% = 25%

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

$=$> Â $\frac{125}{100}\text{CP}=640$

$=$> Â $\text{CP}=â‚¹512$

Hence, the correct answer is Option C

Question 23:Â Salma buys an article and then sells it for $â‚¹ 810.$ If she loses 10%, then at what price should she sell it to gain 4%?

a)Â $â‚¹ 900$

b)Â $â‚¹ 936$

c)Â $â‚¹ 864$

d)Â $â‚¹ 729$

Solution:

Given,

Selling Price of the article = $â‚¹ 810$

Loss% = 10%

Let the Cost Price of the article = C.P

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

$=$> Â $\text{C.P}=â‚¹ 900$

When gain is 4% then

Selling Price of the article =Â $\frac{104}{100}\text{C.P}=\frac{104}{100}\times900=â‚¹ 936$

Hence, the correct answer is Option B

Question 24:Â A mobile phone was sold for â‚¹31,500 after giving two successive discounts of 30% and 10%, respectively. What was the marked price of the mobile?

a)Â â‚¹55,000

b)Â â‚¹50,000

c)Â â‚¹35,000

d)Â â‚¹52,500

Solution:

Given,

Selling Price of the mobile phone = $â‚¹31,500$

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

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

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

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

$=$> Â $\text{M.P}=â‚¹50000$

$\therefore\$Marked Price of the mobile phone = $â‚¹50,000$

Hence, the correct answer is Option B

Question 25:Â If the marked price of a television set is $â‚¹ 24,500,$ then its selling price after a 12% discount on it is:

a)Â $â‚¹ 21,460$

b)Â $â‚¹ 21,640$

c)Â $â‚¹ 21,650$

d)Â $â‚¹ 21,560$

Solution:

Given,

Marked Price of the television set = $â‚¹ 24,500$

Discount% = 12%

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

$\therefore\$Selling Price = 24,500 – 2940 =Â $â‚¹ 21,560$

Hence, the correct answer is Option D