The amount spent to purchase an article is cost price of the article, and the amount received for selling an article is called selling price.

* Profit = Selling Price − Cost Price

* Loss = Cost Price − Selling Price

**DISCOUNTS**

The price at which the article is marked is the marked price or listed price or labelled price or catalogue price or printed price. The discount is allowed on marked price.

**Note: **Discount percents are always calculated on Marked Price. When discount is deducted from the marked price, the remainder becomes the selling price. To find Marked Price from Cost Price, the following formula can be used.

**1. **In order to obtain an income of Rs.650 from 10% stock at Rs.96 one must make an investment of

a) Rs.67.70 b) Rs.6,240 c) Rs.6,040 d) Rs.960

**Sol:** 10% stock at Rs.96 = 10% of Rs.96 = Rs.9.60

Total investment = Rs.650 × 9.60

= Rs.6,240

**Ans: b **

**2.** A person sold his watch for Rs.24 and got a profit percentage equal to the cost price, then the cost price is

a) Rs.20 b) Rs.18 c) Rs.22 d) Rs.16

**Sol:** Let the cost price be ‘x’ Then, profit % = Cost price

Hence, x = Rs.20

**Ans: a **

**3. **A shopkeeper bought 60 pens at the rate of Rs.25 per pen. If the marked price of pens is Rs.30 per pen and the shopkeeper gives a discount of 12% on the marked price, then what will be the percentage profit gained by the shopkeeper?

a) 25% b) 56% c) 5.6% d) 20%

**Sol: **Cost price of the pens = 25 × 60 = Rs.1,500

Selling price of the pens = 30 × 0.88 × 60 = Rs.1,584

= 5.6%

**Ans: c **

**4. **If CP of 36 books is equal to SP of 30 books, then the gain percentage is (You have to assume that all the books cost same.)

**Sol: **Let the total investment = 36 × 30 = Rs.1,080.

CP of one book = Rs.30,

SP of one book = Rs.36 36 − 30

**Ans: d **

**5. **Suvakar was very much excited about an offer from Reebok that read 'Buy things worth Rs.2,000 and get things worth Rs.1,000 absolutely free!'. How much discount was there in the offer?

a) 50% b) 100% c) 33 1/3% d) 25% 3

**Sol: **In fact, you get things worth Rs.3,000, but you pay Rs.2,000 only. So, you are getting a discount

**Ans: c**

**6.** If an article is sold at 8% profit instead of 8% loss, it would have brought Rs.12 more. Find out the cost price of the article

a) Rs.75 b) Rs.72 c) Rs.60 d) Rs.70

**Sol:** Let the CP of the article be x.

1.08x − 0.92x = 12

**Ans: a **

**7. **A dealer sells a set of furniture at 20% loss. Had he sold it for Rs.900 more, he would have made a 25% profit. At what price should he sell in order to make 20% profit?

a) Rs.1,800 b) Rs.2,000 c) Rs.2,400 d) Rs.2,800

**Sol:** Let price of furniture set be x. Then,

1.25x − 0.8x = 900

⇒ 0.45x = 900

To make 20% profit he should sell it at 2000 × 1.2 = Rs.2,400.

**Ans: c **

**8.** The par value of the shares of company X and Y is Rs.10. The market price of the shares are Rs.40 and Rs.50 respectively. Find the ratio of the return on investment for an investor if the dividends are 20% and 40% respectively. Investment in both the cases is same.

a) 5 : 8 b) 8 : 5 c) 8 : 13 d) 13 : 8

Therefore, number of shares each of them bought

= a/40, a/50

(Dividend) Income

⇒ 20% of 10 = 2 ⇒ 40% of 10 = 4

**9.** If the profit made on a packet of sugar is Rs.40 and the cost price of the packet is Rs.200, then how much is the profit percentage?

a) 20% b) 25% c) 30% d) 15%

**10.** A man sells two items such that the cost price of one is equal to the selling price of the second, and the selling price of the first is equal to the cost price of the second. Which of the following is true?

a) He makes a profit b) He makes a loss c) He makes neither profit nor loss d) None of these

**Sol: **CP_{1} = SP_{2}

CP_{2} = SP_{1}

Hence, total CP =

CP1 + CP2 = SP2 + SP1 = total SP

So, he makes neither profit nor loss

**Ans: c **

**11.** When an article is sold for Rs.X, loss percentage is equal to L%. However, when the same article is sold for Rs. Y, profit percentage is equal to P%. What is the cost price of that article?

Adding (i) and (ii), we get

**Ans: c**

**12.** A fruit vendor buys certain numbers of oranges at 20 per Rs.15 and twice this number of oranges at 30 per Rs.20. He sells all the oranges at 24 per Rs.18. At most what discount percentage can he offer so that he does not has a loss?

a) 8% b) 7.41% c) 7.14% d) None

**Sol: **Let 60 oranges of type-1 and 120 oranges of type-2 has been bought by vendor.

Total cost of oranges = 3 × 15 + 4 × 20 = Rs.125

**Ans: b**

**13.** By selling an article at 2/5 th of the marked 5 price, there is a loss of 25%. The ratio of the marked price and the cost price of the article is

a) 8 : 15 b) 8 : 5 c) 15 : 8 d) Data Inadequate

**Sol: **Let the marked price be x. Then,

∴ Ratio of marked price : cost price

**Ans: c **

**14. **The difference between a discount of 35% and two successive discounts of 20% on a certain bill was Rs.22. Find the amount of the bill

a) Rs.244.44 b) Rs.1,100 c) Rs.4,400 d) Rs.2,200

**Sol: **Effective% change of x% and y%

Now x = 20% and y = 20%

For two successive discounts the net discount

Now let the amount of the bill be Rs.x.

(Two successive 20% discounts on x) − 35% of x = Rs.22

⇒ 36% of x − 35% of x = 22

⇒ 1% of x = 22

**Ans: d **

**15. **The marked price of a watch was Rs.720. A man bought the same for Rs.550.80 after getting two successive discounts, the first being 10%. What was the second discount?

a) 10% b) 18% c) 15% d) 20%

**Sol:** After the first discount of 10% the revised list price = 90% of Rs.720 = Rs.648

Now discount on revised list price = 648 − 550.80 = Rs.97.20.

Now let the second discount be x%

⇒ x% of Rs.648 = Rs.97.20

**Ans: c **

**16. **A shopkeeper bought some pencils at 2 for Rs.1, and an equal number at 3 for Rs.2. He sold the entire lot at 5 for Rs.3. Find out his gain or loss percentage

**Sol: **Take LCM of 2, 3, 5, i.e. 30.

So, cost of 30 pencils at the rate of 2 per rupee = Rs.15 and cost of 30 pencils at the rate of 3 per Rs.2 = Rs.20.

Hence, total cost of 60 pencils = 15 + 20 = Rs.35. Selling price of 60 pencils at the rate of 5 per Rs.3 = Rs.36.

** Ans: c **

**17.** A trader bought 10 kg oranges for Rs.405, of which 1 kg was found rotten. If he wishes to make a profit of 10%, at what rate per kg should he sell the remaining oranges?

a) Rs.44.55 b) Rs.48.66 c) Rs.51.25 d) Rs.49.50

**Sol:** Cost of 10 kg of oranges = Rs.405.

It is to be noted here that after 1 kg rotten oranges is found, he sells only 9 kg, but the cost to him will remain Rs.405.

For 10% profit, he should sell the oranges at (1.1 × 405) = Rs.445.50 So, SP of 9 kg = Rs.445.50

**Ans: d**

**18. **A person sold his pen for Rs.24 and his profit percentage was numerically equal to the cost price. What was the cost price of the pen? (SSC-CGL-2017)

A) 12 B) 14 C) 16 D) 20

**Sol:** Let the cost price be Rs.x

∴ x + x% of x = 24

⇒ 100x + x^{2} /100 = 24 100

x^{2} + 100x - 2400 = 0

⇒ x = +20, - 120

∴ Cost price is 20

**Shortcut: **Solve the question by options

**Ans: D **

**19. **A man sold an article for Rs.79.20 at a loss of 12%. At what price should he have sold it to gain 12%?

A) Rs.102.40 B) Rs.95 C) Rs.100.80 D) Rs.105.60

**Sol: **S.P = 79.20, Loss% = 12%

**Ans: C **

**20. **A person sells an article at 10% below its cost price. Had he sold it for Rs.332 more, he would have made a profit of 20%. What is the original selling price (in Rs) of the article? (SSC-CGL-2020)

A) 1328 B) 1028 C) 896 D) 996

**Sol: **Let the C.P of the article be Rs.100 then S.P = Rs.90

To get 20% profit, he should sell at Rs.120 Difference = 120 - 90 = 30

If it is Rs.30 more original selling price is Rs.90

If it is Rs.332 more, then the selling price

= 332/30 × 90 = Rs.996

**Ans: D**

**21. **A sells an article to B at a gain of 15% and B sells it to C at a gain of 10%. If C pays Rs.3,162.50 for it, what did it cost to A?

A) Rs.3500 B) Rs.2250 C) Rs.2500 D) Rs.3205

**Sol: **Let the C.P of A be Rs.x. then 115% of 110% of x = 3162.50

**Ans: C **

**22.** Renu bought an item for 1240 and sold it at a loss of 25%. With that amount, she bought another item and sold it for 40% profit. What percentage of profit did Renu get? (SSC-CGL-2018)

A) 12% B) 5% C) 6 2/3% D) 15%

**Sol: **75% of 140% of 1240 = Rs.1302

Profit is 1302 − 1240 = 62

Profit% = 62/1240 × 100 = 5%

**Ans: B **

**23. **For an article the profit is 170% of the cost price. If the cost price increases by 20% but the selling price remains same, then what is the new profit percentage? (SSC-CGL-2017)

A) 41% B) 50% C) 75% D) 125%

**Sol: **Let the cost price be Rs.100 then selling price = 100 + 170 = Rs.270

New C.P = Rs.120 (20% increment)

New Profit is = 270 − 120 = Rs.150

**Ans: D **

**24. **A fruit seller buys 20 mangoes for Rs.270. Five mangoes were spoilt in transportation. If he sells the remaining mangoes at Rs.21 each, find his profit or loss percent.

A) 25% loss B) 16 2/3% profit C) 20% profit D) 35% profit

**Sol: **Cost Price = Rs.270

Selling Price = 15 × Rs.21 = Rs.315

Profit = 315 − 270 = Rs.45

**25. **A man purchases 70 pens. He sells 40 pens at a profit of 10% and 30 pens at a profit of 20%. Had he sold all of them at a uniform profit of 15% he would have got Rs.35 less. Find the cost price of each pen?

A) Rs.70 B) Rs.45 C) Rs.35 D) Rs.40

**Sol: **Let the C.P of each pen be Rs.100

S.P of 30 pens = 110 × 30 = 3300

S.P of 40 pens = 120 × 40 = 4800

Total S.P = Rs.8100

At a uniform price of 15%, S.P of 70 pens

= 70 × 115 = 8050

Difference is 8100 - 8050 = Rs.50

If the difference is Rs.50, C.P is Rs.100

If the difference is Rs.35, then C.P

= 35/50 × 100 = Rs.70

**Ans: A **

**26.** The price of a chair is Rs. 500. It has been sold at two successive discounts of 10% each. What is its selling price? (SSC-CGL-2016)

A) Rs.400 B) Rs.405 C) Rs.415 D) Rs.425

**Sol: **Selling Price = 90% of 90% of 500

**Ans: B **

**27. **By selling 18 table fans for Rs.11664 a man incurs a loss of 10%. How many fans should he sell for Rs.17424 to earn 10% profit? (SSC-CGL-2019)

A) 22 B) 23 C) 18 D) 20

**28.** An article is marked at Rs.1800 and 20% discount is offered on it. How many such articles can be bought for Rs.46080?

A) 28 B) 32 C) 36 D) 24

**Sol: **M.P = Rs.1800, Discount = 20% S.P = 80% of 1800 = Rs.1440

∴ article is available at Rs.1440

∴ Number of articles bought for Rs. 46080 = 46080/1440 = 32

**Ans: B **

**29. **A shopkeeper buys an article for Rs.616. He offers 12% discount on selling the article and yet gains 15%. Find the rate at which he marked the article?

A) Rs.715 B) Rs.805 C) Rs.795 D) Rs.675

**Sol:** Marked Price

**30.** A person marked his goods at a price that would give him 40% profit. But declared a sale and allowed 20% discount on the marked price. What is the profit percentage of the person in the whole transaction? (SSC-CGL-2019)

A) 15% B) 25% C) 12% D) 14%

**Sol: **Let the C.P be Rs. 100

Marked price = Rs. 140

Selling Price after discount = 80% of 140 = Rs. 112

Profit = Rs. 112 - Rs. 100 = Rs. 12

∴ Profit% = 12 /100 × 100 = 12%

**Ans: C **

**31. **A dishonest dealer professes to sell his goods at the cost price, but uses only 800 grams in place of a kilogram weight. Find his profit percent?

A) 20% B) 25% C) 30% D) 15%

**Sol: **

**32. **A shopkeeper marks his goods at 40% more than its cost price and allows a discount of 25% on the marked price. His gain or loss percent is? (SSC-CGL-2019)

A) 5% loss B) 15% gain C) 10% loss D) 5% gain

**Sol: **Let the C.P be Rs.100 Marked price = Rs. 140

Selling Price after discount = 75% of 140 = Rs. 105

Profit = Rs. 105 − Rs. 100 = Rs. 5

∴ Profit % = 5/100 × 100 = 5%

**Ans: D**

**33. **A man bought some articles at the rate of 16 for Rs.24 and sold them at the rate of 12 for Rs.22.50. What is the profit percent?

A) 40% B) 60% C) 50% D) 25%

**Sol: **LCM of 16 and 12 is 48 C.P of 16 articles = Rs. 24

**Ans: D **

**Some More Exercises**

**1. **The dealer charges his customers 12% more than the cost price. If a customer paid Rs. 14336 for a Television, then what was the cost price of the Television?

1) Rs. 14800 2) Rs. 12800 3) Rs. 16800 4) Rs. 12600 5) None

**2.** A man buys 120 oranges for Rs.720. He sells 70 oranges for Rs.8 each and remaining at Rs.5 each. Find his overall profit/loss%?

1) 2.78% loss 2) 3.12% profit 3) 12% profit 4) 12.5% loss 5) None

**3.** A fruit seller buys 60 oranges for Rs.480. Five oranges were spoilt in transportation. If he sells the remaining oranges at Rs.12 each, find his profit or loss percent.

1) 25% loss 2) 37.5% profit 3) 20% profit 4) 32.5% profit 5) None

**4.** Two items A and B have equal cost price. Item A is sold at 40% profit and item B is sold at an amount 20% less than the selling price of item A. If the total profit is Rs.156 then find the cost price of A.

1) Rs. 300 2) Rs. 350 3) Rs. 400 4) Rs. 450 5) None

**5.** A trader sold an article for Rs.238 at a loss of fifteen percent. At what rate should he have sold the article to earn a profit of twenty five percent?

1) Rs. 300 2) Rs. 350 3) Rs. 285 4) Rs. 240 5) None

**6.** A car dealer sells two cars for Rs.75800 each, neither losing nor gaining in total. If he sold one of the cars at a gain of 25%, then find at what percent loss he sold the other car.

1) 25% 2) 16.67% 3) 12.5% 4) 50% 5) None

**7. **A sells a house to B at a profit of 10%, B sells it to C at a loss of 15% and C sells it to D for Rs.3366000 making a profit of 20%. What did the house cost A?

1) Rs. 2500000 2) Rs. 3000000 3) Rs. 3500000 4) Rs. 2000000 5) Rs. 2800000

**8. **Bhavya purchased a box of pencils at the rate of 6 for Rs.9 and sold all of them at the rate of 7 for Rs.11. If she gains Rs.9, how many pencils did the box contain?

1) 42 2) 21 3) 126 4) Can’t be determined 5) None

**9. **A man buys 5 tables and 10 chairs for Rs.1600. He sells tables at a profit of 15% and tables at a loss of 10% if his over all profit was Rs.90, what is the cost price of a chair?

1) Rs. 60 2) Rs. 200 3) Rs. 75 4) Rs. 180 5) None

**10.** A dishonest dealer professes to sell his goods at the cost price, but uses only 800 grams in place of a kilogram weight. Find his profit percent.

1) 20% 2) 25% 3) 30% 4) 15% 5) None

**11. **A shopkeeper purchased 30 kg of rice at the rate of Rs.17.50 per kg and another 30 kg rice at a certain rate. He mixed the two and sold the entire quantity at the rate of Rs.18.60 per kg and made 20% overall profit. At what price per kg did he purchase the second lot?

1) Rs. 17.60 2) Rs. 15.70 3) Rs. 12.60 4) Rs. 12.30 5) Rs. 13.50

**12. **A shopkeeper buys an article for Rs.528. He offers 12% discount on selling the article and yet gains 18%. Find the rate at which he marked the article.

1) Rs. 713 2) Rs. 578 3) Rs. 708 4) Rs. 653 5) None

**13. **A certain number of articles were purchased for Rs.90. Three more articles could have been purchased for the same amount. If each article was cheaper by Rs. 1. Find the number of articles purchased.

1) 15 2) 25 3) 18 4) 12 5) None

**14.** A discount of 10% enables a man to buy 5 more apples for Rs.225. Find the original price per apple.

1) Rs. 4.50 2) Rs. 5 3) Rs. 4 4) Rs. 3.50 5) None

**15. **A person purchases 90 books and sells 40 books at a gain of 10% and 50 books at a gain of 20%. Had he sold all of them at a uniform profit of 15% he would have got Rs.40 less. Find the cost price of each book.

1) Rs.70 2) Rs.65 3) Rs.80 4) Rs.120 5) None of these

**16.** A trader sells an article at a profit of 30%. Had he purchased it at 10% less and sells for Rs.330 less he would have gained 20%. Find the cost price of the article.

1) Rs.1500 2) Rs.1200 3) Rs.1600 4) Rs.1950 5) None of these

**17.** A student bought 20 pens, 8 packets of wax colours, 6 calculators and 7 pencil boxes, the price of one pen is Rs. 7, one packet of wax colour is for Rs. 22, one calculator is for Rs. 175 and one pencil box costs Rs. 14 more than the combined price of one pen and one packet of wax colours. How much amount did he pay to the shopkeeper?

1) Rs. 491 2) Rs. 1725 3) Rs. 1667 4) Rs. 1527 5) None of these

**18.** A man buys 5 horses and 10 cows for Rs.1600. He sells horses at a profit of 15% and cows at a loss of 10% if his overall profit was Rs.90, what was the cost price of a horse?

1) Rs.170 2) Rs.60 3) Rs.260 4) Rs.200 5) None of these

**19.** A man buys 120 litres of oil for Rs. 3360. He sells 80 litres of oil for Rs. 32 per litre and remaining at Rs.24 per litre. Find his overall profit/loss%?

1) 3.6% loss 2) 4.2% profit 3) 4.8% loss 4) 2.8% loss 5) None of these

**20.** A dealer allows 10% discount on the list price of a certain article and yet makes a profit of 25% on each article. Find the cost price of the article when list price is Rs.50.

1) Rs.36 2) Rs.32 3) Rs.38 4) Rs.42 5) None of these

**ANSWERS: 1-2; 2-5; 3-2; 4-1; 5-2; 6-2; 7-2; 8-3; 9-1; 10-2; 11-5; 12-3; 13-1; 14-2; 15-3; 16-1; 17-3; 18-4; 19-5; 20-1.**

**Explanations**

**1. **Cost Price = 100/100 + 12 x 14336 = Rs. 12800

**Shortcut: **Cost Price is 100% Profit% = 12% therefore S.P = 112%

if 112% = 12336, then 100%

100/112 x 14336 = Rs. 12800

**2. **C. P of 120 oranges = Rs. 720

S. P of 70 oranges at Rs. 8

= 70 × 8 = Rs. 560

S. P. of 50 oranges at Rs. 5 = 50 x 5 = Rs. 250

Total S.P of 120 oranges = 560 + 250 = Rs. 810

Profit = 810 - 720 = Rs. 90

∴ Profit % = 90/720 x 100 = 12.5%

**3. **Cost Price = Rs. 480 Selling price = 55 × Rs. 12 = Rs. 660

Profit = 660 - 480 = Rs. 180

∴ Profit % = 180/480 x 100 = 37.5%

**4. **Let th CP of items A & B be Rs. 100 each SP of item A is 140 (40% profit)

SP of item B is 80% of 140 = 112

Total CP is Rs. 200

Total SP = Rs. 140 + 112 = Rs. 252

Profit = Rs. 52

If the total profit is Rs. 52 CP of item A is Rs.100

If the total profit is Rs. 156, then CP of

A = 152/52 x 100 = Rs. 300

**5. **85% value is Rs. 238

∴ 125% value = 125/85 x 238 = Rs. 350

**6. **Total Cost Price = Total Selling Price

Total SP = Rs. 151600

CP of 1st car = 100/125 × 75800 = Rs. 60640

CP of 2nd car = 151600 - 60640 = Rs. 90960

SP of 2nd car = 75800

∴ Loss % = 75800 - 90960/ 90960 × 100 = 16.67%

**7. **Let the Cost price of the house be Rs.x

⇒ x = Rs. 3000000

**8.** LCM of 6 and 7 is 42 Cost price of 6 pencils is Rs. 9

Cost price of 42 pencils = 42/6 × 9 = Rs. 63

Selling Price of 7 pencils is Rs. 11

Selling Price of 42 pencils = 42/2 × 11

= Rs. 66 ⇒ Gain = 66 − 63 = Rs. 3

If the gain is Rs. 3, he purchased 42 pencils, but gain is Rs. 9, therefore

The number of pencils = 42 × 3 = 126

**9. **Let the C.P of 5 tables be Rs.x, then C.P of 10 chairs = Rs. (1600 - x)

∴ 15% x - 10% (1600 - x) = Rs.90 by solving, x = Rs.1000

C.P of 5 tables = Rs.1000

C.P of 10 chairs = Rs.1600 - Rs.1000 = Rs.600

C.P of one table = 1000/5 = Rs.200

C.P of one chair = 600/10 = Rs.60

**Shortcut: **Use Allegation method

**10. **Profit%

**11. **Let the second lot be Rs.x 120% of (30 × Rs.17.50 + 30 × x)

= (30 + 30) × 18.60 ⇒ x = Rs.13.50

**12. **Marked Price

**13. **Let the number of articles be 'x'

**14. **With 10% money, he buys 5 apples, therefore with 100% money, he buys 50 apples. Without discount he gets only 45 apples.

∴ Original price per apple = 225/45 = Rs.5

**15.** Let the C.P of each book be Rs. 100

S. P. of 40 books = 110 × 40 = Rs. 4400

S. P. of 50 books = 120 × 50 = Rs. 6000

Total S.P. = Rs. 4400 + Rs. 6,000 = Rs. 10400

At a uniform profit of 15% S.P. of 90 books = 90 × 115 = Rs. 10350

Difference = Rs.10,400 - Rs. 10,350 = Rs. 50

If the difference is Rs. 50 then C.P. = Rs. 100

If the difference is Rs. 40

then C.P. = 100 × 40 /50 = Rs. 80

**16. **Let the cost price be Rs. 100

Then S.P. = Rs. 130. (at 30% profit) if he buys 10% less, then C.P. = Rs. 90

Difference in S.P. is (130 - 108) = Rs.22

If the difference in S.P. is Rs.22, the C.P. is Rs. 100

if the difference in S.P. is Rs. 330,

then C.P. = 300/22 × 100 = Rs. 1500

**17****.** Cost price of 20 pens = 20 × 7 = Rs. 140

Cost price of 8 packets wax colours = 8 × 22 = Rs. 176

Cost price of 6 calculators = 6 × 175 = Rs. 1050

Cost price of 7 pencil boxes = 7 × (14 + 7 + 22) = Rs. 301

∴ Total Cost = 140 + 176 + 1050 + 301 = Rs. 1667

**18.** Let the C.P. of 5 horses be Rs. x, then C.P. of 10 cows = Rs (1600 - x)

∴ 15% - 10% (1600 - x) = Rs. 90

⇒ x = Rs. 1000 C.P. of 5 horses = Rs. 1000

∴ C.P. of one horse = 1000/5 = Rs.200

**19.** C. P of 120 litres = Rs. 3360

S.P of 80 litres at Rs. 32 = 80 × 32 = Rs. 2560

S.P. of 40 litres at Rs.24 = 40 × 24 = Rs. 960

∴ Total S.P of 120 litres = 2560 + 960 = Rs. 3520

Profit = 3520 − 3360 = Rs. 160

∴ Profit % = 160/3360 × 100 = 4.8%

**20.** 50 = 100 + 25% /100 - 10 × C.P

C. P = 90/ 125 × 50 = Rs. 36