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
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
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
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
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
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
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
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.
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
⇒ 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: CP1 = SP2
CP2 = SP1
Hence, total CP =
CP1 + CP2 = SP2 + SP1 = total SP
So, he makes neither profit nor loss
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
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
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
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
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
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.
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
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 + x2 /100 = 24 100
x2 + 100x - 2400 = 0
⇒ x = +20, - 120
∴ Cost price is 20
Shortcut: Solve the question by options
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%
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
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
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%
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
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
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
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
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%
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%
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%
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