### Basics

• The price at which a person buys a product is the cost price (CP) of the product for that person.
• The price at which a person sells a product is the selling price (SP) of the product for that person.
• When a person is able to sell a product at a price higher than its cost price, we say that he has earned a profit. That is,
If SP > CP, the difference, SP – CP is known as the profit or gain.
• Similarly, if a person sells an item for a price lower than its cost price, we say that a loss has been incurred.
If, however, SP < CP, then the difference, CP – SP is called the loss.

### Formulae

• Profit = SP – CP
• Loss = CP – SP
• Percentage Profit = (Profit/CP) * 100
• Percentage Loss = (Loss/CP) * 100
(Note: in both % profit and % loss, denominator is CP)

### Practice Questions

1. A shopkeeper sold goods for Rs. 2000 at a profit of 25%. Find the cost price for the shopkeeper.
a. 1600
b. 600
c. 400
d.800

2. A man buys shirt and trousers for Rs. 371. If the trouser costs 12% more than the shirt, find the cost of the shirt.
a. Rs. 125
b. Rs. 150
c. Rs. 175
d. Rs. 200

3. By selling a watch for Rs. 560, a shopkeeper incurs a loss of 20%. Find the cost price of the watch
a. 600
b. 700
c. 750
d. 800

4. By selling bouquets for Rs. 690, a florist gains 15%. At what price should he sell the bouquets to gain 25% on the cost price?
a. Rs.720
b. Rs.750
c. Rs. 660
d. Rs.780

5. A shopkeeper bought 480 chocolates at Rs. 6 per dozen. If he sold all of them at Rs. 0.75 each, what was his profit per cent?
a. 50%
b. 33(1/3) %
c. 75%
d. 20%

6. If Soham while selling two goats at the same price, makes a profit of 10% on one goat and suffers a loss of 10% on the other one (UPSC 2014)
a. He makes no profit and no loss.
b. He makes a profit of 1%
c. He suffers a loss of 1%
d. He suffers a loss of 2%

7. A shopkeeper sells an article at Rs. 40 and gets X% profit. However, when he sells it at Rs. 20, he faces same percentage of loss. What is the original cost of the article? (UPSC 2018)
a. Rs. 10
b. Rs. 20
c. Rs. 30
d. Rs. 40

8. Gopal bought a cell phone and sold it to Ram at 10% profit. Then Ram wanted to sell it back to Gopal at 10% loss. What will be Gopal position if he agreed? (UPSC 2017)
a. Neither loss nor gain
b. Loss 1%
c. Gain 1%
d. Gain 0.5%

9. If the price of an article is decreased by 20% and then the new price is increased by 25%, then what is the net change in the price? (UPSC 2021)
a. 0%
b. 5% increase
c. 5% decrease
d. Cannot be determined due to insufficient data

10. A man sells a plot of land at 8% profit. If he had sold it at 15% profit, he would have received Rs. 630 more. What is the selling price of the land?
a. 9320
b. 9600
c. 9820
d. 9720

11. A person bought a car and sold it for Rs. 3,00,000. If he incurred a loss of 20%, then how much did he spend to buy the car? (UPSC 2020)
a. Rs. 3,60,000
b. Rs. 3,65000
c. Rs. 3,70,000
d. Rs. 3,75,000

12. If books bought at prices ranging from Rs. 200 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling eight books?
a. 600
b. 1200
c. 1800
d. None of these

13. Rakesh had money to buy 8 mobile handsets of a specific company. But the retailer offered very good discount on that particular handset. Rakesh could buy 10 mobile handsets with the amount he had. What was the discount the retailer offered? (UPSC 2020)
a. 15%
b. 20%
c. 25%
d. 30%

14. A reduction in the price of petrol by 10% enables a motorist to buy 5 litres more for rupees 180. What is the original price of the petrol?
a. Rs. 4
b. Rs. 5
c. Rs. 45
d. Rs. 400

15. By selling a mat for ₹690, Ranveer gains 15%. At what price should he sell the mats to gain 25% on the cost price.
a. ₹ 720
b. ₹ 750
c. ₹ 660
d. ₹ 780

16. A sly shopkeeper professes to sell sugar at 30% loss but he uses 200 gm weight instead of 500 gm. Find his actual profit%.
a. 75%
b. 65%
c. 55%
d. 45%

17. A and B started a business with Rs. 1500 and Rs. 2500 and got a profit of Rs. 800. Half of the profit is shared equally the remaining is shared according to their investment. Find their profits respectively.
a. Rs. 400 and Rs. 400
b. Rs. 500 and Rs. 300
c. Rs. 300 and Rs. 500
d. Rs. 350 and Rs. 450

18. Raj sold an item for Rs. 6, 384/- and incurred a loss of 30%. At what price should he have sold the item to have gained a profit of 30%?
a. Rs. 14, 565/-
b. Rs. 11, 856/-
c. Rs. 13, 544/-
d. cannot be determined

19. A vendor bought 6 oranges for Re 10 and sold them at 4 for Re 6. Find his loss or gain percent.
a. 8% gain
b. 10% gain
c. 8% loss
d. 10% loss

20. Pure ghee costs Re 100 per kg. A shopkeeper mixes vegetable oil costing Re 50 per kg and sells the mixture at Re 96 per kg, making a profit of 20%. In what ratio does he mix the pure ghee with the vegetable oil.
a. 3:2
b. 2:3
c. 4:3
d. 3:1

21. Anil buys a calculator for Re 600 and sells it to Vikash at 10% profit. Vikash sells it to Chandan for 5 % profit. Chandan after using it for certain time, sells it to Dinesh at a loss of 20%. For how much Chandan sell the calculator to Dinesh.
a. Rs.550.50
b. Rs.564.40
c. Rs.554.40
d. None of these

22. By celling a cap for ₹29.75, a man gains 6.25%. What will be the cost price of the cap?
a. ₹ 26
b. ₹ 27.5
c. ₹ 28
d. ₹ 27.80

23. Find a single discount equivalent to the discount series of 20%, 25%, 20%.
a. 66%
b. 46%
c. 52%
d. 34%

24. A person buys a horse for 15 pounds. After one year, he sells it for 20 pounds. After one year, again he buys the same horse at 30 pounds and sells it for 40 pounds. What is the overall profit percent for that person over both the transactions?
a. 30.33%
b. 33.33%
c. 35.33%
d. 40.33%

25. The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:
a. 15
b. 16
c. 18
d. 25