Percentage

Introduction

• Percent means ‘for every 100’ and is derived from the French word ‘cent’, which is a French word for 100.
• The basic utility of Percentage arises from the fact that it is one of the most powerful tools for comparison of numerical data and information.

Mathematical definition of Percentage:

• The concept of percentage mainly applies to ratios, and the percentage value of a ratio is arrived at by multiplying by 100 the decimal value of the ratio.
• For example, a student scores 20 marks out of a maximum possible 30 marks. His marks can then be denoted as 20 out of 30 is (20/30) or (20/30) * 100% = 66.66%.

The process for getting this is perfectly illustrated through the unitary method:
If, 20 out of 30 then X out of 100
20 → 30
X → 100
Therefore,
x=20/30×100 = 66.66%

Percentage Change:

• If original value is changed to the new value, then % change is given as -

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Practice Questions

1. Student A scores 20 marks in an examination out of 30 while another student B scores 40 marks out of 70. Who has performed better?
Ans : A

2. In a class, 60% of students are from India and 50% of the students are girls. If 30% of the Indian students are girls, then what percentage of foreign students are boys? (UPSC 2021)
a. 45%
b. 40%
c. 30%
d. 20%

3. A trader gives successive discounts of 10%, 20% and 10% respectively. The percentage of the original cost price he will recover is:
a. 35.2%
b. 64.8%
c. 60.8%
d. 68.8%

4. The length and the breadth of a rectangle are changed by +20% and by –10%, respectively. What is the percentage change in the area of the rectangle?
a. 8%
b. 10.8%
c. 20%
d. data insufficient

5. What is 10% of 20% of 25% of 100?
a. 0.5
b. 0.75
c. 0.25
d. 1.0

6. Which of the following is the largest number?
a. 40% of 400
b. 5% of 800
c. 1000% of 4
d. 200% of 9

7. A’s salary is 20% lower than B’s salary, which is 15% lower than C’s salary. By how much percent is C’s salary more than A’s salary?
a. 44.05%
b. 45.05%
c. 46.05%
d.47.05%

8. 20% of a number when subtracted from 108, gives the number itself. Find the number.
a. 50
b. 80
c. 70
d. 90

9. The population of a town is 5,00,000. The rate of increase is 20% per annum. Find the population at the start of the third year.
a. 6,20,000
b. 7,20,000
c.8,30,000
d. None of these.

10. The population of a town is 6000. If the number of males increases by 10% and the number of females increases by 20%, then the population becomes 6800. Find the population of females in the town.
a. 2500
b. 3000
c. 2000
d. 3500

11. 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?
a. 0%
b. 5% increase
c. 5% decrease
d. Cannot be determined due to insufficient data

12. When 70% of a number x is added to another number y, the sum becomes. 165% of the value of y. When 60% of the number x is added to another number z, then the sum becomes 165% of the value of z. Which one of the following is correct? (UPSC 2022)
a. z<x<y
b. x<y<z
c. y<x<z
d. z<y<x

13. Two candidates X and Y contested an election. 80% of voters cast their vote. and there were no invalid votes. There was no NOTA (None of the above) option. X got 56% of the votes cast and won by 1440 votes. What is the total number of voters in the voters list?
(UPSC 2022)
a. 15000
b. 12000
c. 9600
d. 5000

14. 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

15. P scored 40 marks more than Q in an examination. If Q scored 10% less marks than P, then how much did Q score? (UPSC 2021)
a. 360
b. 380
c. 400
d. 420

16. A student appeared in 6 papers. The maximum marks are the same for each paper. His marks in these papers are in the proportion of 5: 6: 7: 8: 9: 10. Overall he scored 60%. In how many numbers of papers did he score less than 60% of the maximum marks?
(UPSC 2021)
a. 2
b. 3
c. 4
d. 5

17. As a result of a 25% hike in the price of rice per kg, a person is able to purchase 6 kg less rice for Rs 1,200. What was the original price of rice per kg? (UPSC 2020)
a. Rs. 30
b. Rs. 40
c. Rs. 50
d. Rs. 60

18. A and B are heavy steel blocks. If B is placed on the top of A, the weight increases by 60%. How much weight will reduce with respect to the total weight of A and B, if B is removed from the top of A? (UPSC 2019)
a. 60%
b. 45.5%
c. 40%
d. 37.5%

19. A student has to get 40% marks to pass in an examination. Suppose he gets 30 marks and fails by 30 marks, then what are the maximum marks in the examination? (UPSC 2018)
a. 100
b. 120
c. 150
d. 300

20. In a test, a candidate attempted only 8 questions and secured 50% marks in each of the questions. If he obtained a total of 40% in the test and all questions in the test carried equal marks, how many questions were there in the test? (UPSC 2015)
a. 8
b. 10
c. 15
d. 16

21. What is the 10% of 20% of 25% of 100?
a. 0.5
b. 0.75
c. 0.25
d. 1.0

22. A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
a. 588 apples
b. 600 apples
c. 672 apples
d. 700 apples

23. Geeta went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax-free items?
a. 15
b. 15.70
c. 19.70
d. 20

24. A’s salary increases by 20% and then decreases by 20%. What is the net percentage change A’s salary?
a. 16%
b. 4%
c. 2%
d. 8%

25. A number is increased by 20% and then decreased by 20%, the final value of the number is?
a. does not change
b. decreases by 2%
c. increases by 4%
d. decreases by 4%

26. Thirty percent of a number when subtracted form 91, gives the number itself. Find the number.
a. 60
b. 65
c. 70
d. 75

27. The population of a town is 6000. If the number of males increases by 10% and the number of females increases by 20 %, then the. population becomes 6800. Find the population of females in the town.
a. 2500
b. 3000
c. 2000
d. 3500

28. An item is bought for Rs 42 and sold it for Rs. 52.50. Calculate the percentage increase.
a. 20%
b. 80%
c. 22%
d. 25%

29. In a school there are 1000 students in the year 1999. The number of students increased by 20% in the year 2000. And it is increased by 15% in the year 2001. But it is decreased by 20% in 2002. Then what is the strength in 2002?
a. 1200
b. 1300
c. 1150
d. 1104

30. The difference between 42% of a number and 28% of the same number is 210. What is 59% of that number?
a. 630
b. 885
c. 420
d. 900
e. None of these

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