### 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 -

### 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 2, 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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