“Percentage” topic is heart of Arithmetic. This concept almost applicable to all the major topics in quantitative aptitude especially in Data Analysis & Data Interpretation, which are helpful to score better in the competitive examinations.
The word “Percent” means “Per hundred”. It represented by symbol “%”. In order to score maximum marks in the Quant section, one needs to be thorough with the conversations i.e. percentage to fraction and fraction to percentage.
Percentage to Fraction conversion:
Ex: 75% is equal to which fraction?
Some important Percentages to Fractions conversions
Percentage Fraction
100% 1
75% 3/4
50% 1/2
25% 1/4
12 1/2% 1/8
37 1/2% 3/8
62 1/2% 5/8
87 1/2% 7/8
16 2/3% 1/6
33 1/3% 1/3
66 2/3% 2/3
Fraction to Percentage conversion:
Ex: 1/2 fraction is equal to how much percentage?
1/2 × 100 = 50%
Some important fraction to percentage conversions
Fraction Percentage
1 100%
1/2 50%
1/3 33 1/3%
1/4 25%
1/5 20%
1/6 16 2/3%
1/7 14 2/7%
1/8 12 1/2%
1/9 11 1/9%
1/10 10%
1/11 9 1/11%
If we remember the above values in the table we can easily solve the required problems within short time.
1. What is 7% of 70% of 700?
A) 5.67 B) 3.43 C) 34.3 D) 56.7
Ans: C
2. A person's salary has increased from Rs.4000 to Rs.5500. What is the percentage increase in his salary?
A) 25 B) 37.5 C) 62.5 D) 87.5
Ans: B
3. If the price of petrol is increased by 30%, by what percentage should the consumption be decreased by the consumer, if the expenditure on petrol remains unchanged?
A) 49.47% B) 15.67% C) 35.14% D) 23.07%
Ans: D
4. A water pipe is cut into two pieces. The longer piece is 65% of the length of the pipe. By how much percentage is the longer piece longer than the shorter piece?
A) 74.16% B) 85.71% C) 93.36% D) 41.25%
Ans: B
5. The price of sugar has increased by 40%. If a family wants to keep its expenses on sugar unaltered, then the family will have to reduce the consumption of sugar by ...
A) 25.571% B) 40.685% C) 53.215% D) 14.258%
Ans: A
6. The population of a town is 175000. It increases by 20% in the 1st year and decreases by 10% in the 2nd year. What is the population of the town at the end of 2 yr?
A) 135000 B) 189000 C) 198000 D) 150000
Ans: B
7. Income of Sanjay is first increased by 20% and then it is decreased by 20%. What is the change in his income?
A) 10% increase B) 4% decrease C) 4% increase D) 10% decrease
Ans: B
8. Two numbers are respectively 35% and 45% more than the 3rd number. What is the percentage of 2nd with respect to 1st?
A) 107.40% B) 112.25% C) 135.20% D) 145.40%
Ans: A
9. In a particular constituency, 90% of voters cast their votes, out of which 5% were rejected. The winning candidate received 80% of the valid votes and bagged a total of 13680 votes. The total number of voters in the constituency is ....
A) 23000 B) 21000 C) 25000 D) 20000
Ans: D
10. The salary of an employee of a company increases every month by 15%. If his salary in June was Rs.7500, then what would be his approximate salary in the month of August of the same year?
A) 9963.96 B) 9950.25 C) 9975.18 D) 9918.75
Ans: D
11. In an examination, it is required to get 350 marks out of aggregate marks to pass. A student gets 270 marks and is declared failed by 20% marks. What are the maximum aggregate marks a student can get?
A) 600 B) 400 C) 450 D) 900
Ans: B
12. Akash spends 20% of an amount of money on an insurance policy, 30% on food, 20% on children's education and 10% on recreation. He deposits the remaining amount of Rs.600 in the bank. How much total amount does he spend on food and insurance
together?
A) 3000 B) 4500 C) 5500 D) 2500
Ans: A
13. Surya invests 20% of his monthly salary in insurance policies. He spends 40% of his monthly salary on shopping and on household expenses. He saves the remaining amount at Rs.12000. What is Surya's monthly income?
A) 30000 B) 35000 C) 40000 D) 25000
Ans: A
14.The ratio of the number of boys and girls in a school is 4 : 3. If 40% of the boys and 50% of the girls are scholarship holders then the percentage of students who do not get the scholarship is ....
A) 36.36% B) 55.71% C) 40.28% D) 60.14%
Ans: B
15. If radius of a circle is increased by 20%, then area of the circle will be increased by
A) 44% B) 41% C) 39% D) 36%
Ans: A
16. If sides of a square is increased by 35%, then area of the square will be increased by
A) 82.25% B) 75.65% C) 14.36% D) 69.69%
Ans: A
17. 70% of a number is greater than 55% of it by 450. The number is ....
A) 3900 B) 1200 C) 3000 D) 4000
Ans: C
18. The single equivalent discount of two successive discounts 30% and 40% is ....
A) 58 B) 47 C) 36 D) 70
Ans: A
19. A cooler of Rs.4400 is available at 12% discount. The cooler can be purchased for?
A) 4411 B) 4114 C) 3872 D) 3782
Ans: C
20. At a clearance sale, books were sold at 12.5% reduction. A student purchased a book for Rs.700 at the clearance sale. The usual price of the book was ....
A) 750 B) 800 C) 690 D) 544
Ans: B
21. In a Speaker election, a candidate who got 40% of total votes was defeated by his rival by 80 votes. The total number of votes polled was ....
A) 650 B) 550 C) 1000 D) 400
Ans: D
22. The selling price of a certain commodity was reduced by 30%. As a result, the sale increased by 60%. What was the effect of it on cash collected by daily sale?
A) 9% decrease B) 9% increase C) 12% increase D) 12% decrease
Ans: C
Model Questions
1. 72 is what percent of 1440?
1) 15% 2) 12.5% 3) 5% 4) 8% 5) 20%
Explanation: 72/1440 x 100 = 1/20 x 100 = 5%
Ans: 3
2. 0.15% of 33. 1/2 % of Rs.10000 is:
1) Rs.5 2) Rs.150 3) Rs.0.05 4) Rs.105 5) Rs.120 
the examination?
1) 68 2) 76 3) 72 4) 74 5) 92
Explanation: Percentage = 684/950 × 100 = 72%
Ans: 3
7. A person who spends 66 2/3% of his income is able to save Rs.1200 per month. His monthly expenses (in Rs.) is.....
1) 1,200 2) 2,400 3) 3,000 4) 3,200 5) 2,600
Explanation: 66 2/3% = 2/3
income = 3p, expenditure = 2p,
savings = 3p − 2p = p
According to question
Ans: 2
8. In a town, the population was 8000. In one year, male population increased by 10% and female population increased by 8% but the total population increased by 9%. The number of males in the town was....
1) 4000 2) 4500 3) 5000 4) 6000 5) 3500
Explanation: By allegation method
9. A reduction of 10% in the price of an apple enable a man to buy 10 apples more for Rs. 54. The reduced price of apples per dozen is.....
1) Rs.6.48 2) Rs.12.96 3) Rs.10.80 4) Rs.14.40 5) Rs.11.76 
12. In an examination, 34% failed in Mathematics and 42% failed in English. If 20% failed in both the subjects, the percentage of students who passed in both subjects was.....
1) 54% 2) 50% 3) 44% 4) 56% 5) 48%
15. A man spends 40% of his monthly salary on food and one-third of the remaining on transport. If he saves Rs.4,500 per month which is equal to half the balance after spending on food and transport, his monthly salary is.....
1) Rs.11,250 2) Rs.22,500 3) Rs.25,000 4) Rs.45,000 5) Rs.16,500
Explanation: Salary = 100%; Food = 40%
