“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.
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% 
Model Questions
1. Find the value of 55% (240) + 80% (60)
a) 210 b) 145 c) 170 d) 180
2. What should come in place of question mark 10% of ? = 70
a) 600 b) 260 c) 700 d) 145
3. The ratio 2 : 5 expressed as a percent equals:
a) 20% b) 10% c) 30% d) 40%
4. What should come in place of question mark 
a) 476 b) 530 c) 246 d) 125
5. If x% of x is 81, then x is equal to....
a) 40 b) 90 c) 50 d) 81
6. In an examination, 40% of total students failed in Hindi, 35% failed in English and 25% in both. Find the percentage of those who passed in both the subjects.
a) 20% b) 40% c) 50% d) 100%
7. If A's salary is 40% less than B's salary, by how much percent is B's salary more than A's?
a) 12.5% b) 30% c) 16.67% d) 66.67%
8. Akhil's salary was decreased by 50% and then increased by 50%. How much percent does he lose?
a) 25% b) 50% c) 75% d) 33.3%
9. When the price of a product was decreased by 20%, the number sold increased by 40%. What was the effect on the total revenue?
a) 20% increase b) 17% decrease
c) 15% decrease d) 12% increase
10. If 16% of x = 8% of y, then 20% of x is:
a) 10% of y b) 5% of y
c) 25% of y d) 50% of y
11. Two students appeared at an examination. One of them secured 10 marks more than the other and his marks was 60% of the sum of their marks. The marks obtained by them are:
a) 10, 50 b) 20, 30 c) 45, 55 d) 35, 45
12. A fruit seller had some apples. He sells 60% apples and still has 240 apples. Originally, he had....
a) 840 b) 240 c) 450 d) 600
13. What percent of 7.2 kg is 144 gms?
a) 14% b) 12% c) 2% d) 1%
14. In a school 30% of the students play football and 40% play cricket. If 35% of the students neither play football nor cricket, the percentage of the students playing both is.....
a) 5% b) 8% c) 12% d) 40%
15. In a garden, 70% of trees are coconut trees, 25% of the coconut trees are mango trees and 10% of the mango trees are apple trees. If the number of apple trees are 1400, then the number of trees in the garden is...
a) 25000 b) 40000
c) 75000 d) 80000
16. If 40% of x is added to 50% of B, the answer is 90% of B. What percentage of x is B?
a) 50% b) 75% c) 120% d) 100%
17. If 40% of (A + B) = 60% of B, then value of 
a) 
b) 0 c) 4 d) 3
18. If 150% of y is 180, then y is....
a) 250 b) 150 c) 300 d) 120
19. What is 25% of 30% of 1600?
a) 120 b) 240 c) 135 d) 360
20. 35 is what percent of 175?
a) 40% b) 20% c) 25% d) 60%
Explanations
1. 55% (240) + 80% (60) = 132 + 48 = 180
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Percentage failed Hindi or English = 50%
Percentage passed = 100% − 50% = 50%.7
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