“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. 46% of a is same as 23% of y, then 60% of a is same as?
A) 15% of y B) 30% of y C) 20% of y D) 40% of y
Ans: B
2. S% of S is 1225. Then S is equal to.....
A) 450 B) 500 C) 350 D) 150
Ans: C
3. What is the value of 20% of 230% of 600?
A) 4600 B) 2760 C) 460 D) 276
Ans: D
6. When 23 is subtracted from 23% of a number, the result is 23. The number is....
A) 100 B) 200 C) 400 D) 300
Ans: B
7. If 57% of a number is added to 86, then the result is the number itself. The number is....
A) 430 B) 640 C) 200 D) 150
Ans: C
8. What is to be added to 16% of 230 so that the sum is equal to 14% of 320?
A) 16 B) 10 C) 15 D) 8
Ans: D
9. The train ticket fare from places x to y in second class AC and third class AC is Rs.6000 and Rs.4500 respectively. If the fares of second class AC and third class AC are increased by 30% and 20% respectively, then find the ratio of new fares of second class AC and third class AC.
A) 13 : 9 B) 12 : 11 C) 25 : 26 D) 28 : 29
Ans: A
10. A person 'will' 40% of his wealth to charity and rest to his family. What percent of the wealth willed to charity does the family get?
A) 125% B) 150% C) 112.5% D) 140%
Ans: B
11. If a number is 43% more than second number, how much percent is the second number smaller than the first number? (approximately)
A) 35% B) 30% C) 25% D) 40%
Ans: B
12. If X's income is 35% less than Y's income, then Y's income is what percentage more than that of X's income? (approximately)
A) 27% B) 46% C) 53% D) 69%
Ans: C
13. If the price of a soap is increased by 37.5%, then how much percentage should the new price be reduced to bring it down to the original price?
A) 27.27% B) 36.36% C) 45.45% D) 18.18%
Ans: A
14. Two numbers are respectively 35% and 18% more than the third number. Then how much percent is the first number more than the second number?
A) 14.4% B) 19.9% C) 9.9% D) 23.3%
Ans: A
15. Two numbers are respectively 32% more and 19% less than the third number. Find how much percent is the second number less than the first number? (approximately)
A) 42.4% B) 38.6% C) 35.7% D) 23.9%
Ans: B
16. If a number is 60% more than the second number and the second number is 32% less than that of third number. Find how much percent is the third number less than that of the first number? (approximately)
A) 5% B) 12% C) 14% D) 8%
Ans: D
17. If A is 23% less than B and C is 40% of the sum of A and B, then by what percentage is B greater than C? (approximately)
A) 53.4% B) 41.2% C) 62.3% D) 69.5%
Ans: B
18. If A is 56% more than B and C is 25% of the sum of A and B, then by what percentage is B greater than C?
A) 56.25% B) 58.39% C) 54.12% D) 59.36%
Ans: A
Some more...
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% 
