“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. What is 6% of 60% of 600?
A) 15.67 B) 3.43 C) 21.6
D) 56.7 E) 23.41
Sol:
Ans: C
2. A person's salary has increased from Rs.3000 to Rs.4500. What is the percentage increase in his salary?
A) 25 B) 50 C) 62.5
D) 87.5 E) 44.5
Sol: Percentage increase in salary
Ans: B
3. If the price of petrol is increased by 40%, 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) 28.57% E) 22.13%
Sol: Required percentage loss
Ans: D
4. A water pipe is cut into two pieces. The longer piece is 60% of the length of the pipe. By how much percentage is the longer piece longer than the shorter piece?
A) 74.16% B) 50% C) 93%
D) 41.25% E) 40%
Sol:
Ans: B
5. The price of sugar has increased by 30%. If a family wants to keep its expenses on sugar unaltered, then the family will have to reduce the consumption of sugar by ......
A) 23.076% B) 40.685%
C) 53.215% D) 14.258%
E) 13.098%
Sol: Let the original price be Rs.100.
Then, increased price = Rs.130
Therefore, reduction in consumption
Ans: A
6. The population of a town is 1,85,000. 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) 1,35,000 B) 1,99,800 C) 1,98,000
D) 1,50,000 E) 1,32,400
Sol: Formula used:
Required population
Ans: B
7. Income of Sanjay is first increased by 30% and then it is decreased by 30%. What is the change in his income?
A) 10% increase B) 9% decrease
C) 4% increase D) 10% decrease
E) 5% decrease
Sol: According to the formula,
Ans: B
8. Two numbers are respectively 30% and 40% more than the 3rd number. What is the percentage
of 2nd with respect to 1st?
A) 107.69% B) 102.25%
C) 115.20% D) 145.40%
E) 135.40%
Sol: Let the third number be 100
Then the second number = 130
Third number = 140
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 12580 votes. The total number of voters in the constituency is
A) 2300.11 B) 2100.02 C) 2500.21
D) 18391.81 E) 1739.81
Sol: Let the total number of voters = x
According to the question,
Ans: D
10. The salary of an employee of a company increases every month by 25%. If his salary in June was Rs.6500, then what would be his approximate salary in the month of August of the same year? (In Rs.)
A) 9963.96 B) 9950.25 C) 10000.25
D) 10156.25 E) 10346.25
Sol: Required salary in August
Ans: D
11. In an examination, it is required to get 360 marks out of aggregate marks to pass. A student gets 250 marks and is declared failed by 20% marks. What are the maximum aggregate marks a student can get?
A) 600 B) 550 C) 450 D) 900 E) 650
Sol: Let the maximum aggregate marks be x,
According to the question,
20% of x = 360 − 250
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.850 in the bank. How much total amount does he spend on food and insurance together?
A) Rs.4250 B) Rs.4500 C) Rs.5500
D) Rs.2500 E) None of the above
Sol: Let the total amount be Rs.x.
Total expenditure = (20 + 30 + 20 + 10)% = 80%
Remaining money
= (100 − 80)% of x = 20% of x
According to the question,
20% of x = 850
Ans: A
13. Shanmukh 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.15000. What is Shanmukh's monthly income? (In Rs.)
A) 37500 B) 35000 C) 40000
D) 25000 E) None of the above
Sol: Total salary spent on insurance, shopping
and household expenses = 20 + 40 = 60%
Therefore, saving = 100 − 60 = 40%
Let the total salary be x.
Therefore, 40% of x = Rs.15000
Ans: A
* The ratio of the number of boys and girls in a school is 4 : 3. If 30% of the boys and 40 % of the girls are scholarship holders then the percentage of students who do not get the scholarship is ......
A) 36.36% B) 65.71% C) 40.28%
D) 60.14% E) None of the above
Sol: Let the number of boys be 400.
Number of girls = 300
Boys do not holding scholarship = 100 − 30
= 70% (400) = 280
Girls do not holding scholarship = 100 − 40
= 60%(300) = 180
Therefore, percentage of students not holding scholarship
Ans: B
* If radius of a circle is increased by 25%, then
area of the circle will be increased by .....
A) 56.25% B) 41.02% C) 39.12%
D) 36.23% E) None of the above
Sol: Formula used:
Ans: A
* In a Speaker election, a candidate who got 40% of total votes was defeated by his rival by 120 votes. The total number of votes polled was .....
A) 650 B) 550 C) 1000
D) 600 E) 375
Sol: Let the total number of voters = x
According to the question,
60% (x) − 40% (x) = 120
Therefore, 20% of x = 120
Therefore, x = 600
Ans: D
* A cooler of Rs.3400 is available at 12% discount.
The cooler can be purchased for ....
A) Rs.4411 B) Rs.4114 C) Rs.2992
D) Rs.3782 E) None of the above
Sol: Discount = 12%
So cooler can be purchased for 88% of 3400
Purchasing amount = 
= 2992
Ans: C
* At a clearance sale, books were sold at 12.5% reduction. A student purchased a book for Rs.600 at the clearance sale. The usual price of the book was ..... (In Rs.)
A) 750.21 B) 800.01 C) 685.71
D) 544.11 E) None of the above
Sol: Let the price be p.
Ans: C
* 80% of a number is greater than 55% of it
by 650. The number is .....
A) 3900 B) 1200 C) 2600
D) 4000 E) None of the above
Sol: 80%(x) − 55%(x) = 650
Ans: C
* The single equivalent discount of two successive
discounts 40% and 50% is .....
A) 58 B) 47 C) 36
D) 70 E) None of the above
Sol: Formula used:
Ans: D
* If sides of a square is increased by 30%, then area of the square will be increased by...
A) 69% B) 75% C) 14%
D) 70% E) None of the above
Sol: Formula used:
Successive percentage = x + y + ¾¾
Ans: A
1. If a man reduces the selling price of a fan from 500 to 480, his loss increases by 20%. What is the cost price (in Rs.) of the fan?
A) 100 B) 200 C) 400 D) 500 E) 300
Sol: 20% loss = Rs.20
So, total loss (100%) = Rs.100
cost price = selling price + loss
= 500 + 100 = Rs.600
Ans: D
2. Anupama collects antique stamps. She purchased two but found that she needed to raise money urgently, so she sold them for Rs. 7000 each. On one she made 30% & on the other she lost 30%. How much did she gain or lose in the entire transaction?
A) Rs.1266.67 B) Rs. 4441.33 C) Rs.1384.61 D) Rs.1566.33 E) Rs. 4211.60 x2 (30)(30)
Sol:
Ans: C
3. The cost price of 25 articles is equal to the selling price of 16 articles, profit percentage is?
A) 33.33% B) 11.667% C) 25% D) 56.25% E) 46.25% Difference in articles
Sol:
Ans: D
4. A shopkeeper professes to sell his goods at cost price and uses a 780 gm weight instead of a kg. What is his percentage of gain?
A) 12.65% B) 18.53% C) 15.60% D) 28.20% E) 38.20% 220
Sol:
Ans: D
5. A shopkeeper sells two items at the same price. If he sells one of them at a profit of 15% and the other at a loss of 15%, find the percentage profit/ loss.
A) 2.25% loss B) 3.25% loss
C) 1.5% profit D) No profit, no loss E) 4.5% profit
Sol: If the SP is same then
Ans: A
6. The cost price of 30 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is .....
A) 16 B) 32 C) 24 D) 40 E) 28 Difference in articles
Sol:
Ans: C
7. A man buys a dress for Rs.1200 and sells it at a loss of 20%. What is the selling price of the dress? (In Rs.)
A) 960 B) 801 C) 600 D) 900 E) 500
Sol: Cost price = 100% = Rs.1200
Selling price = 80%(1200) = 960
Ans: A
8. Some pens were bought at 7 pens for Rs.5 and sold at 5 pens for Rs.7. Gain percent is:
A) 35% B) 72% C) 96% D) 36% E) 40%
Sol:
Ans: C
9. When a plot is sold for Rs.19,700, the owner loses 20%. At what price (in Rs.) must that plot be sold in order to gain 15%?
A) Rs.28318.75 B) Rs.45000.23 C) Rs.25000.12 D) Rs.30000.22 E) Rs.10000.23
Sol: Take CP = 100%
So, SP = 80% (at 20% loss) = Rs.19,700
Then SP = 115% (At 15% profit)
Ans: A
10. To make a profit of 20% the selling price of the article is Rs.340. The cost price (in Rs.) of the article is .....
A) 100.2 B) 283.3 C) 600.1 D) 450.2 E) 380.2
Sol: Take CP = 100%
SP = 120% (at 20% profit ) = Rs.340
Ans: B
11. If the ratio of the cost price and the selling price of an article be 5 : 8, then the percentage of profit is ......
A) 10% B) 33% C) 60% D) 25% E) 40%
Sol: Let CP and SP be 5x and 8x respectively
Ans: C
12. Ajay sold two washing machine sets for Rs.8000 each. On one he gained 20% and on the other he lost 20%. Loss or gain of Ajay in the whole transaction is ......
A) 11% loss B) 21% loss C) 4% loss D) 27% gain E) 18% gain
Sol: When SP of two washing machine sets is same then
Ans: C
13. A man buys a fan for Rs.2500 and sells it at a loss of 10%. What is the selling price of the fan? (In Rs.)
A) 1800 B) 2400 C) 2250 D) 1600 E) 1050
Sol: SP = 90%(2500 ) = 2250
Ans: C
14. If the cost price of 20 erasers is equal to the selling price of 16 erasers, the gain percent is?
A) 25% B) 55% C) 60% D) 20% E) 40% Difference in articles
Sol:
Ans: A
15. By selling an article at Rs.1200, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%? (In Rs.)
A) 720 B) 340 C) 740 D) 420 E) 120
Sol: SP = 125% (At 25% profit) = 1200
75 × 1200
Ans: A
16. A shopkeeper earns a profit of 31% after selling a book at a 31% discount on the printed price. The ratio of the cost price and selling price of the book is .....
A) 100 : 79 B) 100 : 131 C) 89 : 100 D) 121 : 100 E) 101 : 120
Sol: CP : SP = 100 : 131 (Since SP = 121% at 31% profit)
Ans: B
17. If selling price of 75 articles is equal to the cost price of 65 articles, then the approximate loss or gain percent is.....
A) Loss of 13.3% B) No profit no loss C) Profit of 25.1%
D) Loss of 20.1% E) Profit of 10.2% Difference in articles
Sol:
Ans: A
18. By selling an article for Rs.850, a person loses 20% of its selling price. At what price (in Rs.) should he sell it to gain 20% on its cost price?
A) 1835 B) 2423 C) 8361 D) 1224 E) 1054
Sol: Given SP = Rs.850
Loss = 20%(850) = Rs.170
CP = SP + loss = 850 + 170 = Rs.1020
SP = 120% (At 20% profit) = 120%(1020)
= Rs.1224
Ans: D
19. A shopkeeper bought 25 kg of sugar at Rs.45 per kg. 30 kg of sugar at Rs.50 per kg and 40 kg of sugar at Rs.40 per kg. He spent a sum of Rs.650 on transportation and other expenses. He mixed all the three types of sugar and sold all the stock at Rs.54.5 per kg. His profit percent in the entire transaction is:
A) 6.21% B) 8.25% C) 4.25% D) 7.5% E) 3.2%
Sol: Cost price of the mixture
Ans: A
20. The marked price of an article is Rs.2500. A shopkeeper sells it by giving a 20% discount on its marked price. If the cost price of the article is Rs.1000, then his profit (in Rs.) is:
A) 1319 B) 1189 C) 1229 D) 1000 E) 2202
Sol: SP of the article (at 20% discount)
= 80%(2500) = 2000
CP = Rs.1000 (Given)
Profit = SP − CP = 2000 − 1000 = Rs.1000
Ans: D
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% 
1. First type of mixture contains 20% alcohol, and the second type of mixture contains 15% alcohol. A new type of mixture would be formed from these two types of mixture in the proportion of 12 parts from the 1st type and 8 parts from the second type. Find the percentage of alcohol in the new mixture.
1) 25% 2) 18% 3) 
4) 20% 5) 33%
Explanation:
Ans: 2
2. Arun after spending 18% of his monthly salary in buying groceries and 20% of the monthly salary in repair work of AC. Invested 40% of the remaining amount in fixed deposits. If he was left with Rs.15,345, how much is his monthly salary?
1) Rs.42,500 2) Rs.45,820 3) Rs.39,750
4) Rs.38,640 5) Rs.41,250
Explanation:
Ans: 5
3. Abhay gave 30% of his money to Vijay. 2 Vijay gave 
rd of what he received to his 3 5 mother. Vijay’s mother gave 
th of the 8 money she received from Vijay to the grocer. Vijay’s mother is now left with Rs.600. How much money did Abhay have initially?
1) Rs.6,000 2) Rs.8,000 3) Rs.10,200 4) Rs.6,200 5) Rs.8,200
Explanation:
Ans: 2
4. At Amarvathi public school, 60% of the students are boys and the rest are girls. Further 15% of the boys and 7.5% of the girls are getting a fee waiver. If the number of those getting a fee waiver is 90. Find the total number of students getting 50% concession if it is given that 50% of those not getting a fee waiver are eligible to get half the concession.
1) 320 2) 360 3) 280 4) 330 5) 350
Explanation: Total no. of students is 100%
Ans: 4
5. A vessel of 48 litres capacity is filled with certain amount of water and milk. If only 40% quantity of the milk and only 60% quantity of water are poured into the vessel then it is only 55% full. The initial quantity of milk and water in that vessel is.......
1) 20, 24 2) 12, 36 3) 24, 24 4) 20, 28 5) 18, 30
Explanation:
Ans: 2
6. A salesman gets a commission of X% on first Rs.4000 worth of sales and Y% on the remaining. When his sales were Rs.11,000 his total commission was Rs.2400 and when his sales were Rs.16,000 his total commission was Rs.3600. What is the value of ‘X’ ?
1) 14% 2) 18% 3) 16% 4) 24% 5) 22%
Explanation:
Ans: 2
7. A salesman allowed 12% commission on the total sales made by him and a bonus of 1% on the sales over 15000 if the total earning of the sales man is Rs.7650. Find the total sales.
1) 40000 2) 60000 3) 36000
4) 48000 5) 45000
Explanation:
Ans: 2
8. An empty fuel tank of a car was filled with Atype petrol. When the tank was half empty, it was filled with B-type petrol. Again, when the tank was half-empty, it was filled with A-type petrol. When the tank was half-empty again, it was filled with B-type petrol. What is the percentage of A-type petrol at present in the tank?
1) 50% 2) 40% 3) 33.5%
4) 37.5% 5) 32.5%
Explanation:
Ans: 4
9. Gopal went to a fruit market with certain amount of money. With this money he can buy either 50 oranges or 40 mangoes. He retains 10% of the money for taxi fare. If he buys 20 mangoes, then the number of oranges he can buy is....
1) 25 2) 18 3) 20 4) 16 5) 12
Explanation:
Ans: 3
10. 120 litre mixture of alcohol and water contains 30% alcohol. How many litres of pure alcohol should be added to this mixture to make alcohol percentage 44%?
1) 40 2) 30 3) 36 4) 48 5) 45
Explanation:
Ans: 2
11. 30 kgs fresh watermelon contains 84% water, after some time water remains 80%. Find the present weight of watermelon.
1) 40 2) 24 3) 36 4) 48 5) 45
Explanation:
Ans: 2
12. Fresh fruit contains 62% water and dry fruit contains 22% water. How many kg of dry fruits can be made from 78 kg of fresh fruit?
1) 40 2) 30 3) 38 4) 35 5) 45
Explanation:
Ans: 3
13. A vessel contains pure ghee. In the container 25% of ghee is consumed and diluted by oil. This process was repeated further 2 times. Find the percentage of ghee in that mixture.
1) 25.6% 2) 42.1% 3) 12 ¾%
4) 20% 5) 33%
Explanation:
Ans: 2
14. In every month Rohith consumes 30 kg rice and 12 kg wheat. The price of rice is 25% of the price of wheat and thus he spends total Rs.468 on the rice and wheat per month. If the price of wheat increased by 25% then what is the percentage reduction of rice consumption for the same expenditure of Rs.468? (Given that the price of rice and consumption of wheat is constant.)
1) 52% 2) 64% 3) 45%
4) 40% 5) 30%
Explanation:
Ans: 4
15. A book consists of 30 pages, 25 lines on each page and 35 characters on each line. If this content is written in another note book consisting of 30 lines and 28 characters per line, then the required number of pages is how much percent greater than the previous pages?
1) 2.5% 2) 6.66% 3) 12 ¾%
4) 4.16% 5) 5.32%
Explanation:
Ans: 4
