Percentage Question sheet 3

Percetage Question Practise sheet 3

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Q.1 The salaries of 30 employees of a company are increased by 10% and that of the remaining 20 employees of the same company are increased by 20%. What is the percentage increase in the total salary of the 50 employees?  

a.15%

b.14%

c.26%

d.Cannot be determined

Q.2 Shailesh got an increment such that his contribution to his family's total income increased from 30% to 40%. What is the increase, in percentage points, in Sailesh's contribution to his family's total income?

a.(100/3)%

b.10%

c.25%

d.None of these

Q.3 In an examination 78% students passed Social Studies and 82% students passes in Hindi. If 71% students passed in both the subjects, then what percent of students failed in both the subjects?

a.15%

b.11%

c.8%

Q.4 Yashi scored 265 marks in an examination and Juhi got 65% of the total marks in the same examination. If Juhi obtained 70 marks less than Yashi. If the minimum passing marks is 35%, then what is the minimum marks to pass in the exam?

a.135

b.125

c.115

d.105

Q.5 In a test consisting of 100 questions carrying one mark each, Amar answered 60% of the first 50 questions correctly. What percentage of the other 50 questions does he need to answer correctly so that his total score is 75%?

a.65%

b.70%

c.90%

d.80%

Q.6 In an examination, in which the maximum marks is 600. A scored 20% more marks than B, B scored 50% more marks than C and D scored 25% more marks than C . If A secured 90% marks of the maximum marks, then the marks scored by D is:

a.375

b.240

c.360

d.225

Q.7 What percentage of numbers from 1 to 100 have squares that end with the digit 8?

a.10%

b.20%

c.5%

d.0%

Q.8 In an examination, 15% of the applicants were found ineligible and 65% of the eligible candidates belonged to the general category. If 8925 eligible candidates belonged to other categories, then how many candidates applied for the examination?

a.30,000

b.35,000

c.37,000

d.None of these

Q.9 Difference of two numbers is 621. If 12.5% of one number is 4/9th of the other number, find the sum of  two numbers.

a.1223

b.1107

c.921

d.1009

Q.10 In a class, the ratio of boys to girls is 4 : 5. If four new boys joined the class, the number of boys would increase by 20%. Find the number of girls in the class.

a.30

b.35

c.20

d.25

Q.11 40% of the fruits in a basket are mangoes. One-third of the mangoes are of excellent quality. Two-third of the mangoes of excellent quality are rotten. The number of other type of fruits in the basket should be at least:

a.9

b.27

c.18

d.36

Q.12 An NGO wants to raise money for Bihar Victims, so they make phone calls to their members. By calling 60% of the members they raise 80% of the money required and each of these members donates an average amount of Rs.1,400. If there are no hidden expenses, then what is the average donation (in Rs.) from the remaining members ?

a.520

b.525

c.530

d.535

Q.13 An amount of Rs. 84000 is divided among Rohit, Rajesh and Rakesh. Rohit’s share is 25% more than that of Rajesh’s share and Rakesh’s share is 3 times of Rajesh’s share, then find the difference between Rakesh’s share & Rohit’s share.

a.26,850

b.28,000

c.27,140

d.27,000

Q.14 In an office, 56% of the employees are men and 64% of the employees are married and 75% of the male employees are married. What is the percentage of unmarried women out of total women?

a.30%

b.50%

c.45%

d.25%

Q.15 There are 150 friends in a group, and they want to go for a film. If in the group, 4% of the boys are equal to 6% of the girls, then what is number of girls in the group?

a.50

b.60

c.75

d.90

Q.16  If x% of 600 = y% of 400 and x% of y% of 350 = 84, then x = ?

a.30

b.40

c.50

d.60

Q.17 There are 120 boys in class 6th and 180 girls in class 7th. Number of girls in class 6th are 60% of girls in class 7th. Total students in class 7th are 50% more than the total students in class 6th. Find the number of boys in class 7th. (total students = number of boys + number of girls)

a.142

b.162

c.172

d.184

Q.18 are in German and rest are in French and Russian in ratio 3 : 2. If total number of books in Russian is 6300, then find the number of books in library.

a.25000

b.30000

c.45000

d.50000

Q.19 There were two candidates contesting an election. 12.5% of the total voters did not cast their votes, whereas 10% of the casted votes were declared invalid. If the loosing candidate received votes from 37.5% of the total voters and lose election by 12600 votes, then what is the total number of votes received by the winning candidate?

a.142,200

b.148,500

c.138,600

d.132,300

Q.20 65% of the employees of a certain company are men and 60% of the men earn more than Rs. 22,000 per month. If 46% employees of the company earn more than Rs. 22,000 per month, then what percent of the women employed by the company earn less than or equal to Rs. 22,000 per month?

a.80%

b.70%

c.50%

d.20%

Q.21 For a family, the savings per month are 30% of the total income. If the expenditure on education is increased from 30% to 40% of the total income, then find the savings, as a percentage of the expenditure on education, provided there is no change in the savings and income.

a.(400/3)%

b.100%

c.75%

d.Cannot be determined

Q.22 Before an increment in Ramu 's salary, the total expenditure of the family was 60% of the total income. Ramu's salary was equal to the total savings of the family then. If Ramu got 50% increment in his salary, then what are the new total savings of the family as a percentage of its new total income if its expenditure is kept constant?

a.(100/3)% 

b.50%

c.(200/3)%

d.40%

Q.23 Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

a.2:5

b.3:5

c.4:5

d.6:7

Q.24 In an election only two candidates participated. 25% voters did not vote. 250 votes were declared as invalid. The winner got 400 more votes than the other one, thus he got votes from 40% of the voters in voters’ list. Find the number of voters in the voters’ list

a.3000

b.2000

c.2600

d.3600

Q.25 The length and breadth of a cuboid are increased by 10% and 20%, respectively, and its height is decreased by 20%. The percentage increase in the volume of the cuboid is:

a.5.2%

b.5.4%

c.5.6%

d.5.8%

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Answers For Percentage Questions for CAT

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Frequently Asked Questions — Percentages for CAT & IPMAT 2026

What is the basic percentage formula?

Percentage = (Value / Total Value) × 100. To find x% of a number N: (x/100) × N. To find what percent A is of B: (A/B) × 100. These three forms cover 90% of CAT percentage questions.

What is the percentage change formula?

Percentage Change = [(New Value - Old Value) / Old Value] × 100. If positive, it is an increase; if negative, it is a decrease. CAT frequently tests this in back-to-back change questions.

How do successive percentage changes work?

For two successive changes of a% and b%, the net change = a + b + (ab/100)%. Example: +20% then -20% gives net change = 20 + (-20) + (20×(-20)/100) = -4%. The result is always a net loss when equal % increase and decrease are applied.

What is the multiplier method for percentage problems?

Instead of calculating percentage separately, use multipliers. A 20% increase → multiply by 1.2. A 15% decrease → multiply by 0.85. For successive changes, multiply the factors: 1.2 × 0.85 = 1.02 → net 2% increase.

How is percentage used in data interpretation?

In DI, percentage questions involve computing growth rates, market share, contribution to total, and year-on-year change. Always identify the base clearly before computing percentage. Approximation techniques save time in CAT DI sets.

What is percentage point vs percentage change?

Percentage point is an absolute difference between two percentages. If pass rate increases from 60% to 75%, it is a 15 percentage point increase but a 25% relative increase [(15/60)×100]. CAT and IPMAT test this distinction carefully.

How do I solve population growth / depreciation problems?

Use the formula: Final Value = Initial Value × (1 ± r/100)^n where r is rate per period and n is number of periods. For population increasing at 10% per year for 3 years: Final = P × (1.1)^3 = 1.331P.

What are common CAT-level percentage tricks?

Key tricks: (1) 1/6 ≈ 16.67%, 1/7 ≈ 14.28%, 1/8 = 12.5% — memorise fractions. (2) If A is x% more than B, then B is [x/(100+x)]×100% less than A. (3) In income-expenditure problems, if income rises by a% and expenditure by b%, savings change can be found using the formula.

How many percentage questions appear in CAT?

Percentages appear in 3-5 questions per CAT, both in standalone QA and embedded in DI sets. IPMAT typically has 2-4 direct percentage questions. It is a foundational topic — mastering it speeds up P&L, SI/CI, and ratio problems significantly.