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Percentages aptitude questions

Successive change, percentage points, and turning fractions into percentages fast.

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Formula sheetPercentages: the essentialsFormula sheetPercentages: the essentialsShow

  • Percentage change = (new − old) ÷ old × 100. The base is always the starting value.
  • Successive changes of a% and b%: net a + b + ab/100 per cent, entering falls as negatives. An equal rise and fall of x% is always a net loss of x²/100 per cent.
  • If A is x% more than B, B is 100x/(100 + x) per cent less than A. If A is x% less than B, B is 100x/(100 − x) per cent more than A.
  • Constant expenditure: a price rise of r% needs a consumption cut of 100r/(100 + r) per cent; a price fall of r% allows a rise of 100r/(100 − r) per cent.
  • Growth over n periods multiplies by (1 + r/100)ⁿ, depreciation by (1 − r/100)ⁿ. To go back in time, divide.
  • If x% of A = y% of B, then A : B = y : x.
  • Percentage points are a plain difference: 30% to 36% is 6 points, but a 20% increase.
  • Two overlapping groups: A or B = A + B − both, and neither = 100% − (A or B).

Fractions worth knowing

1/3 = 33⅓%, 1/6 = 16⅔%, 1/7 ≈ 14.29%, 1/8 = 12.5%, 1/9 ≈ 11.11%, 1/11 ≈ 9.09%, 1/12 = 8⅓%.

Example: up 25% and then down 25% is 1.25 × 0.75 = 0.9375, a 6.25% loss, not zero.

Questions41

1

Up 20%, then down 20%

A price is increased by 20% and the new price is then decreased by 20%. What is the net change from the original?

successive change

45s

Easy2

Two years of population growth

A town's population is 50,000 and grows by 10% every year. What will it be after 2 years?

compound growth

45s

Easy3

Passing marks from a fail margin

A student scored 240 marks and failed by 30 marks. If the pass mark is 45% of the total, what is the total?

percent of total

45s

Easy4

If A is 25% more than B

If A is 25% more than B, then B is what percent less than A?

base change

60s

Medium5

Percentage points versus percentage

A company's market share rose from 30% to 36%. By what percentage did its share increase?

percentage points

45s

Medium6

Keeping the sugar bill the same

The price of sugar rises by 25%. By what percent must a family cut its consumption so that its expenditure on sugar stays the same?

expenditure

60s

Medium7

Finding the number from a part

If 30% of a number is 12.6, what is the number?

basics

45s

Easy8

What percent of a day

3 hours is what percent of a day?

basics

45s

Easy9

Total marks from a fail margin

A student must score 33% to pass. He gets 125 marks and fails by 40 marks. What are the maximum marks?

exam marks

45s

Easy10

A is 25% more than B

If A's income is 25% more than B's, then B's income is what percent less than A's?

base change

60s

Medium11

A is 20% less than B

If A's income is 20% less than B's, then B's income is what percent more than A's?

base change

60s

Medium12

Keeping the bill unchanged

The price of sugar rises by 25%. By what percent must a family reduce its consumption so that its expenditure on sugar is unchanged?

expenditure

60s

Medium13

Working back to the price rise

When the price of a commodity rose, a family reduced its consumption by 20% and its expenditure stayed the same. By what percent did the price rise?

expenditure

60s

Medium14

A salary up 20%, then down 20%

A salary is increased by 20% and the new figure is then decreased by 20%. What is the net change?

successive change

45s

Easy15

Price down, sales up

The price of an article is reduced by 20% and its sales rise by 30%. What is the net effect on revenue?

successive change

45s

Medium16

Marked up, then discounted

A shopkeeper raises the price of an article by 30% and then offers a 10% discount. What is the net change in price?

successive change

45s

Easy17

Working back through two changes

A number is increased by 20% and then decreased by 20%, giving 9,600. What was the original number?

successive change

60s

Medium18

Valid votes in an election

In an election between two candidates, 20% of the votes polled were invalid. The winner secured 55% of the valid votes.

elections

75s

Medium19

Winner's share among three candidates

Three candidates polled 1,136, 7,636 and 11,628 votes respectively. What percentage of the total votes did the winner get?

elections

60s

Easy20

Comparing two numbers through a third

Two numbers are respectively 20% and 50% more than a third number. The first is what percent of the second?

comparison

45s

Medium21

40% of 60 is what percent of 240

40% of 60 is what percent of 240?

basics

45s

Easy22

20% of A equals 30% of B

If 20% of A = 30% of B, then A : B is:

ratio

45s

Easy23

B as a percentage of A

If 90% of A = 30% of B and B = x% of A, what is the value of x?

ratio

45s

Medium24

The effect on savings

A man spends 75% of his income. His income rises by 20% and his expenditure by 10%. By what percent do his savings increase?

income and savings

90s

Medium25

Students without a scholarship

In a school 60% of the students are boys and the rest girls. 25% of the boys and 50% of the girls receive a scholarship.

weighted

75s

Medium26

Passing in both subjects

In an examination 35% failed in Mathematics, 45% failed in English and 20% failed in both. What percent passed in both subjects?

set theory

60s

Medium27

Population two years ago

The population of a town is 176,400 and grows at 5% per annum. What was it two years ago?

growth

60s

Medium28

Depreciation over two years

A machine worth ₹1,00,000 depreciates at 10% per annum. What is its value after two years?

depreciation

45s

Easy29

30% exceeds 20% by 18

30% of a number exceeds 20% of it by 18. What is the number?

basics

45s

Easy30

Total from those present

In a class 20% of the students were absent and 32 were present. What is the total strength of the class?

basics

45s

Easy31

Diluting a salt solution

80 kg of a solution contains 15% salt by weight. How much water must be added so that the salt content falls to 10%?

mixtures

75s

Medium32

A fraction after two changes

If the numerator of a fraction is increased by 20% and the denominator decreased by 10%, the new fraction is 20/21. What was the original fraction?

fractions

105s

Hard33

Relating two unknowns

If 8% of x = 4% of y, then 20% of x is what percent of y?

ratio

60s

Medium34

A chain of comparisons

A's marks are 20% more than B's, and B's marks are 25% less than C's. A's marks are what percent of C's?

comparison

60s

Medium35

A percentage of a percentage

25% of 25% of a quantity is 25. What is the quantity?

basics

45s

Easy36

Percent across units

40 quintals is what percent of 2 metric tonnes? (1 metric tonne = 10 quintals.)

units

45s

Medium37

45% of 750

What is 45% of 750?

basics

45s

Easy38

How many are not

72% of 25 students are good at mathematics. How many are not good at it?

basics

30s

Easy39

Undoing a pay cut

A worker's salary is reduced by 20%. By what percent must the reduced salary be increased to bring it back to the original?

base change

60s

Medium40

Solving for the percentage

If x% of 200 = 40, what is the value of x?

basics

30s

Easy41

Two reductions as one

Successive reductions of 10% and 20% are together equivalent to a single reduction of:

successive change

45s

Easy

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Percentages Aptitude Questions with Solutions

41 Percentages questions with hints, worked solutions and time targets — 19 easy · 21 medium · 1 hard.

  • Section: Quantitative Aptitude
  • Questions: 41
  • By difficulty: 19 easy · 21 medium · 1 hard
  • Cost: Free, unlimited on every plan

Successive change, percentage points, and turning fractions into percentages fast.

Percentages: the essentials

  • Percentage change = (new − old) ÷ old × 100. The base is always the starting value.
  • Successive changes of a% and b%: net a + b + ab/100 per cent, entering falls as negatives. An equal rise and fall of x% is always a net loss of x²/100 per cent.
  • If A is x% more than B, B is 100x/(100 + x) per cent less than A. If A is x% less than B, B is 100x/(100 − x) per cent more than A.
  • Constant expenditure: a price rise of r% needs a consumption cut of 100r/(100 + r) per cent; a price fall of r% allows a rise of 100r/(100 − r) per cent.
  • Growth over n periods multiplies by (1 + r/100)ⁿ, depreciation by (1 − r/100)ⁿ. To go back in time, divide.
  • If x% of A = y% of B, then A : B = y : x.
  • Percentage points are a plain difference: 30% to 36% is 6 points, but a 20% increase.
  • Two overlapping groups: A or B = A + B − both, and neither = 100% − (A or B).

Fractions worth knowing

1/3 = 33⅓%, 1/6 = 16⅔%, 1/7 ≈ 14.29%, 1/8 = 12.5%, 1/9 ≈ 11.11%, 1/11 ≈ 9.09%, 1/12 = 8⅓%.

Example: up 25% and then down 25% is 1.25 × 0.75 = 0.9375, a 6.25% loss, not zero.

Questions

  1. Up 20%, then down 20% Easy
    A price is increased by 20% and the new price is then decreased by 20%. What is the net change from the original?
  2. Two years of population growth Easy
    A town's population is 50,000 and grows by 10% every year. What will it be after 2 years?
  3. Passing marks from a fail margin Easy
    A student scored 240 marks and failed by 30 marks. If the pass mark is 45% of the total, what is the total?
  4. If A is 25% more than B Medium
    If A is 25% more than B, then B is what percent less than A?
  5. Percentage points versus percentage Medium
    A company's market share rose from 30% to 36%. By what percentage did its share increase?
  6. Keeping the sugar bill the same Medium
    The price of sugar rises by 25%. By what percent must a family cut its consumption so that its expenditure on sugar stays the same?
  7. Finding the number from a part Easy
    If 30% of a number is 12.6, what is the number?
  8. What percent of a day Easy
    3 hours is what percent of a day?
  9. Total marks from a fail margin Easy
    A student must score 33% to pass. He gets 125 marks and fails by 40 marks. What are the maximum marks?
  10. A is 25% more than B Medium
    If A's income is 25% more than B's, then B's income is what percent less than A's?
  11. A is 20% less than B Medium
    If A's income is 20% less than B's, then B's income is what percent more than A's?
  12. Keeping the bill unchanged Medium
    The price of sugar rises by 25%. By what percent must a family reduce its consumption so that its expenditure on sugar is unchanged?
  13. Working back to the price rise Medium
    When the price of a commodity rose, a family reduced its consumption by 20% and its expenditure stayed the same. By what percent did the price rise?
  14. A salary up 20%, then down 20% Easy
    A salary is increased by 20% and the new figure is then decreased by 20%. What is the net change?
  15. Price down, sales up Medium
    The price of an article is reduced by 20% and its sales rise by 30%. What is the net effect on revenue?
  16. Marked up, then discounted Easy
    A shopkeeper raises the price of an article by 30% and then offers a 10% discount. What is the net change in price?
  17. Working back through two changes Medium
    A number is increased by 20% and then decreased by 20%, giving 9,600. What was the original number?
  18. Valid votes in an election Medium
    In an election between two candidates, 20% of the votes polled were invalid. The winner secured 55% of the valid votes.
  19. Winner's share among three candidates Easy
    Three candidates polled 1,136, 7,636 and 11,628 votes respectively. What percentage of the total votes did the winner get?
  20. Comparing two numbers through a third Medium
    Two numbers are respectively 20% and 50% more than a third number. The first is what percent of the second?
  21. 40% of 60 is what percent of 240 Easy
    40% of 60 is what percent of 240?
  22. 20% of A equals 30% of B Easy
    If 20% of A = 30% of B, then A : B is:
  23. B as a percentage of A Medium
    If 90% of A = 30% of B and B = x% of A, what is the value of x?
  24. The effect on savings Medium
    A man spends 75% of his income. His income rises by 20% and his expenditure by 10%. By what percent do his savings increase?
  25. Students without a scholarship Medium
    In a school 60% of the students are boys and the rest girls. 25% of the boys and 50% of the girls receive a scholarship.
  26. Passing in both subjects Medium
    In an examination 35% failed in Mathematics, 45% failed in English and 20% failed in both. What percent passed in both subjects?
  27. Population two years ago Medium
    The population of a town is 176,400 and grows at 5% per annum. What was it two years ago?
  28. Depreciation over two years Easy
    A machine worth ₹1,00,000 depreciates at 10% per annum. What is its value after two years?
  29. 30% exceeds 20% by 18 Easy
    30% of a number exceeds 20% of it by 18. What is the number?
  30. Total from those present Easy
    In a class 20% of the students were absent and 32 were present. What is the total strength of the class?
  31. Diluting a salt solution Medium
    80 kg of a solution contains 15% salt by weight. How much water must be added so that the salt content falls to 10%?
  32. A fraction after two changes Hard
    If the numerator of a fraction is increased by 20% and the denominator decreased by 10%, the new fraction is 20/21. What was the original fraction?
  33. Relating two unknowns Medium
    If 8% of x = 4% of y, then 20% of x is what percent of y?
  34. A chain of comparisons Medium
    A's marks are 20% more than B's, and B's marks are 25% less than C's. A's marks are what percent of C's?
  35. A percentage of a percentage Easy
    25% of 25% of a quantity is 25. What is the quantity?
  36. Percent across units Medium
    40 quintals is what percent of 2 metric tonnes? (1 metric tonne = 10 quintals.)
  37. 45% of 750 Easy
    What is 45% of 750?
  38. How many are not Easy
    72% of 25 students are good at mathematics. How many are not good at it?
  39. Undoing a pay cut Medium
    A worker's salary is reduced by 20%. By what percent must the reduced salary be increased to bring it back to the original?
  40. Solving for the percentage Easy
    If x% of 200 = 40, what is the value of x?
  41. Two reductions as one Easy
    Successive reductions of 10% and 20% are together equivalent to a single reduction of:

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