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Ratio & Proportion aptitude questions

Splitting, scaling, partnerships and variation.

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Formula sheetRatio & Proportion: the essentialsFormula sheetRatio & Proportion: the essentialsShow

  • A share = its part ÷ the sum of the parts × the total. Find one part once, then multiply.
  • Joining ratios: scale so the shared term matches. A : B = 2 : 3 and B : C = 4 : 5 give A : B : C = 8 : 12 : 15.
  • If 3A = 4B = 6C, then A : B : C = 1/3 : 1/4 : 1/6 = 4 : 3 : 2. Clear a fractional ratio with the LCM of its denominators.
  • In a : b ∷ c : d, ad = bc. The fourth proportional to a, b, c is bc/a; the third proportional to a, b is b²/a; the mean proportional is √(ab).
  • Direct variation keeps x ÷ y fixed; inverse variation keeps x × y fixed, as with men × days.
  • Numbers in the ratio a : b (coprime) with HCF h are ah and bh, and their LCM is abh.
  • If k is added to both terms, solve (ax + k)/(bx + k) = c/d by cross-multiplying.
  • Partnership: profit is shared in the ratio of capital × time.
  • Lengths in the ratio a : b give areas a² : b² and volumes a³ : b³.
  • Coins counted in a ratio: price one set of the ratio, then count the sets.

Example: ₹7,200 in the ratio 3 : 4 : 5. There are 12 parts, one part is ₹600, so C gets ₹3,000.

Questions36

1

Dividing ₹5,400 in the ratio 2 : 3 : 4

₹5,400 is divided among A, B and C in the ratio 2 : 3 : 4. How much does C receive?

sharing

45s

Easy2

Combining A : B and B : C

If A : B = 2 : 3 and B : C = 4 : 5, what is A : B : C?

compound ratio

45s

Easy3

Profit in a partnership

A invests ₹20,000 for 12 months; B invests ₹30,000 for 8 months. A profit of ₹18,000 is shared in proportion to capital × time. How is it split?

partnership

60s

Medium4

Coins in the ratio 2 : 3 : 4

A bag holds ₹1, 50-paise and 25-paise coins in the ratio 2 : 3 : 4 by count, worth ₹90 in total. How many 50-paise coins are there?

coins

75s

Medium5

More men, fewer days

12 men can build a wall in 20 days. Working at the same rate, how many days will 15 men take?

variation

45s

Easy6

The fourth proportional

What is the fourth proportional to 4, 6 and 10?

proportion

45s

Easy7

Dividing ₹1,200 in the ratio 2 : 3 : 7

₹1,200 is divided among A, B and C in the ratio 2 : 3 : 7. How much does C receive?

sharing

45s

Easy8

Combining A : B and B : C

If A : B = 2 : 3 and B : C = 4 : 5, what is A : B : C?

compound ratio

45s

Easy9

Chaining A : B and B : C again

If A : B = 5 : 7 and B : C = 6 : 11, what is A : B : C?

compound ratio

60s

Medium10

Adding 10 to both numbers

Two numbers are in the ratio 3 : 5. If 10 is added to each, the ratio becomes 5 : 7. What is the smaller number?

algebra

75s

Medium11

Adding 7 to both

Two numbers are in the ratio 1 : 2. If 7 is added to each, the ratio becomes 3 : 5. What is the larger number?

algebra

75s

Medium12

LCM from a ratio and an HCF

Two numbers are in the ratio 3 : 4 and their HCF is 4. What is their LCM?

hcf · lcm

60s

Medium13

Numbers from a ratio and an LCM

Two numbers are in the ratio 4 : 5 and their LCM is 180. What is their sum?

lcm

75s

Medium14

Evaluating an expression from a ratio

If x : y = 5 : 2, what is (8x + 9y) : (8x + 2y)?

algebra

60s

Medium15

A ratio of two expressions

If a : b = 3 : 4, what is (2a + 3b) : (3a + 2b)?

algebra

45s

Easy16

Sum over difference

If x/y = 2/3, what is the value of (x + y)/(x − y)?

algebra

45s

Medium17

When 3A = 4B = 6C

If 3A = 4B = 6C, what is A : B : C?

algebra

60s

Medium18

Sharing in a fractional ratio

₹782 is divided among three people in the ratio ½ : ⅔ : ¾. What is the first share?

sharing · fractions

90s

Medium19

Shares described through one another

A sum of ₹3,400 is divided among A, B and C so that A gets ⅔ of what B gets, and B gets ¼ of what C gets. What is B's share?

sharing

105s

Hard20

Sharing under two linked ratios

₹3,500 is divided among A, B and C such that A : B = 2 : 3 and B : C = 4 : 5. What is C's share?

sharing · compound ratio

90s

Medium21

Three numbers from two ratios

The sum of three numbers is 98. The ratio of the first to the second is 2 : 3, and of the second to the third is 5 : 8. What is the second number?

compound ratio

90s

Medium22

Salaries after different increments

The salaries of A, B and C are in the ratio 2 : 3 : 5. If they receive increments of 15%, 10% and 20% respectively, what is the new ratio?

percentages

75s

Medium23

Incomes, expenditures and equal savings

The incomes of two people are in the ratio 3 : 4 and their expenditures in the ratio 5 : 7. If each saves ₹200, what is the income of the first?

algebra · savings

150s

Hard24

Coins of three denominations

A bag contains ₹1, 50-paise and 25-paise coins in the ratio 5 : 6 : 8, worth ₹210 in all. How many 50-paise coins are there?

coins

105s

Hard25

Reversing a milk-and-water ratio

A 60-litre mixture has milk and water in the ratio 2 : 1. How much water must be added to make the ratio 1 : 2?

mixtures

75s

Medium26

Mixing two alloys in equal weights

One alloy has copper and zinc in the ratio 5 : 3, another in the ratio 7 : 5. Equal weights of the two are melted together.

alloys

120s

Hard27

Scholarship holders in a ratio

The ratio of boys to girls in a school is 3 : 2. If 20% of the boys and 25% of the girls hold scholarships, what percent of students do not hold one?

percentages

75s

Medium28

Fourth proportional to 5, 8 and 15

What is the fourth proportional to 5, 8 and 15?

proportion

45s

Easy29

Third proportional to 4 and 12

What is the third proportional to 4 and 12?

proportion

45s

Easy30

Mean proportional between 9 and 16

What is the mean proportional between 9 and 16?

proportion

45s

Easy31

Solving a proportion

If 0.75 : x ∷ 5 : 8, what is the value of x?

proportion

45s

Easy32

Fewer days, more men

15 men can complete a piece of work in 20 days. How many men are needed to finish it in 12 days?

variation

45s

Easy33

Ratio of areas from a ratio of radii

The radii of two circles are in the ratio 2 : 3. What is the ratio of their areas?

geometry

45s

Easy34

From p : q and q : r to p : r

If p : q = 3 : 4 and q : r = 8 : 9, what is p : r?

compound ratio

45s

Easy35

Dividing 60 in the ratio 2 : 3

Divide 60 into two parts in the ratio 2 : 3. What is the smaller part?

sharing

30s

Easy36

A ratio that changes with time

The present ages of two people are in the ratio 4 : 5. After 5 years the ratio becomes 5 : 6. What is the present age of the younger?

ages

75s

Medium

Showing 36 of 36

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Ratio & Proportion Aptitude Questions with Solutions

36 Ratio & Proportion questions with hints, worked solutions and time targets — 15 easy · 17 medium · 4 hard. Splitting, scaling, partnerships and variation.

  • Section: Quantitative Aptitude
  • Questions: 36
  • By difficulty: 15 easy · 17 medium · 4 hard
  • Cost: Free, unlimited on every plan

Splitting, scaling, partnerships and variation.

Ratio & Proportion: the essentials

  • A share = its part ÷ the sum of the parts × the total. Find one part once, then multiply.
  • Joining ratios: scale so the shared term matches. A : B = 2 : 3 and B : C = 4 : 5 give A : B : C = 8 : 12 : 15.
  • If 3A = 4B = 6C, then A : B : C = 1/3 : 1/4 : 1/6 = 4 : 3 : 2. Clear a fractional ratio with the LCM of its denominators.
  • In a : b ∷ c : d, ad = bc. The fourth proportional to a, b, c is bc/a; the third proportional to a, b is b²/a; the mean proportional is √(ab).
  • Direct variation keeps x ÷ y fixed; inverse variation keeps x × y fixed, as with men × days.
  • Numbers in the ratio a : b (coprime) with HCF h are ah and bh, and their LCM is abh.
  • If k is added to both terms, solve (ax + k)/(bx + k) = c/d by cross-multiplying.
  • Partnership: profit is shared in the ratio of capital × time.
  • Lengths in the ratio a : b give areas a² : b² and volumes a³ : b³.
  • Coins counted in a ratio: price one set of the ratio, then count the sets.

Example: ₹7,200 in the ratio 3 : 4 : 5. There are 12 parts, one part is ₹600, so C gets ₹3,000.

Questions

  1. Dividing ₹5,400 in the ratio 2 : 3 : 4 Easy
    ₹5,400 is divided among A, B and C in the ratio 2 : 3 : 4. How much does C receive?
  2. Combining A : B and B : C Easy
    If A : B = 2 : 3 and B : C = 4 : 5, what is A : B : C?
  3. Profit in a partnership Medium
    A invests ₹20,000 for 12 months; B invests ₹30,000 for 8 months. A profit of ₹18,000 is shared in proportion to capital × time. How is it split?
  4. Coins in the ratio 2 : 3 : 4 Medium
    A bag holds ₹1, 50-paise and 25-paise coins in the ratio 2 : 3 : 4 by count, worth ₹90 in total. How many 50-paise coins are there?
  5. More men, fewer days Easy
    12 men can build a wall in 20 days. Working at the same rate, how many days will 15 men take?
  6. The fourth proportional Easy
    What is the fourth proportional to 4, 6 and 10?
  7. Dividing ₹1,200 in the ratio 2 : 3 : 7 Easy
    ₹1,200 is divided among A, B and C in the ratio 2 : 3 : 7. How much does C receive?
  8. Combining A : B and B : C Easy
    If A : B = 2 : 3 and B : C = 4 : 5, what is A : B : C?
  9. Chaining A : B and B : C again Medium
    If A : B = 5 : 7 and B : C = 6 : 11, what is A : B : C?
  10. Adding 10 to both numbers Medium
    Two numbers are in the ratio 3 : 5. If 10 is added to each, the ratio becomes 5 : 7. What is the smaller number?
  11. Adding 7 to both Medium
    Two numbers are in the ratio 1 : 2. If 7 is added to each, the ratio becomes 3 : 5. What is the larger number?
  12. LCM from a ratio and an HCF Medium
    Two numbers are in the ratio 3 : 4 and their HCF is 4. What is their LCM?
  13. Numbers from a ratio and an LCM Medium
    Two numbers are in the ratio 4 : 5 and their LCM is 180. What is their sum?
  14. Evaluating an expression from a ratio Medium
    If x : y = 5 : 2, what is (8x + 9y) : (8x + 2y)?
  15. A ratio of two expressions Easy
    If a : b = 3 : 4, what is (2a + 3b) : (3a + 2b)?
  16. Sum over difference Medium
    If x/y = 2/3, what is the value of (x + y)/(x − y)?
  17. When 3A = 4B = 6C Medium
    If 3A = 4B = 6C, what is A : B : C?
  18. Sharing in a fractional ratio Medium
    ₹782 is divided among three people in the ratio ½ : ⅔ : ¾. What is the first share?
  19. Shares described through one another Hard
    A sum of ₹3,400 is divided among A, B and C so that A gets ⅔ of what B gets, and B gets ¼ of what C gets. What is B's share?
  20. Sharing under two linked ratios Medium
    ₹3,500 is divided among A, B and C such that A : B = 2 : 3 and B : C = 4 : 5. What is C's share?
  21. Three numbers from two ratios Medium
    The sum of three numbers is 98. The ratio of the first to the second is 2 : 3, and of the second to the third is 5 : 8. What is the second number?
  22. Salaries after different increments Medium
    The salaries of A, B and C are in the ratio 2 : 3 : 5. If they receive increments of 15%, 10% and 20% respectively, what is the new ratio?
  23. Incomes, expenditures and equal savings Hard
    The incomes of two people are in the ratio 3 : 4 and their expenditures in the ratio 5 : 7. If each saves ₹200, what is the income of the first?
  24. Coins of three denominations Hard
    A bag contains ₹1, 50-paise and 25-paise coins in the ratio 5 : 6 : 8, worth ₹210 in all. How many 50-paise coins are there?
  25. Reversing a milk-and-water ratio Medium
    A 60-litre mixture has milk and water in the ratio 2 : 1. How much water must be added to make the ratio 1 : 2?
  26. Mixing two alloys in equal weights Hard
    One alloy has copper and zinc in the ratio 5 : 3, another in the ratio 7 : 5. Equal weights of the two are melted together.
  27. Scholarship holders in a ratio Medium
    The ratio of boys to girls in a school is 3 : 2. If 20% of the boys and 25% of the girls hold scholarships, what percent of students do not hold one?
  28. Fourth proportional to 5, 8 and 15 Easy
    What is the fourth proportional to 5, 8 and 15?
  29. Third proportional to 4 and 12 Easy
    What is the third proportional to 4 and 12?
  30. Mean proportional between 9 and 16 Easy
    What is the mean proportional between 9 and 16?
  31. Solving a proportion Easy
    If 0.75 : x ∷ 5 : 8, what is the value of x?
  32. Fewer days, more men Easy
    15 men can complete a piece of work in 20 days. How many men are needed to finish it in 12 days?
  33. Ratio of areas from a ratio of radii Easy
    The radii of two circles are in the ratio 2 : 3. What is the ratio of their areas?
  34. From p : q and q : r to p : r Easy
    If p : q = 3 : 4 and q : r = 8 : 9, what is p : r?
  35. Dividing 60 in the ratio 2 : 3 Easy
    Divide 60 into two parts in the ratio 2 : 3. What is the smaller part?
  36. A ratio that changes with time Medium
    The present ages of two people are in the ratio 4 : 5. After 5 years the ratio becomes 5 : 6. What is the present age of the younger?

Placement tests that ask ratio & proportion