August 17, 2026

20 Ratio and Proportion Aptitude Questions with Answers and Solutions

Ratio and Proportion is an important topic in quantitative aptitude and appears frequently in placement tests, competitive examinations, entrance tests, and recruitment assessments. A strong understanding of ratios is also useful for solving problems involving percentages, mixtures, ages, partnerships, time and work, and data interpretation.

This practice test contains 20 original Ratio and Proportion aptitude questions with detailed step-by-step solutions. The questions progress from basic ratio simplification to moderately challenging applications.

📚 Want to practice more aptitude topics? Visit our [Free Aptitude Tests and MCQs for Placements, Competitive Exams and Interview Preparation] page for topic-wise tests covering Quantitative Aptitude, Logical Reasoning, Verbal Ability, Computer Aptitude, Data Interpretation, and placement preparation.

Try solving all 20 questions before checking the solutions.

Detailed answers and solutions are provided after Question 20.

Ratio and Proportion Aptitude Test

Question 1

What is the simplest form of the ratio 48 : 72?

A. 2 : 3
B. 3 : 4
C. 4 : 5
D. 4 : 7

Question 2

If the ratio of two numbers is 3 : 5 and the first number is 27, what is the second number?

A. 35
B. 40
C. 45
D. 50

Question 3

Divide ₹840 in the ratio 3 : 4. What is the larger share?

A. ₹360
B. ₹420
C. ₹480
D. ₹520

Question 4

The ratio of boys to girls in a class is 5 : 7. If there are 48 students altogether, how many girls are there?

A. 20
B. 24
C. 28
D. 30

Question 5

If (x : y = 4 : 9) and (y = 63), what is the value of (x)?

A. 24
B. 28
C. 32
D. 36

Question 6

The ages of Juhi and Cherry are in the ratio 4 : 5. If their total age is 36 years, what is Cherry’s age?

A. 16 years
B. 18 years
C. 20 years
D. 24 years

Question 7

If 8 notebooks cost ₹360, what will 14 notebooks cost at the same rate?

A. ₹560
B. ₹600
C. ₹630
D. ₹650

Question 8

If (a:b=2:3) and (b:c=4:5), what is (a:b:c)?

A. 8 : 12 : 15
B. 6 : 12 : 15
C. 8 : 10 : 15
D. 4 : 6 : 10

Question 9

Two numbers are in the ratio 7 : 11. Their difference is 52. What is the smaller number?

A. 78
B. 84
C. 91
D. 98

Question 10

The ratio of income to expenditure of a person is 8 : 5. If the monthly income is ₹48,000, how much is saved each month?

A. ₹15,000
B. ₹18,000
C. ₹20,000
D. ₹30,000

Question 11

If (15:x = 25:40), what is the value of (x)?

A. 20
B. 22
C. 24
D. 26

Question 12

A recipe requires flour and sugar in the ratio 5 : 2. If 750 g of flour is used, how much sugar is required?

A. 250 g
B. 275 g
C. 300 g
D. 350 g

Question 13

A sum of ₹2,100 is divided among three people in the ratio 2 : 3 : 5. What is the largest share?

A. ₹840
B. ₹900
C. ₹1,000
D. ₹1,050

Question 14

The ratio of two numbers is 5 : 8. If 6 is added to each number, their ratio becomes 2 : 3. What is the smaller original number?

A. 24
B. 30
C. 36
D. 40

Question 15

In a mixture of 54 litres, milk and water are in the ratio 7 : 2. How many litres of water are present?

A. 10 litres
B. 12 litres
C. 14 litres
D. 16 litres

Question 16

The present ages of Kanchan and Nyra are in the ratio 7 : 4. After 8 years, their ages will be in the ratio 3 : 2. What is Nyra’s present age?

A. 12 years
B. 16 years
C. 20 years
D. 24 years

Question 17

If 12 workers can complete a particular quantity of work in 18 days, how many workers are required to complete the same work in 12 days, assuming equal efficiency?

A. 15
B. 16
C. 18
D. 20

Question 18

Two numbers are in the ratio 4 : 7. If 8 is subtracted from each number, their ratio becomes 2 : 5. What is the larger original number?

A. 21
B. 24
C. 28
D. 35

Question 19

A company’s employees are divided among three departments in the ratio 3 : 5 : 7. If the department with the largest number has 56 employees, how many employees are there altogether?

A. 105
B. 112
C. 120
D. 126

Question 20

The ratio of two numbers is 3 : 7. If 12 is added to the smaller number and 8 is subtracted from the larger number, the resulting numbers become equal. What is the sum of the original numbers?

A. 40
B. 45
C. 50
D. 60

Answers and Detailed Solutions

Answer 1: A — 2 : 3

Given ratio:

[
48:72
]

The HCF of 48 and 72 is 24.

Divide both terms by 24:

[
48\div24:72\div24
]

[
=2:3
]

Therefore:

Correct Answer: 2 : 3

Answer 2: C — 45

The ratio is:

[
3:5
]

The first number is 27.

Therefore:

[
3\text{ parts}=27
]

One part:

[
27\div3=9
]

The second number represents 5 parts:

[
5\times9=45
]

Therefore:

Correct Answer: 45

Answer 3: C — ₹480

The ratio is:

[
3:4
]

Total number of parts:

[
3+4=7
]

Total amount = ₹840.

Value of one part:

[
840\div7=120
]

The larger share represents 4 parts:

[
4\times120=480
]

Therefore:

Correct Answer: ₹480

Answer 4: C — 28

Ratio of boys to girls:

[
5:7
]

Total parts:

[
5+7=12
]

Total students = 48.

One part:

[
48\div12=4
]

Girls represent 7 parts:

[
7\times4=28
]

Therefore:

Correct Answer: 28 girls

Answer 5: B — 28

Given:

[
x:y=4:9
]

and:

[
y=63
]

Therefore:

[
9\text{ parts}=63
]

One part:

[
63\div9=7
]

So:

[
x=4\times7
]

[
=28
]

Therefore:

Correct Answer: 28

Answer 6: C — 20 years

The age ratio is:

[
4:5
]

Total parts:

[
4+5=9
]

Their total age is 36 years.

One part:

[
36\div9=4
]

Cherry’s age represents 5 parts:

[
5\times4=20
]

Therefore:

Correct Answer: 20 years

Answer 7: C — ₹630

Eight notebooks cost ₹360.

Cost of one notebook:

[
360\div8=45
]

Cost of 14 notebooks:

[
14\times45=630
]

Therefore:

Correct Answer: ₹630

This is an example of direct proportion: as the number of notebooks increases, the total cost increases in the same proportion.

Answer 8: A — 8 : 12 : 15

Given:

[
a:b=2:3
]

and:

[
b:c=4:5
]

We need to make the value corresponding to (b) equal in both ratios.

LCM of 3 and 4:

[
12
]

Multiply the first ratio by 4:

[
a:b=8:12
]

Multiply the second ratio by 3:

[
b:c=12:15
]

Therefore:

[
a:b:c=8:12:15
]

Correct Answer:

8 : 12 : 15

Answer 9: C — 91

The numbers are in the ratio:

[
7:11
]

Let them be:

[
7x \text{ and } 11x
]

Their difference is 52.

Therefore:

[
11x-7x=52
]

[
4x=52
]

[
x=13
]

The smaller number is:

[
7\times13=91
]

Therefore:

Correct Answer: 91

Answer 10: B — ₹18,000

Income : Expenditure:

[
8:5
]

Income = ₹48,000.

Eight parts correspond to ₹48,000.

One part:

[
48000\div8=6000
]

Expenditure:

[
5\times6000=30000
]

Savings:

[
48000-30000=18000
]

Therefore:

Correct Answer: ₹18,000

Alternatively, savings represent:

[
8-5=3\text{ parts}
]

Therefore:

[
3\times6000=₹18,000
]

Answer 11: C — 24

Given:

[
15:x=25:40
]

Therefore:

[
\frac{15}{x}=\frac{25}{40}
]

Cross multiply:

[
15\times40=25x
]

[
600=25x
]

[
x=24
]

Therefore:

Correct Answer: 24

Answer 12: C — 300 g

Flour : Sugar:

[
5:2
]

Flour = 750 g.

Five parts correspond to 750 g.

One part:

[
750\div5=150
]

Sugar represents two parts:

[
2\times150=300
]

Therefore:

Correct Answer: 300 g

Answer 13: D — ₹1,050

The ratio is:

[
2:3:5
]

Total parts:

[
2+3+5=10
]

Total amount = ₹2,100.

One part:

[
2100\div10=210
]

The largest share represents 5 parts:

[
5\times210=1050
]

Therefore:

Correct Answer: ₹1,050

Answer 14: B — 30

The two numbers are in the ratio:

[
5:8
]

Let the numbers be:

[
5x \text{ and } 8x
]

After adding 6 to each:

[
\frac{5x+6}{8x+6}=\frac{2}{3}
]

Cross multiply:

[
3(5x+6)=2(8x+6)
]

[
15x+18=16x+12
]

Therefore:

[
x=6
]

The smaller original number is:

[
5\times6=30
]

Therefore:

Correct Answer: 30

Check:

Original numbers:

30 and 48.

Add 6:

36 and 54.

[
36:54=2:3
]

Correct.

Answer 15: B — 12 litres

Milk : Water:

[
7:2
]

Total parts:

[
7+2=9
]

Total mixture = 54 litres.

One part:

[
54\div9=6
]

Water represents two parts:

[
2\times6=12
]

Therefore:

Correct Answer: 12 litres

Answer 16: B — 16 years

Present age ratio:

[
7:4
]

Let Kanchan’s age be:

[
7x
]

and Nyra’s age be:

[
4x
]

After 8 years:

[
\frac{7x+8}{4x+8}=\frac{3}{2}
]

Cross multiply:

[
2(7x+8)=3(4x+8)
]

[
14x+16=12x+24
]

[
2x=8
]

[
x=4
]

Nyra’s present age:

[
4x=4\times4=16
]

Therefore:

Correct Answer: 16 years

Check:

Kanchan = 28 years

Nyra = 16 years

After 8 years:

36 : 24

[
=3:2
]

Correct.

Answer 17: C — 18 workers

For the same quantity of work:

Workers × Days = Constant

Therefore:

[
12\times18=x\times12
]

[
216=12x
]

[
x=18
]

Therefore:

Correct Answer: 18 workers

This is an example of inverse proportion.

As the number of available days decreases, more workers are required.

Answer 18: C — 28

The original numbers are in the ratio:

[
4:7
]

Let them be:

[
4x \text{ and } 7x
]

After subtracting 8 from each:

[
\frac{4x-8}{7x-8}=\frac{2}{5}
]

Cross multiply:

[
5(4x-8)=2(7x-8)
]

[
20x-40=14x-16
]

[
6x=24
]

[
x=4
]

The larger original number is:

[
7\times4=28
]

Therefore:

Correct Answer: 28

Check:

Original numbers:

16 and 28.

After subtracting 8:

8 and 20.

[
8:20=2:5
]

Correct.

Answer 19: C — 120

Department ratio:

[
3:5:7
]

The largest department represents 7 parts.

Seven parts = 56 employees.

One part:

[
56\div7=8
]

Total parts:

[
3+5+7=15
]

Total employees:

[
15\times8=120
]

Therefore:

Correct Answer: 120 employees

Answer 20: C — 50

The two numbers are in the ratio:

[
3:7
]

Let them be:

[
3x \text{ and } 7x
]

According to the question:

12 is added to the smaller number and 8 is subtracted from the larger number.

The resulting numbers are equal.

Therefore:

[
3x+12=7x-8
]

Move the terms:

[
12+8=7x-3x
]

[
20=4x
]

[
x=5
]

Original numbers:

[
3\times5=15
]

and:

[
7\times5=35
]

Their sum:

[
15+35=50
]

Therefore:

Correct Answer: 50

Check:

15 + 12 = 27

35 − 8 = 27

Correct.

Quick Answer Key

Question	Answer	Question	Answer
1	A	11	C
2	C	12	C
3	C	13	D
4	C	14	B
5	B	15	B
6	C	16	B
7	C	17	C
8	A	18	C
9	C	19	C
10	B	20	C

How Did You Score?

Correct Answers	Performance
18–20	Excellent — You have a strong understanding of ratio and proportion.
15–17	Very Good — Your fundamentals are strong; practice the more complex applications.
11–14	Good — Review combined ratios, ages, and changed-ratio problems.
6–10	Needs Practice — Revise basic ratio concepts and direct/inverse proportion.
0–5	Beginner — Begin with simplifying ratios and dividing quantities in a given ratio.

Important Ratio and Proportion Formulas

Basic Ratio

The ratio of (a) to (b) is written as:

[
a:b
]

or:

[
\frac{a}{b}
]

Equivalent Ratios

Multiplying or dividing both terms by the same non-zero number does not change the ratio.

For example:

[
4:6
]

Dividing both terms by 2:

[
2:3
]

Therefore:

[
4:6=2:3
]

Proportion

If:

[
a:b=c:d
]

then:

[
\frac{a}{b}=\frac{c}{d}
]

Therefore:

[
a\times d=b\times c
]

This is called cross multiplication.

Dividing a Quantity in a Ratio

Suppose ₹900 must be divided in the ratio:

[
2:3
]

Total parts:

[
2+3=5
]

First share:

[
900\times\frac{2}{5}=360
]

Second share:

[
900\times\frac{3}{5}=540
]

Therefore:

[
₹360:₹540=2:3
]

Direct Proportion

Two quantities are in direct proportion when increasing one causes the other to increase proportionally.

For example:

If 4 notebooks cost ₹200, then 8 notebooks at the same price per notebook cost ₹400.

More notebooks → More cost

Inverse Proportion

Two quantities are inversely proportional when increasing one causes the other to decrease proportionally.

For example:

If more workers perform the same job at the same efficiency, fewer days may be required.

For a fixed amount of work:

[
\text{Workers}\times\text{Days}=\text{Constant}
]

Combining Two Ratios

Suppose:

[
a:b=2:3
]

and:

[
b:c=4:5
]

Make the common term (b) equal.

LCM of 3 and 4 = 12.

Therefore:

[
a:b=8:12
]

and:

[
b:c=12:15
]

Hence:

[
a:b:c=8:12:15
]

This technique is useful in many placement aptitude questions.

Common Mistakes in Ratio Questions

Comparing quantities with different units

Always convert quantities to the same unit before creating a ratio.

For example:

2 metres : 50 centimetres

Convert 2 metres to 200 centimetres:

[
200:50
]

[
=4:1
]

not:

[
2:50
]

Forgetting to add all ratio parts

If a quantity is divided in the ratio:

[
2:3:5
]

the total number of parts is:

[
2+3+5=10
]

Adding the same number to ratio terms incorrectly

If two numbers are in the ratio 3 : 5, adding 2 to both ratio terms does not necessarily represent adding 2 to the actual numbers.

Use variables to represent the original numbers when solving such problems.

Topics Covered in This Test

This Ratio and Proportion aptitude test covered:

Simplifying ratios
Finding missing quantities
Dividing amounts in ratios
Class composition
Age ratios
Direct proportion
Combined ratios
Difference-based ratio problems
Income and expenditure
Proportion equations
Mixtures
Three-part ratios
Changed ratios
Inverse proportion
Work and workers

Ratio and proportion concepts also form an important foundation for Percentages, Profit and Loss, Time and Work, Mixtures, Partnership, Ages, and Data Interpretation.

Frequently Asked Questions

What is a ratio?

A ratio compares two quantities of the same kind.

For example:

[
10:15
]

can be simplified to:

[
2:3
]

What is a proportion?

A proportion states that two ratios are equal.

For example:

[
2:3=8:12
]

because:

[
\frac{2}{3}=\frac{8}{12}
]

How do I simplify a ratio?

Find the HCF of both terms and divide each term by it.

For example:

[
36:54
]

HCF = 18.

Therefore:

[
36\div18:54\div18
]

[
=2:3
]

How do I divide an amount in a given ratio?

First add all the ratio terms.

Then divide the total amount by the total number of parts and multiply by the required ratio term.

What is direct proportion?

In direct proportion, both quantities move in the same direction.

If one increases, the other increases proportionally.

What is inverse proportion?

In inverse proportion, one quantity increases while the other decreases proportionally.

Workers and time required for a fixed job are a common example.

Are ratio questions important for placement tests?

Yes. Ratio and proportion questions are common in quantitative aptitude and also support many other topics such as percentages, mixtures, ages, time and work, partnership, and data interpretation.

Conclusion

Ratio and Proportion is much more than simply simplifying expressions such as 4 : 6.

A strong understanding of ratios helps solve practical aptitude problems involving:

money,
ages,
mixtures,
workers,
expenditure,
distribution, and
comparisons.

The key is to first identify what each part of the ratio represents and then translate the relationship into numbers or equations.

With regular practice, many ratio problems that initially appear complicated can be solved using only a few steps.

📚 Continue your aptitude preparation: Return to [Free Aptitude Tests and MCQs for Placements, Competitive Exams and Interview Preparation] to explore the complete collection of Quantitative Aptitude, Logical Reasoning, Verbal Ability, Computer Aptitude, Data Interpretation, and Placement Preparation tests.

Previous Test:
20 Percentage Aptitude Questions with Solutions

Next Test: 20 Profit and Loss MCQs with Answers

20 Ratio and Proportion Aptitude Questions with Answers and Solutions

20 Ratio and Proportion Aptitude Questions with Answers and Solutions

Ratio and Proportion Aptitude Test

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Answers and Detailed Solutions

Answer 1: A — 2 : 3

Answer 2: C — 45

Answer 3: C — ₹480

Answer 4: C — 28

Answer 5: B — 28

Answer 6: C — 20 years

Answer 7: C — ₹630

Answer 8: A — 8 : 12 : 15

Answer 9: C — 91

Answer 10: B — ₹18,000

Answer 11: C — 24

Answer 12: C — 300 g

Answer 13: D — ₹1,050

Answer 14: B — 30

Answer 15: B — 12 litres

Answer 16: B — 16 years

Answer 17: C — 18 workers

Answer 18: C — 28

Answer 19: C — 120

Answer 20: C — 50

Quick Answer Key

How Did You Score?

Important Ratio and Proportion Formulas

Basic Ratio

Equivalent Ratios

Proportion

Dividing a Quantity in a Ratio

Direct Proportion

Inverse Proportion

Combining Two Ratios

Common Mistakes in Ratio Questions

Comparing quantities with different units

Forgetting to add all ratio parts

Adding the same number to ratio terms incorrectly

Topics Covered in This Test

Frequently Asked Questions

What is a ratio?

What is a proportion?

How do I simplify a ratio?

How do I divide an amount in a given ratio?

What is direct proportion?

What is inverse proportion?

Are ratio questions important for placement tests?

Conclusion

Further Reading

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