Ratio Problems and Solutions for Competitive Exams

Ratios are one of the most frequently tested topics in competitive exams. Whether you're preparing for SSC, Banking, CAT, GMAT, UPSC, Railway, Police, or other aptitude-based examinations, mastering ratio problems can significantly improve your score.

Most ratio questions test your ability to compare quantities, simplify relationships, and apply logical reasoning under time constraints.

In this guide, you'll learn common ratio question types, shortcut methods, solved examples, and exam-focused strategies to solve ratio problems quickly and accurately.

If you'd like to verify your answers instantly, you can use our ratio calculator to simplify and compare ratios in seconds.

What Is a Ratio?

A ratio compares two or more quantities.

It is commonly written as:

a:b
a to b
a/b

Example:

20 boys and 10 girls

Ratio:

20:10

Simplified:

2:1

This means there are 2 boys for every 1 girl.

Why Are Ratios Important in Competitive Exams?

Ratio questions help examiners assess:

Numerical ability
Logical thinking
Problem-solving skills
Data interpretation skills
Speed and accuracy

Ratio-based questions frequently appear in:

SSC CGL
SSC CHSL
Banking Exams
CAT
MAT
Railway Exams
UPSC CSAT
State Government Exams

Shortcut Rules for Solving Ratio Questions

Rule 1: Always Simplify First

Example:

40:20

Simplified:

2:1

Working with smaller numbers makes calculations easier.

Rule 2: Convert Units Before Comparing

Incorrect:

5 meters : 200 centimeters

Correct:

500 cm : 200 cm

Ratio:

5:2

Rule 3: Preserve Ratio Order

5:3 is different from 3:5.

Always maintain the specified order.

Ratio Problem 1: Basic Simplification

Question

Simplify:

36:24

Solution

Find GCD:

Divide both numbers:

36 ÷ 12 = 3

24 ÷ 12 = 2

Answer:

3:2

Ratio Problem 2: Student Distribution

Question

The ratio of boys to girls in a classroom is 3:2.

If there are 30 boys, how many girls are there?

Solution

Ratio:

3:2

30 boys represent 3 parts.

1 part = 30 ÷ 3 = 10

Girls:

2 × 10 = 20

Answer:

20 girls

Ratio Problem 3: Total Population

Question

The ratio of men to women is 4:3.

If the total population is 350, find the number of women.

Solution

Total parts:

4 + 3 = 7

Women's share:

(3 ÷ 7) × 350

= 150

Answer:

150 women

Ratio Problem 4: Money Distribution

Question

A sum of $8,000 is divided between A and B in the ratio 3:5.

Find their shares.

Solution

Total parts:

3 + 5 = 8

A's Share:

(3 ÷ 8) × 8,000

= $3,000

B's Share:

(5 ÷ 8) × 8,000

= $5,000

Answer:

A = $3,000
B = $5,000

Ratio Problem 5: Age Ratio

Question

The ratio of Rahul's age to Amit's age is 5:7.

If Rahul is 20 years old, find Amit's age.

Solution

5 parts = 20

1 part = 4

Amit:

7 × 4 = 28

Answer:

28 years

Ratio Problem 6: Profit Sharing

Question

Three partners invest money in the ratio 2:3:5.

The profit is $20,000.

Find each partner's share.

Solution

Total parts:

2 + 3 + 5 = 10

Partner A:

(2 ÷ 10) × 20,000

= $4,000

Partner B:

(3 ÷ 10) × 20,000

= $6,000

Partner C:

(5 ÷ 10) × 20,000

= $10,000

Answer:

A = $4,000
B = $6,000
C = $10,000

Ratio Problem 7: Exam Scores

Question

The ratio of marks obtained by two students is 7:9.

If the first student scored 56 marks, find the second student's marks.

Solution

7 parts = 56

1 part = 8

Second student:

9 × 8 = 72

Answer:

72 marks

Ratio Problem 8: Mixture Problem

Question

Milk and water are mixed in the ratio 4:1.

If the mixture contains 20 liters of water, find the amount of milk.

Solution

1 part = 20 liters

Milk:

4 × 20

= 80 liters

Answer:

80 liters

Ratio Problem 9: Competitive Exam Favorite

Question

The ratio of boys and girls is 5:3.

The total number of students is 320.

Find the number of girls.

Solution

Total parts:

5 + 3 = 8

Girls:

(3 ÷ 8) × 320

= 120

Answer:

120 girls

Ratio Problem 10: Salary Comparison

Question

The salaries of A and B are in the ratio 7:5.

If A earns $56,000 annually, what is B's salary?

Solution

7 parts = 56,000

1 part = 8,000

5 × 8,000

= $40,000

Answer:

$40,000

Practice Questions

Try solving these yourself:

Simplify 48:36.
Divide $12,000 in the ratio 2:4.
The ratio of boys to girls is 7:5. If there are 70 boys, find the number of girls.
A recipe uses flour and sugar in the ratio 3:1. How much sugar is needed for 15 cups of flour?
The ratio of two numbers is 4:7 and their sum is 55. Find the numbers.

Common Ratio Mistakes in Exams

Forgetting to Simplify

Always reduce ratios to their lowest terms.

Ignoring Total Parts

Many students forget to add ratio parts before calculating shares.

Reversing Values

A:B is not the same as B:A.

Unit Conversion Errors

Always convert measurements before comparing.

Tips to Solve Ratio Questions Faster

Simplify ratios immediately.
Memorize common ratio patterns.
Practice percentage-to-ratio conversions.
Learn fraction-to-ratio shortcuts.
Check calculations using an online ratio calculator when practicing.

Frequently Asked Questions

Are ratio questions important for competitive exams?

Yes. Ratio questions frequently appear in aptitude, banking, SSC, CAT, and government examinations.

What is the fastest way to solve ratio problems?

Simplify the ratio first and calculate the value of one part.

Can ratios have more than two quantities?

Yes. Ratios can compare three or more values.

How do I verify ratio answers?

You can use a ratio calculator to simplify and verify your answers instantly.

How much should I practice ratio questions?

Aim for at least 20–30 ratio questions daily while preparing for competitive exams.

Conclusion

Ratio questions are among the easiest scoring topics in competitive exams when you understand the underlying concepts. Most problems follow a predictable pattern involving simplification, proportional distribution, and comparison of quantities.

By practicing regularly and learning shortcut techniques, you can solve ratio questions quickly and accurately under exam conditions.

For instant verification and simplification of ratios, try our ratio calculator and practice with confidence.