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Ratio and Proportion Aptitude: Formulas, Tricks, Solved Examples & Practice Questions

21 July 2026 · Pocket Aptitude Team

Ratio and Proportion Aptitude: Formulas, Tricks, Solved Examples & Practice Questions

Ratio and Proportion Aptitude

Ratio and Proportion is one of the most important topics in quantitative aptitude. It forms the foundation for many arithmetic chapters such as Percentage, Profit and Loss, Partnership, Mixture and Alligation, Average, Time and Work, and Probability. Whether you’re preparing for TCS NQT, Infosys, Accenture, Wipro, Cognizant, Capgemini, SSC, Banking, Railways, CAT, or other competitive exams, mastering Ratio and Proportion can significantly improve your problem-solving speed and accuracy.

Many aptitude questions are based on comparing quantities or dividing values in a given ratio. Once you understand the core concepts, solving these questions becomes much easier.

In this guide, you’ll learn:

  • What Ratio and Proportion mean
  • Important formulas
  • Key properties and rules
  • Solved examples with step-by-step explanations
  • Shortcut tricks
  • Common mistakes to avoid
  • Practice questions to test your understanding

By the end of this article, you’ll have a strong understanding of Ratio and Proportion and be ready to solve aptitude questions with confidence.

Quick Answer

A ratio compares two quantities of the same kind, while a proportion states that two ratios are equal.

Example

Suppose a classroom has:

  • 15 Boys
  • 10 Girls

The ratio of boys to girls is:

15 : 10 = 3 : 2

Now consider another classroom with:

  • 30 Boys
  • 20 Girls

The ratio is:

30 : 20 = 3 : 2

Since both ratios are equal,

15 : 10 = 30 : 20

This is called a proportion.

Why is Ratio and Proportion Important?

Ratio and Proportion is one of the highest-scoring arithmetic topics in aptitude exams. Many questions can be solved in less than a minute if you know the concepts well.

It is widely used in questions involving:

  • Percentage
  • Profit and Loss
  • Discount
  • Partnership
  • Average
  • Mixture and Alligation
  • Time and Work
  • Pipes and Cisterns
  • Speed, Time and Distance
  • Probability

Importance in Competitive Exams

ExamImportance
Campus Placements⭐⭐⭐⭐⭐
TCS NQT⭐⭐⭐⭐⭐
Banking Exams⭐⭐⭐⭐⭐
SSC CGL⭐⭐⭐⭐⭐
Railways⭐⭐⭐⭐☆
CAT⭐⭐⭐⭐☆

Pocket Aptitude Tip: Mastering Ratio and Proportion makes many arithmetic topics easier because they are built on proportional relationships.

What is a Ratio?

A ratio is a way of comparing two quantities of the same type. It tells us how much one quantity is compared to another.

The general form of a ratio is:

a : b

Where:

  • a is called the Antecedent
  • b is called the Consequent Example of ratio comparing apples and oranges

Example 1

A basket contains:

  • 8 Apples
  • 12 Oranges

Ratio of Apples to Oranges:

8 : 12

Divide both numbers by 4.

= 2 : 3

This means that for every 2 apples, there are 3 oranges.

Real-Life Examples of Ratio

Example 1

A classroom has:

  • 24 Boys
  • 16 Girls

Ratio:

24 : 16

Divide both numbers by 8.

= 3 : 2

Example 2

A cricket team scores:

  • First innings = 180 runs
  • Second innings = 240 runs

Ratio:

180 : 240

Simplify:

= 3 : 4

Example 3

The ratio of tea powder to sugar in a recipe is 4 : 1.

This means for every 4 spoons of tea powder, 1 spoon of sugar is used.

Terms Used in Ratio

Consider the ratio:

5 : 8
  • 5 → Antecedent
  • 8 → Consequent

Knowing these terms can help in theoretical aptitude questions.

Properties of Ratio

1. Ratio Has No Unit

A ratio compares similar quantities, so the units cancel out.

Example:

5 kg : 10 kg = 1 : 2

2. Both Quantities Must Have the Same Unit

❌ Incorrect

2 m : 50 cm

✅ Correct

Convert metres into centimetres.

200 cm : 50 cm = 4 : 1

This is one of the most common mistakes students make.

3. Ratios Should Always Be Simplified

Example:

30 : 45

Divide both numbers by 15.

= 2 : 3

Simplified ratios make calculations faster and easier.

4. Multiplying or Dividing Both Terms by the Same Number Does Not Change the Ratio

Example:

3 : 5

Multiply by 2:

6 : 10

Multiply by 3:

18 : 30

All these ratios are equivalent.

What is a Proportion?

A proportion is an equation that states two ratios are equal.

General form:

a : b = c : d

Example:

2 : 5 = 4 : 10

Since

2/5 = 4/10

the two ratios are equal.

Therefore, they are said to be in proportion.

Cross multiplication method in proportion

Cross Multiplication Rule

If

a : b = c : d

then

a × d = b × c

This rule is called cross multiplication and is one of the fastest methods for solving proportion problems.

Example

Find x if

4 : 7 = x : 21

Cross multiply:

4 × 21 = 7 × x
84 = 7x
x = 12

Answer: 12

Difference Between Ratio and Proportion

RatioProportion
Compares two quantitiesCompares two ratios
Written using ”:“Written using ”=“
Shows comparisonShows equality
Example: 3 : 4Example: 3 : 4 = 6 : 8

Remember: A Ratio compares, while a Proportion proves equality.

Difference between ratio and proportion

Important Formulas

ConceptFormula
Ratioa : b
Proportiona : b = c : d
Cross Multiplicationad = bc
Simplified RatioDivide both terms by their HCF

Solved Examples

Example 1: Simplify the Ratio

Simplify:

18 : 30

Solution

HCF of 18 and 30 = 6

18 ÷ 6 = 3
30 ÷ 6 = 5

Answer: 3 : 5

Example 2: Convert Units Before Finding Ratio

Find the ratio:

40 minutes : 2 hours

Solution

Convert 2 hours into minutes.

2 hours = 120 minutes

Ratio:

40 : 120

Divide both numbers by 40.

Answer: 1 : 3

Example 3: Find the Missing Quantity

The ratio of boys to girls is 7 : 5.

If there are 35 boys, how many girls are there?

Solution

7 parts = 35
1 part = 35 ÷ 7 = 5
Girls = 5 × 5

Answer: 25 Girls

Example 4: Find the Missing Term in a Proportion

Find x if:

9 : 15 = x : 25

Solution

9 × 25 = 15 × x
225 = 15x
x = 15

Answer: 15

Example 5: Divide an Amount in a Given Ratio

A sum of ₹6,500 is divided between A and B in the ratio 4 : 9.

Solution

Total parts = 13
One part = ₹6,500 ÷ 13 = ₹500

A = 4 × ₹500 = ₹2,000
B = 9 × ₹500 = ₹4,500

Answer:

  • A = ₹2,000
  • B = ₹4,500

Pocket Aptitude Tip: For sharing problems, always calculate the value of one part first.

Example 6: Age-Based Ratio Problem

The ratio of the ages of A and B is 3 : 5.

If A is 18 years, find B’s age.

Solution

3 parts = 18
1 part = 6
B = 5 × 6 = 30

Answer: 30 years Steps to solve ratio and proportion questions

Time-Saving Tricks

1. Simplify Ratios First

Always reduce the ratio to its simplest form before solving.

Example:

84 : 126

Divide both numbers by 42.

= 2 : 3

2. Convert Units Before Comparing

Never compare different units directly.

❌ Incorrect

3 m : 75 cm

✅ Correct

Convert metres into centimetres.

300 cm : 75 cm
= 4 : 1

3. Use the Total Parts Method

When money, students, or objects are divided in a ratio, first find the total number of parts.

Example:

Ratio = 3 : 7

Total Amount = ₹500

Total Parts = 3 + 7 = 10

One Part = ₹500 ÷ 10 = ₹50

3 Parts = ₹150

7 Parts = ₹350

4. Use Cross Multiplication

Whenever two ratios are equal, use cross multiplication immediately.

Example:

5 : 8 = x : 32

Cross multiply:

5 × 32 = 8 × x

160 = 8x

x = 20

Common Mistakes to Avoid

❌ Comparing Quantities with Different Units

Always convert all quantities into the same unit before finding the ratio.

Example

❌ 2 m : 50 cm

✅ 200 cm : 50 cm = 4 : 1

❌ Forgetting to Simplify the Ratio

Always reduce the ratio to its simplest form.

Example:

30 : 45

= 2 : 3

❌ Reversing the Order of Comparison

Read the question carefully.

Example

Boys : Girls ≠ Girls : Boys

Changing the order changes the meaning of the ratio.

❌ Applying Cross Multiplication Incorrectly

Multiply diagonally and solve step by step.

❌ Treating a Ratio as a Fraction

A ratio compares two quantities, while a fraction represents a part of a whole.

Pocket Aptitude Tip: Spend a few extra seconds checking the units and the order of comparison before solving. This helps avoid common mistakes in aptitude exams.

Practice Questions

Try solving these questions before checking the answers.

Question 1

Simplify the ratio:

24 : 36

Answer: 2 : 3

Question 2

Find the ratio:

45 minutes : 3 hours

Answer: 1 : 4

Question 3

The ratio of boys to girls is 5 : 4.

If there are 40 boys, how many girls are there?

Answer: 32

Question 4

Find x if

4 : 7 = x : 28

Answer: 16

Question 5

The ratio of two numbers is 2 : 5.

Their sum is 42.

Find the numbers.

Answer: 12 and 30

Formula Summary

ConceptFormula
Ratioa : b
Proportiona : b = c : d
Cross Multiplicationad = bc
Simplified RatioDivide both terms by their HCF

Revision Tips

Before your exam, remember these important points:

  • Convert quantities into the same unit before comparing.
  • Always simplify ratios whenever possible.
  • Use cross multiplication to solve proportions.
  • Read the order of comparison carefully.
  • Apply the Total Parts Method for sharing problems.
  • Practice different types of ratio questions to improve your speed and accuracy.

Frequently Asked Questions (FAQs)

1. What is a ratio

A ratio compares two quantities of the same kind and shows their relationship using the symbol :.

2. What is a proportion?

A proportion is an equation that states two ratios are equal.

Example

2 : 3 = 4 : 6

3. Why should ratios be simplified?

Simplified ratios make calculations easier, reduce errors, and help solve aptitude questions more quickly.

4. What is cross multiplication?

Cross multiplication is a shortcut used to solve proportions.

If a : b = c : d,

then

a × d = b × c

5. Is Ratio and Proportion important for placement exams?

Yes. Ratio and Proportion is one of the most frequently asked arithmetic topics in placement tests and competitive exams such as TCS NQT, Infosys, Accenture, Wipro, SSC, Banking, Railways, and CAT.

6. Which aptitude topics are based on Ratio and Proportion?

Many arithmetic topics use the concepts of Ratio and Proportion, including:

  • Percentage
  • Profit and Loss
  • Discount
  • Average
  • Partnership
  • Mixture and Alligation
  • Time and Work
  • Probability
  • Speed, Time and Distance

Related Articles

Continue your aptitude preparation with these guides on Pocket Aptitude:

Final Thoughts

Ratio and Proportion is one of the most important building blocks of quantitative aptitude. Instead of memorizing formulas, focus on understanding how quantities relate to each other. Once you grasp the concepts and practice different types of questions, you’ll be able to solve problems quickly and confidently.

Whether you’re preparing for campus placements, banking exams, SSC, Railways, CAT, or other competitive exams, mastering Ratio and Proportion will strengthen your arithmetic skills and make many advanced aptitude topics easier to learn.

Pocket Aptitude Exam Tip: Spend a few minutes revising Ratio and Proportion every week. Since many arithmetic topics are based on proportional relationships, a strong foundation in this chapter will improve your overall aptitude performance.