NIMCET Quantitative Aptitude Ratio: Concepts, Formulas, & Practice Questions

Ratio is a fundamental topic in Quantitative Aptitude that helps you compare two or more quantities. It is used in questions based on distribution, proportion, speed and time, work, income and expenditure, and averages. A clear understanding of ratios can also help you approach related arithmetic topics with greater ease.

While preparing for the exam, you should first understand the basic meaning and properties of ratios. You should then move to combined ratios, fractional ratios, direct and inverse proportion, and different types of proportion. Learning these concepts with examples and practising questions can help you apply the correct method during the exam.

What Is Ratio?

A ratio compares two or more quantities by division. It is generally written as a and read as “a is to b.”

In the ratio a:

• a is called the antecedent.

• b is called the consequent.

• The quantity being compared is placed first.

• The reference quantity is placed second.

For example, if the ages of A and B are 30 years and 20 years, their ratio is:

30:20 = 3:2

The ratio should be reduced to its simplest form by dividing all its terms by their HCF.

For three quantities, a ratio can be written as a:b. For example:

30:20:15 = 6:4:3

A ratio shows the relative relationship between quantities. If a = 3:7, their actual values do not have to be 3 and 7. They can be 30 and 70 or 300 and 700. In general:

a = 3x and b = 7x

where x is a common positive factor.

Properties of Ratio

Understanding the basic properties of ratio helps you solve questions with fewer calculations.

If:

a:b = 3:7

then:

• a is a multiple of 3.

• b is a multiple of 7.

• a + b is a multiple of 10.

• b − a is a multiple of 4.

• ab is a multiple of 21.

These properties can help you eliminate options in objective questions.

For example, if a quantity is divided in the ratio 2:3:4:5, the total number of ratio parts is:

2 + 3 + 4 + 5 = 14

Therefore, if the complete quantity is an integer multiple of these parts, its value should be compatible with 14. This can help you check options quickly.

Ratio in Distribution Problems

Ratio is commonly used when a total quantity has to be divided among two or more people.

Suppose ₹80,000 is divided between A and B in the ratio 3:7.

Total parts:

3 + 7 = 10

A's share:

3/10 × ₹80,000 = ₹24,000

B's share:

7/10 × ₹80,000 = ₹56,000

This fraction-based method is useful for solving distribution questions without introducing unnecessary variables.

Similarly, if ₹60,000 is divided among A, B, and C in the ratio 2:3:1:

Total parts:

2 + 3 + 1 = 6

A's share = ₹20,000

B's share = ₹30,000

C's share = ₹10,000

This method is useful when you are revising from NIMCET Ratio Notes and want to remember a simple approach for distribution questions.

Fractional Ratios

Sometimes, the terms of a ratio are given as fractions. You can convert them into whole numbers by multiplying all terms by the LCM of the denominators.

For example:

a:b:c = 1/2 : 1/3 : 1/5

The LCM of 2, 3, and 5 is 30.

Multiplying each term by 30:

a:b:c = 15:10:6

The same idea works for more complicated fractional ratios.

For example:

a:b:c = 2/3 : 3/5 : 1/4

Multiplying by 60 gives:

40:36:15

Always simplify the final ratio if a common factor exists.

Equated Multiples

A special type of ratio question gives equal expressions such as:

3a = 5b = 7c

To find a:b:c, take the LCM of 3, 5, and 7.

LCM = 105

Therefore:

a = 105/3 = 35

b = 105/5 = 21

c = 105/7 = 15

Hence:

a:b:c = 35:21:15

A shortcut is also possible. For each variable, multiply the coefficients of the other variables:

• a = 5 × 7 = 35

• b = 3 × 7 = 21

• c = 3 × 5 = 15

This is one of the useful NIMCET Ratio Tricks for questions involving equal products or expressions.

Combining Two Ratios

You may also get two ratios that have a common term.

Suppose:

a:b = 5:7

and

b:c = 2:3

The common term is b. Its values are 7 and 2 in the two ratios, so make them equal.

LCM of 7 and 2 = 14.

Thus:

a:b = 10:14

and:

b:c = 14:21

Therefore:

a:b:c = 10:14:21

This technique becomes useful when solving NIMCET Ratio and Proportion problems involving multiple quantities.

Direct Proportion

Direct proportion describes a relationship where two quantities increase or decrease together.

If x and y are directly proportional:

x ∝ y

Therefore:

x = ky

where k is a constant.

The ratio between the two quantities remains constant:

x/y = constant

For two sets of values:

x₁/y₁ = x₂/y₂

Example

Suppose 15 books cost ₹900. Find the cost of 22 identical books.

Since cost and the number of books are directly proportional:

900/c = 15/22

Therefore:

c = (900 × 22)/15

c = ₹1,320

So, the cost of 22 books is ₹1,320.

Inverse Proportion

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

If x and y are inversely proportional:

x ∝ 1/y

Therefore: xy = constant

For two sets of values: x₁y₁ = x₂y₂

Speed and Time Example

A car travels a fixed distance at 60 km/h in 4 hours. How much time will it take at 80 km/h?

Since the distance is fixed, speed and time are inversely proportional.

60 × 4 = 80 × t

Therefore: t = 240/80 = 3 hours

So, the required time is 3 hours.

Time and Work Example

Suppose 12 workers complete a job in 8 days. How many workers are required to complete the same job in 6 days?

Workers and days are inversely proportional.

12 × 8 = m × 6

Therefore: m = 16

Hence, 16 workers are required.

Direct and Inverse Proportion: Difference

The main difference is the way the two quantities change.

Direct proportion

• Both quantities increase or decrease together.

• Their ratio remains constant.

• Formula: x/y = constant

Inverse proportion

• One quantity increases when the other decreases.

• Their product remains constant.

• Formula: xy = constant

Before applying a formula, first identify whether the relationship is direct or inverse. This prevents errors in calculation.

Proportion and Its Types

A proportion is formed when two ratios are equal.

If: a/b = c/d

Then: a:b::c:d

Here:

• a and d are the extreme terms.

• b and c are the mean terms.

• Product of extremes = Product of means.

Therefore: a × d = b × c

This property is useful in many ratio-based questions.

Mean Proportion

If x is the mean proportion between a and b:

a:x::x:b

Therefore: x² = ab

So: x = √ab

For example, the mean proportion between 4 and 9 is: √(4 × 9) = √36 = 6

Third Proportion

The third proportion x for a and b satisfies:

a:b::b:x

Therefore: ax = b²

So: x = b²/a

For 4 and 6: x = 6²/4 = 36/4 = 9

Fourth Proportion

If: a:b::c:x

Then: ax = bc

Therefore: x = bc/a

These formulas can help you solve direct proportion questions without lengthy calculations.

Ratio in Income and Expenditure Problems

Ratio can also be used in questions involving income, expenditure, and savings.

Suppose the incomes of A and B are in the ratio 3:2, while their expenditures are in the ratio 5:3. If both save ₹1,000, their income and expenditure can be represented as:

Income of A = 3x

Income of B = 2x

Expenditure of A = 5y

Expenditure of B = 3y

Using the savings condition:

3x − 5y = 1,000

2x − 3y = 1,000

These equations can then be solved to find the required quantity.

Ratio and Averages

Ratio questions may also involve averages. In such questions, avoid assuming that every quantity must be an integer.

For example, if: P:Q = 11:12

And P:R = 9:8

Reverse the second ratio: R:P = 8:9

Then align the common term P and combine the ratios.

You get: Q:R = 108:88

which simplifies to: 27:22

When the quantities can have decimal values, check the result carefully before using divisibility-based shortcuts.

Ratio Questions in NIMCET Preparation

While preparing NIMCET Ratio Questions, focus on understanding the relationship between quantities rather than memorising formulas alone.

You should practise questions based on:

• Basic ratio and simplification

• Distribution of quantities

• Fractional ratios

• Equated multiples

• Combined ratios

• Direct proportion

• Inverse proportion

• Speed and time

• Time and work

• Income and expenditure

• Mean and third proportion

Solving NIMCET Ratio and Proportion Questions regularly can help you become familiar with different question formats.

You can also use Ratio NIMCET 2026 resources for previous exam-oriented practice, but check the relevance of the questions against the current NIMCET syllabus and preparation requirements.

How to Solve Ratio Questions Quickly

Use the following approach while solving ratio-based questions:

1. Identify the quantities: Understand what is being compared.

2. Write the ratio correctly: Keep the reference quantity in the second position.

3. Simplify the ratio: Divide all terms by their HCF.

4. Check the relationship: Decide whether it is direct or inverse proportion.

5. Use the appropriate formula: Do not interchange direct and inverse relationships.

6. Check the options: Divisibility and ratio properties can help eliminate incorrect choices.

7. Verify the answer: Substitute the result into the original condition.

For NIMCET PYQ topic-wise preparation, group previous questions under these concepts. This makes it easier to identify which type of ratio problem you are solving.

Common Mistakes to Avoid

Ratio questions can become confusing if the basic comparison is not set correctly. Keep these points in mind:

• Do not reverse the antecedent and consequent.

• Always reduce a ratio to its simplest form.

• Do not assume that ratio terms are the actual values.

• Use HCF when simplifying a ratio.

• Do not use direct proportion when quantities have an inverse relationship.

• In inverse proportion, remember that the product remains constant.

• Check all terms when simplifying a three-term ratio.

• Do not rely on divisibility shortcuts when decimal values are possible.

• Verify the final answer with the conditions given in the question.

Ratio forms a useful foundation for several Quantitative Aptitude concepts. It is applied in distribution, proportion, speed-time, work, income-expenditure, and other arithmetic problems. You should first build clarity on basic ratio properties and then move to combined ratios, fractional forms, direct proportion, and inverse proportion.

For NIMCET Quantitative Aptitude Ratio preparation, focus on correct comparison, simple calculations, and regular practice. Once you are comfortable with the basic methods, use previous-year questions and practice sets to improve your approach to different problem types. NIMCET Ratio Practice Questions can further help you test your understanding and identify areas that need revision.

Preparation Resources:

• PW NIMCET Online Batches

• PW NIMCET YouTube Channel

• NIMCET Fundamentals of Calculations

• NIMCET Alphanumeric Series