Hello Aspirants,

I am Rahul Sir, and over the years I have trained thousands of banking aspirants preparing for IBPS PO, IBPS Clerk, SBI PO, RBI Assistant, and other competitive examinations. Among all aptitude topics, Ratio and Proportion is one of the most scoring yet misunderstood chapters. Students often memorize formulas without understanding the relationships between quantities, leading to unnecessary mistakes in the examination.

Ratio and Proportion questions are frequently asked in IBPS exams directly and indirectly through topics like Partnership, Mixture & Allegation, Profit & Loss, Ages, Time & Work, and Data Interpretation. If your basics are clear, you can solve many questions mentally within seconds.

The secret is not learning dozens of formulas but understanding the concept behind ratios. Once you know how quantities compare, you can easily solve even lengthy-looking problems using smart tricks. In this guide, I will explain every important concept, shortcuts, and examination strategies with solved examples that will help you maximize your score.

Let’s master Ratio and Proportion the smart way.

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1. Understanding Ratio and Proportion Basics

Ratio represents the comparison between two quantities of the same kind using division. If two quantities are A and B, their ratio is written as A or A/B.

Proportion states that two ratios are equal.

For example,

3:5 = 12:20

Since both represent the same relationship, they are said to be in proportion.

Important Formula

If

a = c

then

a × d = b × c

This is called cross multiplication.

Example

The ratio of boys to girls is 4:5.

If there are 36 girls, find the number of boys.

Solution

Girls = 5 parts

1 part = 36 ÷ 5 = 7.2

Boys = 4 × 7.2

= 28.8

Instead of decimals, use multiplication.

5 parts = 36

4 parts = (36 × 4)/5

= 144/5

= 28.8

In competitive exams, values are generally chosen to give whole numbers.

Suppose girls are 45.

Then

1 part = 9

Boys = 36

Shortcut

Always calculate one part first whenever total value of one side is given.

Common Mistakes

• Confusing ratio with difference.
• Ignoring simplification.
• Using addition instead of multiplication.
• Comparing different units.

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2. Simplifying Ratios Quickly

One of the fastest ways to solve questions is learning to simplify ratios mentally.

Example

48:72

Find HCF

HCF = 24

Ratio

= 2:3

Shortcut

Always divide by highest common factor.

Decimal Ratio

0.8 : 1.2

Multiply by 10

8:12

Simplify

2:3

Fraction Ratio

1/2 : 3/4

Multiply both by LCM of denominators

LCM = 4

Ratio

2:3

Example

25 kg : 500 g

Convert units

25 kg = 25000 g

Ratio

25000:500

50:1

Exam Trick

Always convert units before taking ratio.

Practice

150:210

Answer

5:7

Speed Tips

• Remove common zeros.
• Divide by common factors.
• Convert fractions into integers.
• Convert kilograms into grams.
• Convert hours into minutes when required.

The faster you simplify, the faster every question becomes.

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3. Finding Unknown Values Using Ratio

Many IBPS questions involve finding missing values.

Suppose

A = 7:9

If A = 56

Find B.

Solution

7 parts = 56

1 part = 8

9 parts = 72

Answer = 72

Shortcut Formula

Unknown = (Known × Required Ratio)/Known Ratio

Example

Ratio of pens and pencils = 5:8

Pens = 30

Pencils = ?

= (30 × 8)/5

= 48

Reverse Question

Ratio = 3:8

Second quantity = 80

First =

(80 × 3)/8

=30

Trick

Never calculate total unless asked.

Go directly using proportional multiplication.

Practice

Ratio

8:11

Second quantity = 44

First?

Answer

32

These direct questions should take less than 20 seconds.

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4. Dividing Quantities According to Ratio

Sharing money or objects according to ratio is a favorite IBPS topic.

Example

Divide ₹1800 in ratio 4:5.

Solution

Total parts

4+5=9

One part

1800/9=200

Shares

4×200=800

5×200=1000

Shortcut Formula

Share

(Total × Individual Ratio)/(Sum of Ratios)

Example

Divide ₹3900 in ratio

2:3:8

Total parts

13

Shares

600

900

2400

Speed Trick

Always calculate one part first.

Then multiply.

Practice

₹960

Ratio

5:3

Shares

600

360

Common Mistake

Students divide using difference instead of total parts.

Always use addition of ratios.

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5. Compound Ratio Made Easy

Compound ratio combines two or more ratios.

Example

2:3

and

4:5

Compound ratio

2×4 : 3×5

8:15

Example

3:7

5:9

Compound ratio

15:63

Simplify

5:21

Applications

Compound ratio appears in

• Partnership
• Successive comparisons
• Production
• Mixture

Shortcut

Multiply numerators together.

Multiply denominators together.

Simplify.

Practice

6:5

2:9

Compound ratio

12:45

4:15

Easy marks if practiced properly.

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6. Proportion Tricks and Cross Multiplication

Cross multiplication saves enormous time.

If

x:15 = 12:20

Then

20x

=15×12

180

x=9

Example

5 =10:18

Cross multiply

90=10x

x=9

Direct Formula

a=c

Then

ad=bc

Practice

8:12 = x:18

8×18=12x

144=12x

x=12

Shortcut

Never expand ratios unnecessarily.

Use cross multiplication directly.

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7. Ratio Changes After Increase or Decrease

These questions are very common.

Example

Ratio

3:5

Both increase by 6.

New ratio

?

Suppose original

3x and 5x

(3x+6)/(5x+6)

Use new condition if provided.

Example

Ratio

2:3

After adding 10 to each

3:4

Find original numbers.

Solution

2x+10

3x+10

Cross multiply

4(2x+10)

=

3(3x+10)

8x+40

9x+30

x=10

Numbers

20

30

Trick

Represent original values as multiples of x.

Never assume actual values.

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8. Advanced Ratio Problems in IBPS

Example

Income ratio

5:7

Expenses ratio

4:5

Savings

₹2000 and ₹3000

Find incomes.

Represent incomes

5x

7x

Expenses

4y

5y

Use savings equations.

Solve simultaneously.

Another Example

Age ratio

3:5

After 10 years

5:7

Represent ages

3x

5x

Apply condition.

These questions appear difficult but become easy using variables.

Tips

• Use variables.
• Don’t substitute random values.
• Keep equations simple.
• Solve mentally whenever possible.

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9. Ratio Questions in Data Interpretation

Pie charts, bar graphs and tables often require ratio calculations.

Example

Company A

120 employees

Company B

180 employees

Ratio

2:3

Percentage to Ratio

40%

60%

Ratio

2:3

Example

Male

240

Female

360

Ratio

2:3

Shortcut

Convert percentages into ratios.

25%

75%

1:3

20%

80%

1:4

30%

70%

3:7

These shortcuts save valuable seconds during DI.

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10. Exam Strategies, Tricks and Practice Plan

To master Ratio and Proportion:

Daily Practice

Solve 20 questions daily.

Memorize Common Ratios

1:2

2:3

3:5

4:7

5:8

These appear repeatedly.

Learn Percentage-Ratio Conversion

20%=1:4

25%=1:3

40%=2:3

50%=1:1

60%=3:2

75%=3:1

Time Target

Easy Question

20 seconds

Moderate

40 seconds

Difficult

60 seconds

Avoid These Mistakes

• Wrong unit conversion
• Ignoring simplification
• Incorrect total parts
• Calculation mistakes
• Random assumptions

Final Advice

Concepts are more important than formulas. Practice enough questions so that identifying the method becomes automatic. With consistent revision, Ratio and Proportion can become one of your highest-scoring topics in the IBPS PO and Clerk examination.

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How Teachers from OdTutor Can Help

At OdTutor, our experienced aptitude faculty provides structured preparation specifically designed for IBPS PO, Clerk, SBI, RBI, SSC, and other competitive examinations. Our teachers simplify Ratio and Proportion using conceptual explanations, shortcut techniques, live problem-solving sessions, and exam-oriented practice sets. Students receive chapter-wise notes, mock tests, previous year question discussions, and personalized doubt-clearing sessions. Regular speed tests help improve calculation accuracy and time management. Whether you are a beginner or an advanced learner, OdTutor’s expert guidance ensures you build strong fundamentals and develop the confidence to solve even the toughest aptitude questions accurately during the examination.

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