Back to Home
Back to Blog

📊 Percentage & Ratio: The Arithmetic Soul

Master the Fraction Chart & Ratio Merging Tricks - The Foundation of All Quant Problems! Trusted by 50,000+ IBPS, SBI, SSC aspirants!

Topic: Arithmetic Basics Reading Time: 15 mins Updated: Dec 2024 Foundation Topic

Why Percentage & Ratio is the "Soul" of Arithmetic?

Percentage and Ratio are not just standalone chapters — they are the building blocks of almost every Quant topic. Without mastering these, you cannot solve Profit & Loss, SI/CI, Mixture & Alligation, Partnership, Data Interpretation, and more!

Think of Percentage as the language of Quantitative Aptitude. Every calculation, every shortcut, every trick ultimately uses percentage and ratio concepts.

Why This Topic is a Game-Changer?

In IBPS PO 2023, over 20 questions directly or indirectly used percentage/ratio concepts. The Fraction Method allowed toppers to solve problems 3x faster! That's 10+ minutes saved for the entire Quant section!

Part 1: The Golden Fraction Chart

This is the alphabet of Quant. Memorize these fraction-to-percentage conversions — they appear in almost every problem!

1/250%
1/333.33%
1/425%
1/520%
1/616.67%
1/714.28%
1/812.5%
1/911.11%
1/1010%
1/119.09%
1/128.33%
1/156.67%
1/166.25%
1/205%
1/254%
1/502%

Pro-Tip: Extended Fractions

For multiples, just multiply!
2/5 = 2 × 20% = 40%
3/8 = 3 × 12.5% = 37.5%
5/6 = 5 × 16.67% = 83.33%

Part 2: The Reversibility Rule

This is one of the most powerful shortcuts in Percentage. It saves time when direct calculation is difficult.

📌 THE GOLDEN RULE
A% of B = B% of A
1

Identify the Hard Percentage

Look at the question. Is one percentage easier to calculate than the other?

2

Flip the Numbers

Use A% of B = B% of A. Swap the percentage and the base number.

3

Calculate the Easy One

Now solve the easier calculation. The answer is the same!

Solved Example 1: Reversibility

Question: Find 64% of 25.

Solution:

• 64% of 25 is hard to calculate directly
• Using Reversibility: 64% of 25 = 25% of 64
• 25% = 1/4, so 64 ÷ 4 = 16

Answer: 16 (Solved in 2 seconds!)

Solved Example 2: Real Exam Question

Question: Find 37.5% of 48.

Solution:

• 37.5% of 48 = 48% of 37.5 (Not easier)
• Better approach: 37.5% = 3/8
• 48 × 3/8 = 48/8 × 3 = 6 × 3 = 18

Answer: 18

Part 3: Product Constancy Rule

Use this when Price × Consumption = Constant Expenditure. If one goes up, the other must come down!

📌 THE FRACTION TRICK
If Price ↑ by x/n, Consumption ↓ by x/(n+x)
Solved Example 3: Price Increase

Question: Price of sugar increases by 25%. By how much % should consumption reduce to keep expenditure same?

Solution using Fraction Method:

• 25% increase = +1/4
• To reduce: Keep numerator (1), add numerator to denominator (4+1)
• Reduction = 1/5
• 1/5 = 20%

Answer: Reduce consumption by 20%

Pro-Tip: Quick Reference

10% increase → 9.09% decrease (1/11)
20% increase → 16.67% decrease (1/6)
25% increase → 20% decrease (1/5)
50% increase → 33.33% decrease (1/3)

Part 4: Successive Percentage Change

When a value changes multiple times successively, use this formula to find the net change:

📌 SUCCESSIVE CHANGE FORMULA
Net Change = X + Y + (X×Y / 100) %

Note: Use + for increase, - for decrease in X and Y values.

Solved Example 4: Two Changes

Question: A salary increases by 20%, then decreases by 10%. Find net change.

Solution:

• X = +20, Y = -10
• Net = 20 + (-10) + (20 × -10 / 100)
• Net = 10 - 2 = +8%

Answer: 8% Net Increase

Solved Example 5: Same Increase & Decrease

Question: Price increases by 20%, then decreases by 20%. Net change?

Solution:

• X = +20, Y = -20
• Net = 20 - 20 + (20 × -20 / 100)
• Net = 0 - 4 = -4%

Answer: 4% Net Decrease (Always a loss!)

Part 5: Ratio Merging (Plot Method)

When you have two ratios with one common element, use the Plot Method (Kabza Method) to merge them:

1

Write Ratios in a Grid

Place both ratios in a table format with common element aligned.

2

Fill Empty Spaces

Copy the neighbor's value to fill empty positions (shown in red below).

3

Multiply Downwards

Multiply each column vertically to get the final merged ratio.

Solved Example 6: Merge Two Ratios

Question: If A:B = 2:3 and B:C = 4:5, find A:B:C.

A B C
2 3 3
4 4 5
2×4 = 8 3×4 = 12 3×5 = 15

Answer: A:B:C = 8:12:15

5 Pro-Tips to Master Percentage & Ratio

Tip 1: Memorize the Fraction Chart

Spend 10 minutes daily until 1/2 to 1/20 conversions become automatic. This is non-negotiable!

Tip 2: Always Check for Reversibility

Before calculating, ask: "Can I flip this?" 64% of 25 → 25% of 64. Saves seconds every time!

Tip 3: Same % Up & Down = Always Loss

20% up then 20% down ≠ 0%. It's always a net loss = (X/10)² %. Quick trap check!

Tip 4: Use 100 as Base for Percentage

When solving, assume base = 100. 20% increase on 100 = 120. Much easier than actual numbers!

Tip 5: Practice DI with Percentages

Data Interpretation is 80% percentage calculation. Practice 10 DI sets to master percentage applications.

Frequently Asked Questions (FAQ)

Q1: How to convert percentage to fraction quickly?
Memorize the Golden Fraction Chart: 50%=1/2, 33.33%=1/3, 25%=1/4, 20%=1/5, 12.5%=1/8, 10%=1/10. For any percentage, divide by 100 and simplify. Example: 75% = 75/100 = 3/4
Q2: What is the Reversibility Rule?
A% of B = B% of A. This allows you to flip any percentage calculation to make it easier. Example: 64% of 25 = 25% of 64 = 16. Always check if flipping makes the calculation simpler!
Q3: How many questions use Percentage in Bank exams?
Directly: 4-6 questions. Indirectly (DI, P&L, SI/CI, etc.): 15-20 questions. That's over 50% of the Quant section! Percentage is truly the "soul" of arithmetic.
Q4: How to merge three or more ratios?
Use the Chain Method: First merge A:B and B:C to get A:B:C. Then merge A:B:C with C:D to get A:B:C:D. Always ensure the common element (B or C) has the same value before merging.
Q5: What's the trick for successive percentage changes?
Use formula: Net = X + Y + (XY/100). Remember: Use + for increase, - for decrease. Special case: Same % up then down always gives net loss = -(X/10)²%.

Quick Reference Cheat Sheet

🔄 Reversibility

A% of B = B% of A

📈 Successive Change

X + Y + (XY/100)

⚡ Product Const.

↑x/n → ↓x/(n+x)

⚠️ Same % Trap

Loss = (X/10)²%

🚀 Ready to Practice?

Ab aapko Percentage & Ratio ki poori samajh aa gayi! Time to test your skills with real exam-level questions!

Start Practice Now →