Percentage

Percentage — IBPS Clerk Prelims Study Notes

Overview

Percentage is one of the most fundamental topics in Numerical Ability and forms the backbone of several other topics like Profit & Loss, Simple & Compound Interest, and Data Interpretation. In IBPS Clerk Prelims, you can expect 2–4 direct or indirect questions on percentage, often embedded within DI sets or mixed arithmetic problems.

Mastering percentage is non-negotiable because it's rarely tested in isolation—it's the calculation engine behind 40–50% of quant questions. The good news: Clerk-level percentage questions are straightforward and reward students who know fraction-percentage equivalents by heart and can calculate quickly.

Your goal is speed with accuracy. Learn the shortcuts, memorize the common conversions, and practice until percentage calculations become mental math.

Key Concepts

• Basic Definition: Percentage means "per hundred." If 25 out of 100 students pass, the pass percentage is 25%. Formula: (Part / Whole) × 100.
• Fraction-Percentage Equivalence: Every fraction has a percentage equivalent. Memorizing these (1/2 = 50%, 1/4 = 25%, 1/5 = 20%, etc.) eliminates calculation time.
• Percentage Change: When a value increases or decreases, percentage change = (Change / Original) × 100. Always use the original value as the base, not the new value.
• Successive Percentage Change: When two percentage changes occur one after another, they don't simply add up. Use the net effect formula: a + b + (ab/100).
• Percentage of a Percentage: Finding "20% of 30% of 500" means multiplying sequentially: 0.20 × 0.30 × 500.
• Reverse Percentage: If a value after 20% increase is 600, the original = 600 / 1.20 = 500. Work backward using multipliers.
• Base Matters: "A is 25% more than B" and "B is 25% less than A" are NOT the same. The base changes the calculation entirely.

Formulas / Key Facts

Core Formulas:

• Percentage = (Part / Whole) × 100
• Part = (Percentage / 100) × Whole
• Percentage Increase = [(New − Original) / Original] × 100
• Percentage Decrease = [(Original − New) / Original] × 100
• Net effect of successive changes of a% and b% = a + b + (ab / 100)
• If a value is increased by R%, multiply by (100 + R) / 100
• If a value is decreased by R%, multiply by (100 − R) / 100

Must-Memorize Fraction-Percentage Table:

Quick Multipliers:

• 10% increase → multiply by 1.1
• 20% decrease → multiply by 0.8
• 25% increase → multiply by 1.25 (or × 5/4)
• 33.33% decrease → multiply by 2/3

Worked Examples

Example 1: Basic Percentage Calculation

A student scores 72 marks out of 90. What is the percentage?

Percentage = (72 / 90) × 100 = (72 × 100) / 90 = 7200 / 90 = 80%

Shortcut: 72/90 = 8/10 = 4/5 = 80%

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Example 2: Percentage Change

The price of a commodity increases from ₹400 to ₹480. Find the percentage increase.

Change = 480 − 400 = 80 Percentage increase = (80 / 400) × 100 = 20%

Shortcut: 80 is what fraction of 400? → 80/400 = 1/5 = 20%

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Example 3: Successive Percentage Change

A shopkeeper increases price by 20% and then decreases it by 10%. What is the net percentage change?

Using formula: a + b + (ab / 100) = 20 + (−10) + (20 × −10) / 100 = 20 − 10 − 2 = 8% increase

Verification: If original = 100 After 20% increase: 120 After 10% decrease: 120 × 0.9 = 108 Net change = 8% increase ✓

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Example 4: Reverse Percentage

After a 15% discount, a shirt costs ₹425. Find the original price.

Let original price = x x − 15% of x = 425 0.85x = 425 x = 425 / 0.85 = 500

Original price = ₹500

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Example 5: Comparing Two Values

A's salary is 20% more than B's salary. By what percentage is B's salary less than A's?

Let B's salary = 100 A's salary = 120

Difference = 20 B is less than A by = (20 / 120) × 100 = 16.67% or 50/3%

Key insight: The base changed from B (100) to A (120).

Common Mistakes

• Wrong base in percentage change → Students calculate increase/decrease using the new value instead of the original. Fix: Always divide by the ORIGINAL value.
• Adding successive percentages directly → Thinking 20% increase + 10% decrease = 10% increase. Fix: Use the formula a + b + (ab/100), which accounts for the compounding effect.
• Confusing "more than" and "less than" → If A is 25% more than B, students assume B is 25% less than A. Fix: The percentage differs because the base changes. Calculate separately.
• Forgetting to convert percentage to decimal → Writing 20% as 20 in calculations instead of 0.20. Fix: Always convert—20% = 20/100 = 0.20.
• Misreading "of" vs "than" → "20% of 50" means 10, but "20% more than 50" means 60. Fix: "Of" triggers multiplication; "more/less than" triggers addition/subtraction.
• Slow calculation without fractions → Calculating 33.33% the long way instead of recognizing it as 1/3. Fix: Memorize the fraction table cold.

Quick Reference

• Percentage = (Part / Whole) × 100 — always use original as base for change problems
• Successive change formula: a + b + (ab/100) — handles two consecutive changes
• 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%, 1/3 = 33.33% — know these instantly
• For reverse problems: divide by the multiplier (e.g., after 20% increase, divide by 1.2)
• "A is x% more than B" ≠ "B is x% less than A" — base matters
• When in doubt, assume base = 100 and work with actual numbers