Percentage

Percentage — IBPS PO Prelims Study Notes

Overview

Percentage is the foundation of almost every arithmetic topic in IBPS PO Quantitative Aptitude. Questions on profit-loss, simple/compound interest, data interpretation, and even partnership are fundamentally percentage calculations in disguise. Mastering this topic means faster solving across 60–70% of the Quant section.

In IBPS PO Prelims, percentage appears directly in simplification, approximation, and DI sets. You'll rarely see a standalone "calculate 25% of 840" question—instead, percentages are embedded in word problems involving increase/decrease, successive changes, or ratio conversions. The key is to build mental math reflexes for common percentage-fraction equivalents and understand the logic of percentage change rather than memorising formulas mechanically.

Key Concepts

• Percentage means "per hundred": x% = x/100. This simple conversion is the basis of every calculation.
• Percentage-to-fraction shortcuts save time: Knowing that 25% = 1/4, 12.5% = 1/8, 33.33% = 1/3 lets you calculate mentally instead of on paper.
• Percentage change has a direction: Increase means adding to the base; decrease means subtracting. The formula always uses the original value as the base, not the new value.
• Successive percentage changes don't simply add: A 10% increase followed by a 10% decrease does NOT return you to the original—it results in a 1% net decrease.
• "Of" means multiplication: "What is 20% of 450?" translates to (20/100) × 450.
• Percentage points vs. percentage change: Going from 40% to 50% is a 10 percentage-point increase but a 25% relative increase.
• Reverse percentage (finding the original): If a value after x% increase is A, then original = A × 100/(100 + x).

Formulas / Key Facts

Basic Percentage Calculation x% of N = (x × N) / 100

Percentage Change Percentage Change = [(New Value − Original Value) / Original Value] × 100

• Positive result = increase; Negative result = decrease

Finding Original Value If final value after x% increase = A, then Original = A × (100 / (100 + x)) If final value after x% decrease = A, then Original = A × (100 / (100 − x))

Successive Percentage Change Net effect of a% and b% successive changes = a + b + (ab/100)

• Use signs: increase = +, decrease = −

Fraction-Percentage Equivalents (Memorise These)

Worked Examples

Example 1: Basic Percentage Change

Problem: A shopkeeper's sales increased from ₹24,000 to ₹27,000. Find the percentage increase.

Solution:

• Change = 27,000 − 24,000 = 3,000
• Percentage increase = (3,000 / 24,000) × 100
• = (1/8) × 100 = 12.5%

Answer: 12.5% increase

---

Example 2: Successive Percentage Changes

Problem: The price of a laptop increased by 20% and then decreased by 10%. What is the net percentage change?

Solution:

• Using formula: Net = a + b + (ab/100)
• Here a = +20, b = −10
• Net = 20 + (−10) + (20 × −10)/100
• = 20 − 10 − 2 = 8%

Answer: Net 8% increase

---

Example 3: Finding Original Value

Problem: After a 15% discount, a TV costs ₹10,200. What was the original price?

Solution:

• Final price = Original × (100 − 15)/100
• 10,200 = Original × (85/100)
• Original = 10,200 × (100/85)
• = 10,200 × (20/17) = 12,000

Answer: ₹12,000

---

Example 4: Percentage in Ratios

Problem: A's income is 25% more than B's income. By what percentage is B's income less than A's?

Solution:

• Let B's income = 100, so A's income = 125
• B is less than A by = 125 − 100 = 25
• Percentage = (25/125) × 100 = 20%

Answer: B's income is 20% less than A's

Key insight: "X% more" and "Y% less" are NOT the same percentage. Always recalculate with the new base.

Common Mistakes

Mistake 1: Using the wrong base for percentage change

• Wrong: Price went from 80 to 100, so change = (20/100) × 100 = 20%
• Correct: Base is the ORIGINAL value (80), so change = (20/80) × 100 = 25%

Mistake 2: Adding successive percentages directly

• Wrong: 10% increase then 10% decrease = 0% change
• Correct: Use the formula → 10 − 10 + (10 × −10)/100 = −1% (net decrease)

Mistake 3: Confusing "more than" with "of"

• Wrong: "A is 20% more than B" interpreted as A = 0.20 × B
• Correct: A = B + 20% of B = 1.20 × B

Mistake 4: Reversing the percentage incorrectly

• Wrong: If A is 25% more than B, then B is 25% less than A
• Correct: If A = 125% of B, then B = (100/125) × A = 80% of A → B is 20% less than A

Mistake 5: Forgetting to convert percentage to decimal in calculations

• Wrong: 15% of 200 = 15 × 200 = 3000
• Correct: 15% of 200 = 0.15 × 200 = 30

Quick Reference

• Percentage change = (Difference / Original) × 100 — always divide by the OLD value.
• Successive changes: a + b + ab/100 — signs matter (+ for increase, − for decrease).
• 12.5% = 1/8; 16.67% = 1/6; 33.33% = 1/3 — memorise for DI speed.
• "X% more than Y" ≠ "Y is X% less than X" — recalculate with new base.
• To find original after x% change: multiply final by 100/(100 ± x).
• In exams, approximate first—IBPS options are usually well-separated.