Banking Notes / Quantitative Aptitude / Chapter 5
Chapter 5 of 26

Percentage

The fraction-equivalent method that turns percentage calculations into mental math, plus successive change and application-based problems.

📖 ~9 min read 🏦 Banking Quantitative Aptitude

Introduction

Percentage means "per hundred." It is the single most-used concept in banking quant — Profit & Loss, Interest, Data Interpretation and Data Sufficiency are all built on percentage logic. Mastering the fraction-equivalent table below removes almost all long division from percentage questions.

Percentage-to-Fraction Table

%Fraction%Fraction
50%1/216.67%1/6
33.33%1/314.28%1/7
25%1/412.5%1/8
20%1/511.11%1/9
10%1/106.25%1/16

Successive Percentage Change

If a value changes by a% then b%, the net effective change is:

Net % change = a + b + (a×b)/100 — use negative signs for decreases.
Q. A number is increased by 20% and then decreased by 10%. Find the net percentage change.
Net change = 20 + (−10) + (20×−10)/100 = 20 − 10 − 2 = +8% (net increase of 8%).
Q. In an exam, 40% of candidates failed in Maths and 30% failed in English, while 15% failed in both. What percentage passed in both subjects?
Failed in at least one = 40 + 30 − 15 = 55%. Passed in both = 100 − 55 = 45%.

Percentage Change vs Base Change

⚠️ Key Insight: If A is x% more than B, then B is NOT x% less than A. Use: B is [x / (100+x)] × 100 % less than A. This trap appears frequently in bank prelims.
✅ Practice Focus: Fraction-equivalent mental math · Successive change formula · "More than / less than" base-swap trap · Population and income growth applications.

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