Percentage

About 6 min · Aptitude and Mental Ability · English

Time worked out from the lesson's 434 words at 150 words a minute, plus a minute for each question.

Percentage is one of the most fundamental topics in the Aptitude section of TNPSC Group II/IIA. The word "percent" literally means "per hundred" — it represents a fraction with denominator 100. Almost every quantitative topic you'll encounter (profit-loss, simple/compound interest, data interpretation, ratio-proportion) builds upon percentage calculations.

Key ideas

Basic Definition: x% = x/100. To find x% of a number N, calculate (x × N)/100 or equivalently N × (x/100).
Fraction-Percentage Conversion: Any fraction a/b can be converted to percentage by multiplying by 100. Thus, a/b = (a/b) × 100 %.
Percentage Increase: When a quantity increases from A to B, percentage increase = [(B − A)/A] × 100. Always divide by the original value.
Percentage Decrease: When a quantity decreases from A to B, percentage decrease = [(A − B)/A] × 100.
Successive Percentage Change: For two successive changes of a% and b%, the net effect = a + b + (ab/100) %. This single formula handles both increases (positive) and decreases (negative).

Watch out for

Wrong base selection → When asked "A is what percent more than B," students often divide by A instead of B. Fix: The phrase "more than B" means B is the base; divide by B.
Adding successive percentages directly → Students calculate 20% increase followed by 20% decrease as "net zero." Fix: Use the formula a + b + (ab/100). Here: 20 − 20 − 4 = −4%, a net decrease.
Confusing percentage change with percentage points → If interest rate moves from 8% to 10%, the increase is 2 percentage points, but 25% change. Fix: Read questions carefully for "percentage points" vs "percent change."

Quick reference

x% of N = N × x/100 — multiply first, then divide for easier calculation.
Percentage change = (Difference/Original) × 100 — original is always the base.
Successive changes: a + b + ab/100 — signs matter; use negative for decrease.
To reverse an x% increase, multiply by 100/(100+x).
1/8 = 12.5%, 1/6 = 16.67%, 1/7 ≈ 14.28% — memorize these for speed.

Check yourself: 3 questions

1. A shopkeeper marks his goods 25% above the cost price and then allows a discount of 10%. What is his net profit percentage?
2. In an examination, a student scored 35% marks and failed by 40 marks. Another student scored 45% marks and secured 10 marks more than the passing marks. What is the maximum marks for the examination?
3. The population of a town increases by 10% in the first year and decreases by 10% in the second year. What is the net change in population after two years?

This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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