Percentage

About 6 min · Mathematics · English

Time worked out from the lesson's 410 words at 150 words a minute, plus a minute for each question.

It forms the foundation for Profit & Loss, Simple & Compound Interest, and many Data Interpretation questions. The word "percent" means "per hundred" — so 25% literally means 25 out of every 100.

Key ideas

Definition: Percentage expresses a number as a fraction of 100. If a quantity is x% of another, it means x/100 of that quantity.
Base value matters: "30% of 200" means (30/100) × 200 = 60. Always identify what the percentage is calculated on — the base or reference value.
Percentage increase/decrease: If a value V increases by r%, new value = V × (1 + r/100). If it decreases by r%, new value = V × (1 – r/100).
Successive percentage changes: Two successive changes of a% and b% do NOT simply add. Net effect = a + b + (ab/100). The sign depends on increase (+) or decrease (–).
Reverse percentage problems: If new value after r% increase is N, original value = N/(1 + r/100). Similarly for decrease, original = N/(1 – r/100).

Watch out for

Wrong base for percentage: Calculating "A is 20% more than B" as B + 20% of A instead of B + 20% of B. Fix: Always take percentage of the reference (base) value mentioned after "than" or "of."
Adding successive percentages directly: Thinking 10% increase followed by 10% decrease returns to original. Fix: Use the formula a + b + ab/100 or calculate step-by-step. A 10% gain then 10% loss yields 1% net loss.
Confusing percentage change with percentage points: Saying tax increased from 10% to 12% is a "2% increase" when it's actually a 20% relative increase. Fix: Percentage point = absolute difference; percentage change = relative to original.

Quick reference

Percent to fraction: Divide by 100. Example: 40% = 40/100 = 2/5
Fraction to percent: Multiply by 100. Example: 7/20 = (7/20) × 100 = 35%
r% increase: Multiply by (100 + r)/100
r% decrease: Multiply by (100 – r)/100
Successive changes a%, b%: Net = a + b + ab/100 (signs matter: + for increase, – for decrease)

Check yourself: 3 questions

1. A student scored 360 marks out of 500 in an examination. What is his percentage score?
2. The price of rice increases from Rs. 40 per kg to Rs. 50 per kg. What is the percentage increase in the price?
3. A man spends 60% of his income. If his income is Rs. 15000, how much does he save?

This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 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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