Percentage
About 6 min · Quantitative Ability · English
Time worked out from the lesson's 401 words at 150 words a minute, plus a minute for each question.
Percentage is one of the most fundamental topics in Quantitative Ability and forms the backbone for several other topics like Profit & Loss, Simple & Compound Interest, and Data Interpretation.
Key ideas
- Basic Definition: x% means x out of 100, written as x/100 or 0.01x in decimal form.
- Conversion Rule: To convert a fraction to percentage, multiply by 100. To convert percentage to fraction, divide by 100.
- Percentage of a Number: x% of N = (x × N)/100. This is the most frequently used calculation.
- Percentage Change: When a quantity changes from old value to new value, percentage change = [(New − Old)/Old] × 100.
- Successive Percentage Change: When two successive changes of a% and b% occur, the net effect = a + b + (ab/100)%.
Watch out for
- Wrong base selection → Students calculate "A is what % of B" but use A in denominator instead of B. Always identify what the "base" or "reference" quantity is — it goes in the denominator.
- Sign errors in successive changes → When one change is increase (+) and another is decrease (−), students forget to use negative sign in the formula. Always assign + for increase and − for decrease.
- Confusing "more than" with "of" → "A is 25% more than B" is different from "A is 25% of B." The first means A = 1.25B; the second means A = 0.25B.
Quick reference
- x% of N = xN/100; always remember the base is 100.
- % Change = (Difference/Original) × 100 — Original is always the base.
- Successive % change: a + b + ab/100 (use signs carefully).
- 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%, 1/3 = 33.33% — memorize these.
- "More than" problems: denominator is the smaller quantity.
Check yourself: 3 questions
1. A man spends 75% of his income. If his income increases by 20% and his expenditure increases by 10%, by what percentage does his savings increase?
2. The population of a town is 50,000. If the population increases by 10% in the first year and decreases by 20% in the second year, what is the population at the end of the second year?
3. In an election between two candidates, one candidate got 55% of the total valid votes. If 20% of the votes were declared invalid and the total number of votes was 7,500, find the number of valid votes polled in favour of the winning candidate.
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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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