Percentages
Percentage questions are the most frequent single question-type in CLAT quant, and almost every other quant topic secretly reduces to one.
10 questions · 5 minutes · instant scoring
What this topic actually tests
Percentage is just 'per hundred' — a fraction with denominator 100 written as a single number. CLAT rarely asks you to compute a percentage from scratch; instead it gives you one known percentage relationship and asks for another, so the fastest method is to convert the percentage into a fraction you can multiply mentally rather than doing long division. 10% of a number is that number divided by 10; 5% is half of that; 1% is the number divided by 100. Build any awkward percentage from these building blocks: 35% of 480 = 10%(48) x 3 + 5%(24) = 144 + 24 = 168. For percentage change questions, always identify the base (the 'of what' the percentage refers to) before calculating — this is the single most common source of error on this topic. When a value changes from A to B, the percentage change is always (B - A)/A x 100, using the original value A as the base, never the new value. For successive percentage changes (e.g., a 20% increase followed by a 10% decrease), never add or subtract the percentages directly; instead multiply the retained fractions: 1.20 x 0.90 = 1.08, meaning a net 8% increase. Worked example: a shopkeeper's revenue rises from Rs 40,000 to Rs 46,000 in one month. Percentage increase = (46,000 - 40,000)/40,000 x 100 = 6,000/40,000 x 100 = 15%. If revenue then falls by 15% from the new figure, the base for that second calculation is 46,000, not 40,000 — this base-switching is exactly what CLAT tests with two-step percentage passages, and spotting which number is the current base is worth more than any formula.
The common trap on this topic
The single biggest trap in percentage questions is using the wrong base after a change has already occurred. If a price rises by 25% and a student is asked what percentage decrease brings it back to the original price, the instinctive (wrong) answer is 25% — but the decrease must be calculated on the new, larger price, not the original. Since the new price is 125% of the original, undoing it requires removing 25 out of 125, i.e., a 20% decrease, not 25%. This asymmetry appears constantly in 'increase then reverse' and 'successive discount' questions. A second common trap is confusing 'percentage increase' with 'percentage points': if pass marks move from 40% to 45% of the total, that is a 5 percentage-point increase, but only a 12.5% relative increase (5/40 x 100) — CLAT passages are often worded ambiguously enough that you must check exactly which quantity is being asked for. Always re-read the question after solving to check whether it wants the relative percentage change or the raw point difference, and whether the base is the original, the new, or a third reference value stated in the passage.
Take the micro-test
In an election between two candidates, the winner received 60% of the total votes polled and won by 4,200 votes. What was the total number of votes polled?
A number is first increased by 25% and then the result is decreased by 20%. What is the net percentage change in the number?
How many girls are enrolled in the Humanities stream?
What percentage of the total 200 students are enrolled in the Science stream (both boys and girls combined)?
What is the ratio of boys studying Science to girls studying Humanities?
Successive discounts of 20% and then 10% on the marked price of an item are equivalent to a single discount of what percentage?
If 30% of a certain number is 150, what is 45% of that same number?
A student scored 320 marks out of 400 in her first attempt and 360 marks out of 400 in her second attempt. By what percentage did her score increase (relative to her first-attempt score)?
The price of an item was increased by 40%. By approximately what percentage must the new price now be reduced to bring it back to the original price?
A solution of 60 litres contains 25% acid by volume. If 20 litres of water is added to this solution, what is the new percentage of acid in the mixture?
FAQ
Do I need to memorise percentage-to-fraction conversions for CLAT?
Knowing common ones (50% = 1/2, 25% = 1/4, 20% = 1/5, 12.5% = 1/8, 33.33% = 1/3) speeds up mental calculation significantly and is worth the few minutes it takes to memorise, since CLAT is timed and calculators are not allowed.
How do successive percentage change questions differ from simple percentage questions?
A simple percentage question has one base value throughout. A successive-change question changes the base after each step, so you must multiply retained fractions (e.g., 1.10 x 0.95) rather than adding or subtracting the percentages directly.
Is percentage tested standalone or mixed with other topics in CLAT?
Both — CLAT includes standalone percentage questions but also embeds percentage calculations inside profit-and-loss, interest, and data-interpretation passages, so fluency here directly speeds up several other question types.
Keep practising
- → Ratio and Proportion
- → Profit and Loss
- → Averages and Mixtures
- → All Quantitative Techniques practice
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