If you learn only one Quant topic well for CLAT, make it percentages. The Quantitative Techniques section is data-interpretation style — a short passage, table or chart followed by questions — and percentages sit at the heart of nearly every set. Share of a total, growth from one year to the next, the bigger slice of a pie: all of it is percentages. The maths is class-10 simple. The marks come from doing it fast and not falling for the wording traps.
📌 What a percentage really is
'Per cent' means per hundred. A percentage is just a fraction with 100 on the bottom: 37% is 37/100, or 0.37 as a decimal. Every percentage question is therefore a fraction question in disguise — once you see that, the fear disappears and the arithmetic gets short.
The foundation: fraction, percent and decimal
These three are the same number wearing different clothes. Move between them without thinking and half of CLAT Quant becomes mental maths. To turn a fraction into a percentage, multiply by 100; to turn a percentage into a decimal, divide by 100 (shift the point two places left).
- ✓Fraction → percent — multiply by 100. So 3/4 = (3 ÷ 4) × 100 = 75%.
- ✓Percent → decimal — divide by 100. So 45% = 0.45.
- ✓Decimal → percent — multiply by 100. So 0.6 = 60%.
- ✓Percent → fraction — write over 100 and simplify. So 40% = 40/100 = 2/5.
Finding a percentage of a quantity
'x% of N' simply means (x/100) × N. The word 'of' almost always signals multiplication. To find 18% of 250, compute (18/100) × 250 = 45. A faster route on the exam screen: find 1% first (divide by 100), then scale up.
- 1
Find 1% of the numberDivide by 100 — just move the decimal two places left. 1% of 250 is 2.5.
- 2
Multiply up to the percent you needNeed 18%? Then 18 × 2.5 = 45. This 'find 1% first' habit is fast and almost error-proof.
- 3
Use friendly anchors10% is one-tenth, 50% is half, 25% is a quarter. Build odd percentages from these: 35% = 25% + 10%.
💡 'Of' commutes — swap to make it easy
x% of y = y% of x. So 16% of 25 looks awkward, but 25% of 16 is just a quarter of 16 = 4. When one number is friendly (25, 50, 20, 10), flip the statement and the sum solves itself in your head.
Percentage increase and decrease
Most CLAT data questions ask how much a value has gone up or down. The rule never changes: compare the change to the original value, not the new one.
Percentage change = (change ÷ original value) × 100. The denominator is always where you started.
- Increase — a price rises from ₹200 to ₹250. Change = 50; percentage rise = (50 ÷ 200) × 100 = 25%.
- Decrease — a value falls from 80 to 60. Change = 20; percentage drop = (20 ÷ 80) × 100 = 25%.
- The original is the base — divide by the old figure (200, 80), never the new one. This single slip causes most lost marks.
⚠️ Percentage change ≠ percentage point
These are not the same, and CLAT loves the difference. If unemployment rises from 5% to 7%, that is a rise of 2 percentage points — but a percentage change of 40%, because (2 ÷ 5) × 100 = 40%. Read the question: 'by how many percentage points' wants the plain difference (2); 'by what percentage' wants the relative change (40%). Mixing these up is the most common CLAT Quant error.
Worked example — reading a percentage rise
🧩 Worked example
A bookshop sold 1,200 books in 2022. In 2023 it sold 1,500 books. The owner wants to describe the change in sales in her annual report.
By what percentage did the bookshop's sales increase from 2022 to 2023?
A20%
B25%
C30%
D300%
▸ Show solution
Answer: B. Change in sales = 1,500 − 1,200 = 300. The base is the original year, 2022, so divide by 1,200: (300 ÷ 1,200) × 100 = 25%. Option A wrongly divides 300 by 1,500 (the new value). D mistakes the change (300) for the percentage. The answer is B.
Successive percentage changes
When a value changes twice — a price marked up then discounted, a population rising two years running — you cannot simply add the percentages. Each change acts on the new figure, not the original. There is a clean shortcut for two successive changes.
📌 The net-change shortcut
For two successive changes of a% and b%, the net change is a + b + (ab ÷ 100) per cent. Treat decreases as negative. A 20% rise then a 10% rise gives 20 + 10 + (200 ÷ 100) = +31%, not 30%. A 20% rise then a 20% fall gives 20 − 20 + (−400 ÷ 100) = −4% — a net loss.
⚠️ Why a 20% rise then a 20% fall does NOT return to the start
It feels like it should cancel. It doesn't. Start with ₹100. A 20% rise → ₹120. A 20% fall is now 20% of ₹120 = ₹24, so you land at ₹96 — a 4% loss overall. The fall is taken on the larger amount, so it bites harder than the rise. Whenever you see equal up-then-down percentages, the answer is always slightly below where you began.
🧩 Worked example
A shopkeeper marks up the price of a jacket by 25% over its cost price. During a sale, she then offers a 20% discount on the marked price. The cost price of the jacket is ₹800.
What is the net percentage change between the cost price and the final selling price?
A5% profit
B5% loss
C0% (no change)
D45% profit
▸ Show solution
Answer: C. Use the shortcut with a = +25 and b = −20: net = 25 + (−20) + (25 × −20 ÷ 100) = 25 − 20 − 5 = 0%. Check directly: ₹800 marked up 25% = ₹1,000; a 20% discount on ₹1,000 = ₹800 again. The mark-up and discount exactly cancel, so there is no net change. The answer is C — and note it is not 5%, the trap of just adding 25 − 20.
Reverse-percentage: finding the original
Sometimes you are given the figure after a percentage change and asked for the value before. Do not subtract the same percentage back — that is the classic mistake. Instead, treat the known value as a percentage of the original and divide.
- 1
Express the final as a percentage of the originalAfter a 20% rise, the new value is 120% of the original. After a 20% fall, it is 80% of the original.
- 2
Divide to recover the originalOriginal = final ÷ (that percentage as a decimal). If 120% of the original is ₹600, original = 600 ÷ 1.2 = ₹500.
- 3
Sanity-check forwardsTake your answer, apply the change, and confirm you reach the given figure. ₹500 up 20% is ₹600 — correct.
⚠️ Don't just subtract the percentage back
A salary is ₹600 after a 20% rise. The original is not ₹600 minus 20% (= ₹480). The 20% was added to the smaller original, so it equals less than ₹120. Correct method: ₹600 = 120% of original, so original = 600 ÷ 1.2 = ₹500. Always divide by the multiplier, never subtract the same percentage.
🧩 Worked example
After a 12% increase in its annual fee, a coaching institute now charges ₹56,000 per student for the year. A parent wants to know what the fee was before the increase.
What was the annual fee before the 12% increase?
A₹49,280
B₹50,000
C₹44,000
D₹62,720
▸ Show solution
Answer: B. The new fee is 112% of the old fee (100% + 12%). So old fee = 56,000 ÷ 1.12 = ₹50,000. Check: ₹50,000 + 12% = ₹50,000 + ₹6,000 = ₹56,000. ✔ Option A wrongly subtracts 12% of ₹56,000; that is the reverse-percentage trap. The answer is B.
Drill percentages now
10 drills, 150 questions — real CLAT-style data sets on share, growth, mark-up and reverse-percentage, with full step-by-step solutions.
Percentages in data interpretation
This is where CLAT actually tests percentages. You will get a short passage with a table or pie chart and be asked to read percentages off it. Three skills cover almost every question: finding a share of the total, comparing growth rates, and converting between a pie-chart slice and an actual quantity.
- ✓Share of total — a category's value divided by the grand total, times 100. If a state spends ₹30 crore of a ₹120 crore budget on health, health's share is (30 ÷ 120) × 100 = 25%.
- ✓Growth rate — the percentage change between two periods, base = the earlier period. Compare growth rates to spot the fastest-growing item.
- ✓Pie-chart slice → quantity — a slice is a percentage of the whole; multiply that percentage by the total to get the real number. A 30% slice of 4,000 students = 1,200 students.
- ✓Degrees ↔ percent in a pie — the full circle is 360°, so each 1% = 3.6°. A 90° slice is 25% of the whole.
ℹ️ Read the base before you compute
In DI, the trap is the base. 'What percentage of the total?' uses the grand total; 'what percentage of 2022?' uses one column; 'by what percentage did it grow?' uses the earlier year. Underline which base the question wants before touching the numbers — the arithmetic is easy, the base is where marks are lost.
🧩 Worked example
A school of 2,000 students was surveyed about their favourite sport. The results, shown as a pie chart, were: Cricket 40%, Football 25%, Badminton 20%, and Others 15%.
How many more students chose Cricket than chose Badminton?
A200
B300
C400
D800
▸ Show solution
Answer: C. Cricket = 40% of 2,000 = 800 students. Badminton = 20% of 2,000 = 400 students. Difference = 800 − 400 = 400. A quicker route: the gap is 40% − 20% = 20 percentage points, and 20% of 2,000 = 400. Either way the answer is C. Option A mistakes the percentage gap (20%) for a count of 200.
🧩 Worked example
A company's revenue (in ₹ crore) for three products was: Year 2022 — A: 50, B: 80, C: 70. Year 2023 — A: 65, B: 92, C: 84. Management wants to know which product grew the fastest.
Which product had the highest percentage growth in revenue from 2022 to 2023?
AProduct A
BProduct B
CProduct C
DA and C grew equally
▸ Show solution
Answer: A. Compute each growth rate on its own 2022 base. A: (15 ÷ 50) × 100 = 30%. B: (12 ÷ 80) × 100 = 15%. C: (14 ÷ 70) × 100 = 20%. Product A grew fastest at 30%. Note that B started from the largest base (80), so its ₹12 cr rise is only a 15% gain — always compare rates, not raw increases. The answer is A.
Fraction–percent equivalents to memorise
CLAT Quant is timed tight. Knowing these by heart turns 'find 37.5% of 800' from a long division into a one-line answer. Learn them until they are reflex — they appear constantly in pie-chart and share questions.
| Fraction | Percentage | Fraction | Percentage |
|---|---|---|---|
| 1/2 | 50% | 1/8 | 12.5% |
| 1/3 | 33⅓% | 3/8 | 37.5% |
| 2/3 | 66⅔% | 5/8 | 62.5% |
| 1/4 | 25% | 1/6 | 16⅔% |
| 3/4 | 75% | 1/9 | 11⅑% |
| 1/5 | 20% | 1/10 | 10% |
| 2/5 | 40% | 1/12 | 8⅓% |
| 1/7 | ≈14.28% | 1/20 | 5% |
💡 Spot the friendly fraction
When a question says 37.5% of 800, recognise 37.5% as 3/8 and compute 3 × (800 ÷ 8) = 3 × 100 = 300 — instantly. The same trick handles 12.5% (1/8), 62.5% (5/8) and 16⅔% (1/6). Converting an ugly percentage into a clean fraction is the single biggest time-saver in CLAT Quant.
Approximation tricks for the exam screen
CLAT options are usually spaced far enough apart that you rarely need an exact answer — a close estimate picks the right option in seconds. Build estimates from the friendly anchors and adjust.
- ✓Break percentages into 10s and 5s — 35% = 30% + 5% = (10% × 3) + half of 10%. Find 10% (move the decimal), then assemble.
- ✓Round, then correct — 19% of 410 ≈ 20% of 400 = 80; nudge down slightly. Good enough to pick between options of 60, 80 and 120.
- ✓Use 1% as a unit — find 1% of the total once, then scale to any percentage the question throws at you.
- ✓Small successive changes ≈ add them — for changes under ~10%, the (ab ÷ 100) term is tiny, so 4% then 3% ≈ 7%. Use the full formula only when precision matters.
ℹ️ Estimate first, compute only if needed
Glance at how far apart the four options are. If they are 25%, 40%, 55% and 70%, a rough estimate already isolates the answer — no exact arithmetic required. Reserve full calculation for the rare case where two options sit close together.
🎯 Percentages in a nutshell
- A percentage is a fraction over 100 — convert freely between fraction, percent and decimal.
- Percentage change = (change ÷ original) × 100; the base is always where you started.
- Percentage points (a plain difference, 5% to 7% = 2 points) are not the same as percentage change (a relative 40%).
- Successive changes don't add — use a + b + (ab ÷ 100); an equal rise-then-fall always ends below the start.
- For reverse-percentage, divide by the multiplier (÷1.12 for a 12% rise), never subtract the percentage back.
- In DI, fix the base first, memorise the fraction–percent table, and estimate before you calculate.
Common mistakes to stop making
- ✓Dividing by the new value instead of the original when finding percentage change.
- ✓Confusing a percentage-point change with a percentage change in growth questions.
- ✓Adding successive percentages instead of compounding them with the net-change formula.
- ✓Solving reverse-percentage by subtracting the same percentage rather than dividing by the multiplier.
- ✓Misreading the base in a DI table — using the total when the question asks 'as a percentage of last year'.
- ✓Doing long division when a friendly fraction (3/8 = 37.5%) would give the answer instantly.
📊
Quantitative Techniques hub
All CLAT Quant chapters, the DI strategy and every drill in one place.
Section guide
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Next: Ratio & Proportion
Split totals, compare quantities and solve sharing problems — the natural partner to percentages in CLAT DI.
Guide + 10 drills
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Ratio & Proportion teaches you to split totals and compare quantities cleanly — a reliable source of CLAT Quant marks that pairs perfectly with percentages.
Frequently asked questions
What is the difference between a percentage change and a percentage point?
A percentage point is a plain difference between two percentages — if a rate rises from 5% to 7%, that is 2 percentage points. A percentage change is relative to the starting value: (2 ÷ 5) × 100 = 40%. CLAT tests this distinction often, so read whether the question asks 'by how many percentage points' or 'by what percentage'.
Why doesn't a 20% rise followed by a 20% fall return to the original value?
Because the fall is taken on the larger, post-rise amount. Start at ₹100; a 20% rise gives ₹120; a 20% fall is 20% of ₹120 = ₹24, landing you at ₹96 — a 4% net loss. Equal up-then-down percentages always end slightly below where you began. The net-change formula a + b + (ab ÷ 100) gives −4% directly.
How do I find the original value after a percentage increase?
Divide, don't subtract. If a figure is 120% of the original after a 20% rise, divide the new figure by 1.2. For a 12% rise giving ₹56,000, the original is 56,000 ÷ 1.12 = ₹50,000. Subtracting the same percentage from the new value is the classic reverse-percentage trap and gives the wrong answer.
Which fraction–percent equivalents should I memorise for CLAT?
Learn 1/2 = 50%, 1/3 = 33⅓%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16⅔%, 1/8 = 12.5%, 3/8 = 37.5%, 5/8 = 62.5% and 1/10 = 10%, plus their multiples. Recognising 37.5% as 3/8 turns a long calculation into one line, which is decisive in a tightly timed Quant section.
How are percentages tested in CLAT data interpretation?
Through three recurring tasks: finding a category's share of a total, comparing growth rates between years, and converting a pie-chart slice into an actual quantity. The maths is class-10 level; marks are won by reading the correct base and working quickly. Most CLAT Quant sets lean on percentages somewhere.
Do I need an exact answer, or can I estimate?
Usually you can estimate. CLAT options are normally spaced widely, so rounding to friendly numbers — 19% of 410 ≈ 20% of 400 = 80 — isolates the right option fast. Reserve exact calculation for the rare case where two options sit close together. Estimating first saves time across the whole section.
Is the maths in CLAT Quantitative Techniques difficult?
No — it is class-10 level and data-interpretation based. You read a passage, table or chart and answer set questions, mostly involving percentages, ratios and averages. There are no advanced formulas. The challenge is speed and accuracy under the clock, which is exactly what regular drilling builds.