QUANT SHORTCUT | 18 OCTOBER 2026
Sugar goes from ₹40 to ₹48 a kilo, and the household budget for sugar stays at ₹200. How much less sugar reaches the kitchen? Most students answer “20%”, because the price rose 20%. That is the classic trap. The correct answer is 16⅔%, and one formula gets you there in five seconds. This is the core of many CLAT Quantitative Techniques questions on percentage change.
The Price-Consumption Rule
When expenditure is fixed, price × consumption is constant. So if the price rises by r%, consumption must fall by r/(100+r) × 100%. For a 20% rise: 20/120 × 100 = 16⅔%. Check with numbers: ₹200 buys 5 kg at ₹40, but only 200/48 = 4⅙ kg at ₹48. The fall is 5 − 4⅙ = ⅚ kg, and (⅚)/5 = ⅙ = 16⅔%.
The reverse also holds. If the price falls by r%, consumption can rise by r/(100−r) × 100%. A 20% cut gives 20/80 × 100 = 25% more. Notice the asymmetry: the base changes, so a 20% rise and a 20% fall do not cancel out.
10 Percentage Shortcuts for CLAT
- Price up, spending fixed. Consumption falls by r/(100+r) × 100%. Example: price up 20% → 20/120 × 100 = 16⅔% less.
- Price down, spending fixed. Consumption can rise by r/(100−r) × 100%. Example: price down 20% → 20/80 × 100 = 25% more.
- Successive change. Net change = a + b + ab/100. Example: +10% then +20% → 10 + 20 + 2 = 32%.
- Fraction-percentage pairs. 1/6 = 16⅔%, 1/7 ≈ 14.28%, 1/8 = 12.5%, 1/9 = 11.11%, 5/9 = 55.55%. Example: 1/8 of 240 = 12.5% of 240 = 30.
- The “more/less” flip. If A is x% more than B, then B is x/(100+x) × 100% less than A. Example: A is 25% more → B is 25/125 × 100 = 20% less.
- Income, expenditure and savings. Work with income = 100. Income 100, spending 80, so savings 20. Income +25% and spending +10% → 125 and 88, savings 37, a rise of 17/20 = 85%.
- Compound growth. Growth of r% for n years multiplies by (1 + r/100)n. Example: 50,000 at 10% for 2 years = 50,000 × 1.21 = 60,500.
- Area from sides. Use the successive-change rule on both sides. Square side +10% → 10 + 10 + 1 = 21% more area. Length +20%, breadth −10% → 20 − 10 − 2 = 8% more.
- The fixed-difference trick. If A is x% more than B and A − B = d, then B = d × 100/x. Example: 25% more, difference ₹5,000 → B = 5,000 × 4 = ₹20,000.
- x% of y = y% of x. Flip to the easier one. Example: 8% of 50 = 50% of 8 = 4.
Common Traps
Three mistakes cost marks again and again. First, using r% for both the rise and the matching fall: the rise is r%, but the matching fall is r/(100+r). Second, adding percentages when changes are successive, forgetting the ab/100 term. Third, taking the wrong base: “A is 25% more than B” uses B as the base, while “B is less than A” uses A. Before you calculate, write down what the 100 refers to.
Framework: how percentage questions are built
CLAT Quantitative Techniques questions are set on short data or a single scenario. They test whether you pick the correct base, apply the right multiplier and avoid the symmetric-percentage trap. Every shortcut above is a faster form of one idea: the new value equals the old value times (1 ± r/100).
CLAT angle
- Quant sets pair a price change with fixed spending, then ask for the change in consumption.
- Options usually include the “obvious” wrong answer (20% instead of 16⅔%).
- Successive changes appear in data-interpretation style passages with two or three years of figures.
- Fraction-percentage pairs let you skip long division in 30-second questions.
- Area and compound-growth items reward the a + b + ab/100 rule.
Key facts
| Fact | Detail |
|---|---|
| Price rule (up) | r/(100+r) × 100 |
| Price rule (down) | r/(100−r) × 100 |
| 20% rise, spending fixed | 16⅔% less consumption (≈ 16.67%) |
| 20% fall, spending fixed | 25% more consumption |
| Two successive changes | a + b + ab/100 |
| 1/6 as a percentage | 16⅔% |
| 5/9 as a percentage | 55.55% |
| x% of y | Equals y% of x |
Mnemonic
“Rise: add to the bottom. Fall: subtract from the bottom.” For a price rise the denominator is 100 + r; for a price fall it is 100 − r. The change itself, r, always sits on top.
Sources
Standard quantitative aptitude methods for percentage change, price-consumption relations, successive percentage change and compound growth, as taught in CLAT Quantitative Techniques preparation. All worked examples were checked by direct calculation.
Free in the CLAT Gurukul app
These notes (as a PDF lesson) and the 10-question CBT are in the app under Current Affairs → 18 Oct 2026. Get the app on Google Play or open app.clatgurukul.com.
Practice Quiz — 10 CLAT-Style Questions
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