A 10% rise followed by a 10% fall does NOT bring you back to where you started — successive percentage changes never simply cancel out.
Study Zone is free for our students — you just need to log in with your WhatsApp number first.
Log in with WhatsApp →The first two chapters of every book are free once you're logged in. To open this one, request an unlock and we'll get back to you on WhatsApp.
A percentage is just a fraction with a denominator of 100 — converting between the two forms is instant once you know the key fractions.
📊 Fractions worth memorising
| Fraction | Percentage |
|---|---|
| 1/2 | 50% |
| 1/4 | 25% |
| 1/8 | 12.5% |
| 1/3 | 33.33% |
| 3/8 | 37.5% |
| 1/5 | 20% |
To convert a fraction to a percentage, multiply by 100. 3/8 × 100 = 37.5%. To convert a percentage to a fraction, divide by 100 and simplify: 12% = 12/100 = 3/25.
When a value changes by one percentage and then another, the SECOND change always applies to the NEW value, not the original.
📌 The successive-change formula
Net % change = a + b + (ab/100), where a and b are the two percentage changes (use negative for a decrease).
A 10% rise then a 10% fall: net = 10 + (−10) + (10×−10)/100 = 0 − 1 = −1%. Not zero!
Always check with real numbers if unsure: 100 → 110 (rise) → 99 (fall of 10% of 110). That is a net 1% loss.
Olympiad trap: "increased by 20%, then decreased by 20%" is NOT a net 0% change. It is a net LOSS of 4% (because the second 20% is a bigger absolute amount than the first).
When a price rises, spending the SAME total money means you must consume LESS — and the percentage decrease is not the same number as the price increase.
The formula: if price increases by r%, consumption must decrease by [r/(100+r)] × 100% to keep expenditure unchanged. If price rises 25%, consumption must fall by 25/125 × 100 = 20%.
12 questions on percentage conversion, successive change and price-consumption problems.
