Successive Percentage Change and Applications
Successive Percentage Change and Applications
Successive percentage change ties this whole chapter together and shows up across SBI Clerk in population, price, salary and discount questions. When a quantity changes by a%, then by b%, the two do not simply add — the second change acts on the already-changed value. One net-effect formula replaces two separate steps and, once memorised, answers a wide family of questions in a single calculation instead of a slow two-stage one.
The Net Effect Formula
For two successive changes of a% and b%, the net percentage change is a + b + ab/100, where each rise is positive and each fall is negative. A 20% rise followed by a 10% fall gives 20 − 10 − 200/100 = +8%, not 10%. The ab/100 term is the interaction the naive 'just add them' approach ignores, and it is exactly the adjustment that catches unprepared candidates on price-then-discount and rise-then-fall questions.
Net change for a% then b% = a + b + ab/100 (rise +, fall −)
Equal Rise and Fall Always Loses
A special case worth memorising: increase a value by x% and then decrease it by the same x%, and you always end below where you started, by exactly x²/100 percent. A price raised 10% then cut 10% is down 1%, because 10 − 10 − 100/100 = −1. This is a favourite SBI Clerk one-liner precisely because the intuitive answer of 'no change' is wrong, so the formula, not instinct, must decide. The same x²/100 loss appears in the two-article profit-loss case and in successive equal discounts, so recognising the pattern once lets you answer three different question types with a single memorised result.
| Situation | a% and b% | Net effect a + b + ab/100 |
|---|---|---|
| Rise then rise | +10, +20 | +32% |
| Rise then fall | +20, −10 | +8% |
| Fall then fall | −10, −10 | −19% |
| Equal rise & fall | +10, −10 | −1% |
Solved Examples
Example 1: A town's population rises 10% then falls 20%: net = 10 − 20 − 200/100 = −12%. Example 2: A salary up 25% then down 20% → 25 − 20 − 500/100 = 0%, exactly unchanged. Example 3: A price marked up 20% then given a 20% discount ends at −4%, a genuine loss of 4% off the original despite equal percentages.
✗ Adding +20% and −10% to get a net 10% change | ✓ Using 20 − 10 − 200/100 = 8% net change
Population, Price and Chained Applications
The same formula scales to real SBI Clerk scenarios: a population growing at a steady rate over two years, a product discounted twice, or a value swinging up one year and down the next. For more than two changes, apply the two-step formula in pairs — combine the first two into one net figure, then fold in the third — so a chain of any length stays manageable. When a question gives the final value and asks for the original, reverse the multipliers rather than the percentages: a value now 8% higher is the original × 1.08, so divide by 1.08 to go back. Treating every successive-change question as a chain of multipliers, and only converting to the a + b + ab/100 form for a quick two-step answer, keeps you fast and accurate on the trickiest arithmetic the section offers.
क्रमिक प्रतिशत परिवर्तन: पहले a%, फिर b% → कुल परिवर्तन = a + b + ab/100 (वृद्धि +, कमी −)। समान x% वृद्धि व कमी पर हमेशा x²/100 % की हानि होती है।
Exam Pointer — Successive change appears in SBI Clerk as population, price, salary and double-discount questions, usually one or two marks. The trap is adding the percentages directly and missing the ab/100 term. Memorise a + b + ab/100 and the equal-rise-and-fall loss of x²/100 — both are one-line answers that reward the formula over instinct.
60-Second Recap
- Net change for a% then b% = a + b + ab/100.
- Rises are +, falls are −; never just add the percentages.
- Equal x% rise then fall always loses x²/100 percent.
- Chain three or more changes in pairs; reverse multipliers to go back.
Ready to turn these formulas into speed? Practise percentage, profit-loss and interest questions in the SBI Clerk Prelims mock test on ExamAtlas and clock every sum under 34 seconds.