Percentage Change Shortcuts: Master Base Switching and Successive Change Tricks for SSC and Bank Exams
Quick Answer: The successive percentage change formula is Net change = a + b + ab/100, where increases are taken as positive and decreases as negative. Apply it directly to two back-to-back changes without calculating intermediate values. The base-switching trap means percentage change always depends on the original value — so an x% increase followed by an x% decrease never returns to the start; it yields a net decrease of x²/100.
- Why Percentage Change Confuses Aspirants: The Base Problem
- The Successive Percentage Change Formula: a + b + ab/100
- Solved Example: Two Successive Changes in 15 Seconds
- Applying the Formula Three or More Times
- Base Switching Trap: Increase by x% Then Decrease by x%
- Reverse Base Trap: Converting Between Two Quantities
- Common Exam Patterns: Population, Price, and Salary Questions
- Percentage Change vs Percentage Point: A Frequent Confusion
- Speed Drill: 10 Practice Questions with 15-Second Solutions
- Memory Tricks and Final Revision Notes
- Frequently Asked Questions
- Q: What is the successive percentage change formula?
- Q: If a price increases 20% then decreases 20%, what is the net change?
- Q: If A is 25% more than B, what percent is B less than A?
- Q: Can the successive change formula be used for three changes?
- Q: Is percentage change the same as percentage point change?
- Related reading
Why Percentage Change Confuses Aspirants: The Base Problem
Nearly every percentage error in SSC and Bank exams traces back to one issue: the base. Percentage change is always calculated on the original value, and when two changes happen one after the other, the base for the second change is not the same as the base for the first.
Example: if a price of ₹100 increases by 10%, the new price is ₹110. If it then decreases by 10%, the decrease is calculated on ₹110, not ₹100 — so the price falls by ₹11 to ₹99, not back to ₹100. Aspirants who treat both changes as operating on the same base lose marks. The successive change formula exists precisely to handle this shifting base in one step.
The Successive Percentage Change Formula: a + b + ab/100
Suppose a quantity undergoes two successive changes of a% and b%. Taking the original value as 100:
- After the first change: 100 × (100 + a)/100
- After the second change: 100 × (100 + a)/100 × (100 + b)/100
- Final value: (100 + a + b + ab/100)
So the net percentage change is:
Net change = a + b + ab/100
Sign rules:
- For an increase, use the value as positive (e.g., +20).
- For a decrease, use the value as negative (e.g., −20).
- The product term ab/100 follows standard sign rules — positive × negative gives negative.
Check with 10% and 10%: net = 10 + 10 + 100/100 = 21% increase. Verify directly: 100 → 110 → 121. Correct — compounding beats simple addition.
Solved Example: Two Successive Changes in 15 Seconds
Classic SSC question: The price of an article is first increased by 20% and then decreased by 10%. What is the net percentage change?
Shortcut solution:
a = +20, b = −10
Net = 20 + (−10) + (20 × −10)/100 = 10 − 2 = +8%
Net increase of 8%. No intermediate values, no assumed numbers — roughly 15 seconds once the formula is automatic. A quick verification: 100 → 120 → 108, an 8% increase. Consistent.
Applying the Formula Three or More Times
The formula handles two changes at a time, so for three changes, apply it pairwise:
- Combine the first two changes using a + b + ab/100 to get a single net change.
- Combine that net change with the third change using the same formula.
- Repeat for any further changes.
Example: A population increases by 10%, then 20%, then decreases by 10%.
Step 1: 10 + 20 + 200/100 = 32% increase.
Step 2: a = +32, b = −10: net = 32 − 10 − 320/100 = 32 − 10 − 3.2 = 18.8% increase.
Verification: 100 → 110 → 132 → 118.8. Correct.
Base Switching Trap: Increase by x% Then Decrease by x%
A favourite SSC trap: a value is increased by x% and then decreased by x%. Aspirants mark “no change.” That is always wrong.
Applying the formula with a = +x and b = −x:
Net = x − x + (x × −x)/100 = −x²/100
The result is always a net decrease of x²/100 percent, regardless of the order of the two changes.
Worked example: A salary of ₹25,000 is increased by 20% and then decreased by 20%.
Net change = −(20 × 20)/100 = −4% decrease.
New salary = 25,000 × 0.96 = ₹24,000.
Direct check: 25,000 → 30,000 → 24,000. Confirmed. Memorise the x²/100 rule — it appears constantly in multiple-choice options where “no change” is deliberately placed as the trap answer.
Reverse Base Trap: Converting Between Two Quantities
If A is x% more than B, then B is not x% less than A, because the base switches from B to A.
The shortcut:
- If A is x% more than B, then B is [x/(100 + x)] × 100 % less than A — equivalently, use the multiplier 100/(100 + x).
- If A is x% less than B, then B is [x/(100 − x)] × 100 % more than A.
Example: A is 25% more than B. Then B is 25 × 100/125 = 20% less than A, not 25% less.
Reverse example: A is 20% less than B. Then B is 20 × 100/80 = 25% more than A. This mirror pair (25 more ↔ 20 less) is tested extremely often — learn it as an instant recall fact.
Common Exam Patterns: Population, Price, and Salary Questions
Three recurring SSC CGL and Bank PO word-problem types map directly onto the successive change formula:
- Population growth/decline: “A town’s population increases by 10% in year 1, decreases by 5% in year 2, and increases by 10% in year 3. If the present population is 99,000, find the population three years ago.” Apply the formula pairwise for the net multiplier, then divide backwards.
- Price and consumption: “The price of sugar rises by 25% but expenditure must stay the same — consumption falls by 25 × 100/125 = 20%.” This is the reverse-base shortcut in disguise.
- Salary and salary-cuts: Any “increased then decreased” salary question is the x²/100 rule; any “A’s salary is x% more than B’s” question is base switching.
Percentage Change vs Percentage Point: A Frequent Confusion
In banking awareness and data interpretation sets, these are distinct:
- Percentage change: relative change — if RBI’s repo rate moves from 5.50% to 6.00%, that is a change of 0.50/5.50 ≈ 9.09%.
- Percentage point: the simple arithmetic difference — 6.00 − 5.50 = 0.50 percentage points.
Exam questions and economic surveys (see RBI notifications and MoSPI releases) report rate and inflation movements in percentage points. When a DI set asks “by how many percentage points did the ratio change,” never apply percentage-change math. For official exam syllabi and patterns, always cross-check the SSC and IBPS websites.
Speed Drill: 10 Practice Questions with 15-Second Solutions
- Price up 20%, then up 20%: net? +44% (20 + 20 + 400/100)
- Price up 10%, then down 10%: net? −1% (−100/100)
- Population up 25%, down 20%: net? 0% (25 − 20 − 500/100)
- Value down 20%, down 20%: net? −36% (−20 − 20 + 400/100)
- Up 30%, down 10%: net? +17% (30 − 10 − 300/100)
- Salary ₹40,000: up 10%, down 10%. New salary? ₹39,600 (−1%)
- A is 40% more than B; B is what % less than A? 40/140 × 100 ≈ 28.57%
- B is 25% less than A; A is what % more than B? 25/75 × 100 = 33.33%
- Population rises 10%, 10%, 10% over 3 years: net? +33.1% (10+10+1 = 21; then 21+10+2.1 = 33.1)
- Repo rate moves from 5.50% to 6.25%: change in percentage points? 0.75 percentage points (not 13.64%)
Memory Tricks and Final Revision Notes
| Concept | Formula / Rule |
|---|---|
| Two successive changes a% and b% | Net = a + b + ab/100 |
| Signs | Increase positive, decrease negative |
| Up x% then down x% | Net decrease of x²/100 (always a loss) |
| A is x% more than B | B is x × 100/(100+x) % less than A |
| A is x% less than B | B is x × 100/(100−x) % more than A |
| Three or more changes | Apply formula pairwise, left to right |
| Percentage point vs percentage change | Percentage point = simple difference of two percentages |
Final tips: never mark “no change” for an up-x-then-down-x question; always identify the base before converting between two quantities; and in DI sets, read carefully whether the question asks for percentage change or percentage points. Practise the speed drill until each answer arrives in under 15 seconds.
Frequently Asked Questions
Q: What is the successive percentage change formula?
Net change = a + b + ab/100, where increases are taken as positive and decreases as negative. The product term ab/100 captures the compounding effect of the shifting base.
Q: If a price increases 20% then decreases 20%, what is the net change?
A net decrease of 4%, using the x²/100 rule: (20 × 20)/100 = 4. “No change” is the trap answer — the second change operates on the increased base, so the result is always a small net loss.
Q: If A is 25% more than B, what percent is B less than A?
Use the base-switch shortcut: 25 × 100/125 = 20%. B is 20% less than A, because the base has switched from B (original comparison) to A (new comparison).
Q: Can the successive change formula be used for three changes?
Yes. Apply it pairwise: combine the first two changes into one net change using a + b + ab/100, then combine that result with the third change using the same formula. Continue for any number of changes.
Q: Is percentage change the same as percentage point change?
No. Percentage point is the arithmetic difference between two percentages (e.g., 5.50% → 6.00% is 0.50 percentage points), while percentage change is relative (≈9.09%). This distinction is common in banking DI sets and current-affairs questions.
Related reading
- Syllogism Shortcut: Venn Diagram Rules and 'Some Not' Cases for Banking Prelims
- Percentage to Fraction Table (1/8 to 1/25): 10-Second Calculation Trick for SSC & Bank Exams
Quick revision
- After the first change: 100 × (100 + a)/100
- After the second change: 100 × (100 + a)/100 × (100 + b)/100
- Final value: (100 + a + b + ab/100)
- For an increase, use the value as positive (e.g., +20).
- For a decrease, use the value as negative (e.g., −20).
- The product term ab/100 follows standard sign rules — positive × negative gives negative.
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