How to Solve Successive Percentage Change Problems
Solve successive percentage change aptitude problems with the a+b+ab/100 shortcut, a worked example, and practice questions with answers.
Expected Interview Answer
Successive percentage changes never add or subtract directly; two changes of a% and b% combine to a net change of a + b + (ab/100) percent, where a negative sign is used for a decrease.
Each percentage change multiplies the current value by a factor of (1 + change/100), so applying a% then b% multiplies the original by (1 + a/100)(1 + b/100), which expands to 1 + a/100 + b/100 + ab/10000 — the extra ab/100 term is the interaction that a naive sum misses. This combined-factor rule generalizes to any number of successive changes by chaining more multipliers. It also explains the classic trap: a 20% increase followed by a 20% decrease is NOT a net zero change, it is a net 4% decrease, because 20 + (-20) + (20)(-20)/100 = -4. Always convert each change to a multiplying factor first, then multiply the factors together.
- One formula handles any chain of increases and decreases
- Prevents the classic +20%/-20% "cancels out" trap
- Generalizes cleanly to three or more successive changes
AI Mentor Explanation
A team’s run rate rises 25% in the powerplay, then falls 20% in the middle overs. You cannot just add 25 and -20 to get 5; you must multiply the factors — 1.25 times 0.80 equals 1.00, a net change of exactly 0%, not the 5% a naive sum would suggest. The combined-percentage formula a + b + ab/100 confirms it: 25 + (-20) + (25)(-20)/100 = 25 - 20 - 5 = 0. Every successive run-rate swing across overs compounds this way, never by plain addition.
Worked example
Increase factor
- 1 + 20/100 = 1.20
Decrease factor
- 1 - 20/100 = 0.80
Net change
- 1.20 x 0.80 = 0.96
- Net = -4%
Step-by-Step Explanation
Step 1
Convert each change to a factor
An increase of a% becomes (1 + a/100); a decrease of b% becomes (1 - b/100).
Step 2
Multiply the factors
Chain every successive change as a product, never as a sum of percentages.
Step 3
Apply the shortcut formula
Net % change = a + b + ab/100, using negative values for decreases.
Step 4
Extend to three or more changes
Combine two changes first into a net factor, then chain the next change onto that result.
What Interviewer Expects
- Recognition that percentages multiply, not add, across successive changes
- Correct use of the a + b + ab/100 shortcut with proper signs
- Ability to spot that equal +a%/-a% swings never net to zero
- Extending the two-change method correctly to three or more changes
Common Mistakes
- Simply adding or subtracting the percentages instead of multiplying factors
- Forgetting the sign convention when a change is a decrease
- Applying both changes to the original base instead of chaining them sequentially
- Assuming a percentage increase followed by the same percentage decrease returns to the original value
Best Answer (HR Friendly)
“I always convert each percentage change into a multiplying factor and chain them together rather than adding the percentages. A 20% increase followed by a 20% decrease is not zero net change — it is a 4% decrease, because the shortcut formula a plus b plus ab over 100 captures the interaction between the two changes that a simple sum misses.”
Follow-up Questions
- How would you find the single equivalent percentage change for three successive changes?
- How does successive percentage change relate to compound interest calculations?
- If a value decreases by x% and must be restored by an increase, how do you find that required increase?
- How would you apply this to a discount followed by a tax addition on a bill?
MCQ Practice
1. A price rises by 10% and then falls by 10%. What is the net percentage change?
Net = 10 + (-10) + (10)(-10)/100 = 10 - 10 - 1 = -1%, a 1% decrease.
2. A salary is increased by 25% and then by 20% of the new salary. What is the overall percentage increase?
Net = 25 + 20 + (25)(20)/100 = 25 + 20 + 5 = 50%.
3. A value increases by 30% and then decreases by 30%. Compared to the original, the final value is?
Net = 30 + (-30) + (30)(-30)/100 = 30 - 30 - 9 = -9%, so the final value is 9% lower.
Flash Cards
Successive percentage change formula? — Net % = a + b + ab/100, with negative values for decreases.
Does +20% then -20% cancel out? — No — it nets to -4%, because of the interaction term ab/100.
How to combine three successive changes? — Combine the first two into a net factor, then chain the third change onto that result.
Why do factors multiply instead of add? — Each change scales the CURRENT value, not the original, so the changes compound multiplicatively.