Quick answer: use a multiplier for each change. An increase of r% multiplies a value by 1 + r/100; a decrease of r% multiplies it by 1 − r/100.
The multiplier method
If an amount A changes by p%, the new amount is A(1 ± p/100). For two changes p and q, use A(1 ± p/100)(1 ± q/100). The second percentage is applied to the changed amount, so adding the percentages can be wrong.
Example: two increases
A phone price of ₹1,000 rises by 10% and then 20%. New price = 1,000 × 1.10 × 1.20 = ₹1,320. The total increase is ₹320, or 32%, not 30%.
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Example: an increase followed by a decrease
A quantity rises by 20% and then falls by 20%. The multiplier is 1.20 × 0.80 = 0.96, so the final value is 96% of the original. It is a net decrease of 4%, because the 20% fall is taken from the larger intermediate value.
Reverse percentage questions
If the sale price after a 20% discount is ₹800, divide by 0.80: original price = 800/0.80 = ₹1,000. Do not add 20% to ₹800; the base of the discount was the original price.
Exam checklist
- Write the original amount as A.
- Convert each percentage to a multiplier.
- Multiply in the order given.
- Compare the final value with A to find the net change.
Practice
A ₹2,500 fee is reduced by 10% and then increased by 10%. Answer: ₹2,475, a net decrease of 1%.
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