How to Calculate Two Successive Percentage Discounts
Learn the a+b-ab/100 formula for two successive percentage discounts, with a worked example and practice questions with answers.
Expected Interview Answer
Two successive discounts of a% and b% are NOT equivalent to a single (a+b)% discount; the true single equivalent discount is a + b - ab/100, because the second discount applies to the already-reduced price, not the original.
After the first discount of a%, the price becomes (1 - a/100) of the original; applying the second discount of b% to that reduced price gives (1 - a/100)(1 - b/100) of the original. Expanding this product and converting back to a percentage-off form yields the single equivalent discount a + b - ab/100, which is always less generous to the buyer than the naive sum a + b because the ab/100 term subtracts back some of the apparent saving. This matters commercially too: retailers advertise successive discounts like '30% off, then extra 10%' precisely because it sounds bigger than the equivalent flat 37% off. Always multiply the retained fractions in sequence rather than adding percentages when discounts stack.
- One formula replaces sequential percentage arithmetic
- Explains why marketed successive discounts look bigger than they are
- Prevents the common error of simply adding discount percentages
- Generalizes to any number of successive discounts by chaining retained fractions
AI Mentor Explanation
A bowler’s economy rate drops 20% after a coaching tweak, then drops a further 10% after a fitness block — but the second drop applies to the already-lower rate, not the original one, so the combined improvement is not 30% but 20+10-2=28%. This is exactly how two successive percentage discounts on a price compound: each cut applies to what remains, not to the starting figure.
Worked example
After 20% off
- 2000 x 0.80 = 1600
After further 10% off
- 1600 x 0.90 = 1440
Equivalent single discount
- 20+10-2 = 28%
- 2000 x 0.72 = 1440
Step-by-Step Explanation
Step 1
Convert each discount to a retained fraction
a% discount leaves (1 - a/100) of the price.
Step 2
Multiply the retained fractions
Final price fraction = (1 - a/100)(1 - b/100).
Step 3
Convert back to equivalent discount
Equivalent discount % = a + b - ab/100.
Step 4
Sanity check
The equivalent discount is always slightly less than the naive sum a + b.
What Interviewer Expects
- Recognizing successive discounts multiply, not add
- Correct derivation of a + b - ab/100
- Applying it to compute a final price directly
- Awareness this is a common marketing/pricing trick
Common Mistakes
- Simply adding the two discount percentages
- Applying the second discount to the original price instead of the reduced price
- Sign errors when converting between discount and retained fraction
- Forgetting the formula only holds for exactly two successive discounts (chain further for more)
Best Answer (HR Friendly)
“Successive discounts don’t add up the way people assume — a 20% discount followed by a 10% discount isn’t 30% off, it’s 28% off, because the second discount is taken on the already-reduced price. I convert each discount to what fraction of the price remains, multiply those fractions together, and convert back to get the single equivalent discount, which is always a bit less than the simple sum.”
Follow-up Questions
- How would you extend the formula to three successive discounts?
- How does a successive discount differ from a successive markup?
- If the equivalent single discount is known, how do you split it into two discounts of a chosen ratio?
- Why do retailers prefer advertising "30% + extra 10%" over a flat 37% off?
MCQ Practice
1. Successive discounts of 10% and 20% are equivalent to a single discount of?
10+20-(10x20)/100 = 30-2 = 28%.
2. A price of 500 after successive discounts of 25% then 10% becomes?
500 x 0.75 x 0.90 = 337.5.
3. Two successive discounts of a% and b% are always equivalent to a single discount that is?
The equivalent discount is a+b-ab/100, which is always less than a+b since ab/100 > 0.
Flash Cards
Formula for equivalent single discount of a% then b%? — a + b - ab/100.
Why is it less than a+b? — The second discount applies to an already-reduced price, so the overlap ab/100 is subtracted back.
How to compute the final price directly? — Multiply the original price by (1 - a/100)(1 - b/100).
Common error to avoid? — Adding the two discount percentages directly instead of multiplying retained fractions.