CAPF AC 2022 Q2: General Mental Ability – Quantitative Aptitude
A person buys an item from a shop for which the shopkeeper offers a discount of 10% on the marked price. The person pays using an e-wallet which gives 10% cash back. Which one of the following is the value of effective discount?
- (a) 20%
- (b) 18%
- (c) 19%
- (d) 21%
Answer: (c) 19%
Explanation
Discount plus cashback
Given: a shopkeeper offers a 10% discount on the marked price, and the e-wallet gives 10% cash back on the amount paid; find the effective discount.
How to think: the cashback is 10% of the reduced price, not of the marked price.
So the two tens do not add up to 20.
Take the marked price as ₹100.
| Step | Working | Amount |
|---|---|---|
| Marked price | Assume | ₹100 |
| After 10% discount | 100 − 10 | ₹90 |
| Cashback | 10% of 90 | ₹9 |
| Net cost | 90 − 9 | ₹81 |
Effective discount: 100 − 81 = 19%.
Formula: for successive discounts a and b, effective discount = a + b − ab/100 = 10 + 10 − 1 = 19.
Answer: (c) 19%.
Why each option is right or wrong
- (a) Incorrect. 20% comes from simply adding the two tens.
- (b) Incorrect. 18% has no basis; the net cost is ₹81 on ₹100.
- (c) CORRECT. 0.9 × 0.9 = 0.81, so the effective discount is 19%.
- (d) Incorrect. The effective discount can never be more than the simple sum of 20%.
Key point
Successive discounts a% and b%: effective discount = a + b − ab/100. Two discounts of 10% each = 19%. Two of 20% each = 36%.
Remember
Two 10% discounts = 19%, not 20%.
Common mistakes
- Adding 10% and 10% to get 20% without thinking about the changed base.
- Working out the cashback on the marked price instead of the amount paid.
- Choosing a value above 20%, which successive discounts can never give.
Exam tip
Educated guess: successive discounts are always a little less than their sum. A little less than 20 is 19.
Sources
- NCERT Class VIII Mathematics — Comparing Quantities (discount)
- R. S. Aggarwal, Quantitative Aptitude — Percentage and Discount