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%
Correct — C, 19%. Take the marked price as 100. The shop's 10% discount brings it to 90, and that 90 is what the person actually hands over through the e-wallet. The wallet then returns 10% of what was paid, which is 9, not 10. Net outgo is 90 − 9 = 81, so the buyer has saved 19 on a marked price of 100 — an effective discount of 19%. The same result comes from multiplying the two factors: 0.90 × 0.90 = 0.81.
- (a)20% — Adds the two tens as though both were reckoned on the marked price. The cash back is calculated on the 90 actually paid, so it is worth 9 and not 10.
- (b)18% — Understates the benefit. It would require the second 10% to be taken on 80, but nothing in the transaction ever brings the base down to 80.
- (d)21% — Adds the cross term instead of subtracting it, giving 10 + 10 + 1. Two reductions stacked on each other always come to less than their sum, never more.
Percentage changes applied one after another multiply rather than add, because the second change is reckoned on the base the first one left behind. Two reductions of x% and y% combine into a single reduction of x + y − xy/100. Here that is 10 + 10 − (10 × 10)/100 = 19.
The phrase that decides this question is 'pays using an e-wallet which gives 10% cash back'. Cash back is a share of what was paid, so its base is the discounted 90. A candidate who reads both tens as coming off the marked price arrives at 20% and moves on satisfied, which is exactly why the paper offers 20% as option (a). Working in hundreds removes the difficulty entirely: no principal is given, so any convenient marked price will do, and 100 makes every step a mental one. Note also that the order does not matter — cash back first and discount second would still leave 81, because multiplication commutes.
- Successive percentage reductions multiply: the net factor here is 0.90 × 0.90 = 0.81.
- The single equivalent reduction for x% then y% is x + y − xy/100.
- Cash back is computed on the amount actually paid, not on the marked price — the base is 90, so the refund is 9.
- Because the factors multiply, swapping the order of the two reductions leaves the answer unchanged.
- A 10% cut followed by a 10% rise does not restore the original price: 100 becomes 90 and then 99.
Two 10% cuts stacked one on the other come to 19%, not 20% — the second is smaller because its base is smaller.
- Adding percentages that are taken on different bases.
- Assuming cash back is calculated on the marked price rather than on the amount paid.
- Getting the sign of the cross term wrong and reporting 21% instead of 19%.
Asked as a two-stage percentage item where the second stage is deliberately described in everyday language — cash back — so that its base has to be worked out rather than read off.
A shopkeeper gives two consecutive discounts of 10% and 5% respectively on his items. He then adds 20% GST on his items. If an item has marked price ₹2,000, how much more or less of the actual price of the item a customer has to pay?
- (a) 2.6% less
- (b) 2.6% more
- (c) Same price
- (d) 5.2% more
Answer(b) 2.6% more
The same multiply-the-factors method with one more stage. Two discounts and then a tax on the discounted figure gives 2000 × 0.90 × 0.95 × 1.20 = 2052, which has to be compared with the marked price rather than with the discounted price.
- practice — not a real PYQ
A shop offers successive discounts of 20% and 10%. The single discount equivalent to these is
- (a)30%
- (b)28%
- (c)26%
- (d)32%
Answer(b) 28% — 100 × 0.80 × 0.90 = 72, so the saving is 28.
- practice — not a real PYQ
The price of an article is first increased by 10% and then decreased by 10%. The net change in price is
- (a)no change
- (b)1% increase
- (c)1% decrease
- (d)2% decrease
Answer(c) 1% decrease — 100 × 1.10 × 0.90 = 99.