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A person buys an item from a shop for which the shopkeeper offers a di

June 1, 2025 by rawan239

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?

20%

18%

19%

21%

This question was previously asked in

UPSC CAPF – 2022

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Let the marked price be Rs. 100. The shopkeeper offers a 10% discount, so the price after the shop discount is $100 \times (1 – 0.10) = 100 \times 0.90 = Rs. 90$. The person pays Rs. 90 using an e-wallet which gives 10% cashback on the amount paid. The cashback amount is $90 \times 0.10 = Rs. 9$. The total reduction from the marked price is the shop discount (Rs. 10) plus the cashback (Rs. 9), which is $10 + 9 = Rs. 19$. The effective discount is the total reduction as a percentage of the marked price: $(\frac{19}{100}) \times 100\% = 19\%$.

The e-wallet cashback is applied to the price *after* the initial discount, not the original marked price. Effective discount is the total benefit (discount + cashback) expressed as a percentage of the original price.

A common mistake is to simply add the percentages (10% + 10% = 20%), which is incorrect because the second percentage is applied to a reduced amount. This problem involves successive discounts/benefits. If the marked price is M, the price paid is $M(1-d_1)$. The cashback is $C = M(1-d_1) \times c$, where $d_1$ is the shop discount rate and $c$ is the cashback rate. The effective price paid is $M(1-d_1) – C = M(1-d_1) – M(1-d_1)c = M(1-d_1)(1-c)$. The total reduction is $M – M(1-d_1)(1-c)$. For this problem, it is $M – M(0.9)(0.9) = M – 0.81M = 0.19M$. The effective discount rate is $0.19 \times 100\% = 19\%$.

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