Rakesh had money to buy 8 mobile handsets of a specific company. But the retailer offered very good discount on that particular handset. Rakesh could buy 10 mobile handsets with the amount he had. What was the discount the retailer offered ?

(a) 15%
(b) 20% ✓ UPSC's answer
(c) 25%
(d) 30%

Why the answer is (b)

• Let the original price of one mobile handset be P and the total amount Rakesh had be M.

• Initially, Rakesh could buy 8 handsets, so M = 8P.

• After the discount, he could buy 10 handsets with the same amount M, so M = 10 * (Discounted Price).

• Equating the two expressions for M: 8P = 10 * (Discounted Price), which means the Discounted Price = 0.8P.

• The discount amount is P - 0.8P = 0.2P.

• The discount percentage is (0.2P / P) * 100 = 20%, which corresponds to option (b).

Why the other options are wrong

(a) 15%: A 15% discount would result in a discounted price of 0.85P, allowing Rakesh to buy approximately 9.41 handsets, not 10.
(c) 25%: A 25% discount would result in a discounted price of 0.75P, allowing Rakesh to buy approximately 10.67 handsets, not 10.
(d) 30%: A 30% discount would result in a discounted price of 0.70P, allowing Rakesh to buy approximately 11.43 handsets, not 10.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.