P scored 40 marks more than Q in an examination. If Q scored 10% less marks than P, then how much did Q score ?

(a) 360 ✓ UPSC's answer
(b) 380
(c) 400
(d) 420

Why the answer is (a)

• Let P's score be P and Q's score be Q.

• The problem states P scored 40 marks more than Q, so P = Q + 40.

• It also states Q scored 10% less than P, which means Q = P - 0.10P = 0.90P.

• Substitute P = Q + 40 into the second equation: Q = 0.90(Q + 40).

• Expanding gives Q = 0.90Q + 36.

• Rearranging yields 0.10Q = 36, so Q = 360.

Why the other options are wrong

(b) 380: 380 is incorrect because if Q scored 380, P would be 420, and 380 is not 10% less than 420 (10% of 420 is 42, so Q should be 378).
(c) 400: 400 is incorrect because if Q scored 400, P would be 440, and 400 is not 10% less than 440 (10% of 440 is 44, so Q should be 396).
(d) 420: 420 is incorrect because if Q scored 420, P would be 460, and 420 is not 10% less than 460 (10% of 460 is 46, so Q should be 414).

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.