In an examination, A has scored 20 marks more than B. If B has scored 5% less marks than A, how much has B scored ?
- (a) 360
- (b) 380 ✓ UPSC's answer
- (c) 400
- (d) 420
Why the answer is (b)
• Let the score of A be $A$ and the score of B be $B$.
• The problem states that A scored 20 marks more than B, so $A = B + 20$.
• It also states that B scored 5% less than A, which means $B = A - 0.05A = 0.95A$.
• Substitute $A = B + 20$ into the second equation: $B = 0.95(B + 20)$.
• Expanding gives $B = 0.95B + 19$.
• Rearranging terms yields $0.05B = 19$, so $B = 19 / 0.05 = 380$.
• Therefore, B scored 380 marks, which corresponds to option (b).
Why the other options are wrong
- (a) 360
- 360 is incorrect because if B scored 360, A would score 380, and 360 is not 5% less than 380 (5% of 380 is 19, so B should be 361).
- (c) 400
- 400 is incorrect because if B scored 400, A would score 420, and 400 is not 5% less than 420 (5% of 420 is 21, so B should be 399).
- (d) 420
- 420 is incorrect because if B scored 420, A would score 440, and 420 is not 5% less than 440 (5% of 440 is 22, so B should be 418).
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.