The class average x in a test increases by 4 when the score of a student is rectified, whose corrected score is 100 instead of 0. Later, the score of another student was found to have been recorded as 81 in place of 56. If there are no other corrections and the final corrected average is y, then y - x is
- (a) 2
- (b) 3 ✓ UPSC's answer
- (c) 5
- (d) 6
Why the answer is (b)
• Changing one score from 0 to 100 raises the total by 100 and the average by 4, so there are 100 ÷ 4 = 25 students.
• The second score was recorded as 81 but should be 56, so the total falls by 25 and the average by 25 ÷ 25 = 1.
• Final average y = x + 4 − 1 = x + 3, so y − x = 3: (b).
Why the other options are wrong
- (a) 2
- 2 subtracts too much; the second correction lowers the average by only 1.
- (c) 5
- 5 adds the second correction instead of subtracting it.
- (d) 6
- 6 ignores the direction of the second correction.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.