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)

• Let the number of students be n and the original total be nx.

• Correcting 0 to 100 raises the total by 100, and the average rises by 4, so 100/n = 4 and n = 25.

• The second correction changes a recorded 81 to the true 56, reducing the total by 25.

• This reduces the average by 25/25 = 1 from the already corrected average x + 4.

• Hence y = x + 4 - 1 = x + 3, so y - x = 3, option (b).

Why the other options are wrong

(a) 2: Option (a) gives 2, but the second correction lowers the average by only 1, making y - x = 3.
(c) 5: Option (c) gives 5, which would ignore the 25-point reduction from correcting 81 to 56.
(d) 6: Option (d) gives 6, which would treat the second correction as an increase instead of the 25-point reduction.

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.