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
Answer & explanation
Answer: (b) 3
Adding 100 marks raised the average by 4, so the class has 25 students. The second correction removes 25 marks, lowering the average by 1, so the net rise is 4 − 1 = 3.
- First correction adds 100 − 0 = 100 marks and raises the average by 4, so number of students = 100 ÷ 4 = 25.
- Second correction: 81 recorded instead of 56 means the total falls by 25.
- Average falls by 25 ÷ 25 = 1.
- y − x = 4 − 1 = 3.
Remember · Change in average = change in total ÷ number of items; find the count from the first change.
Question and answer: UPSC's provisional GS Paper II (2026, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·