UPSC Prelims 2026 CSAT, question 25

Topic: Arithmetic

Q25

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) 3Correct answer
(c) 5
(d) 6

Solution.

Answer: (b) 3

Rectifying the first student's score from $0$ to $100$ adds $100$ marks and raises the class average by $4$ , so the number of students in the class is $\frac{100}{4} = 25$ .
Rectifying the second student's score from $81$ to $56$ reduces the total marks by $81 - 56 = 25$ , which lowers the average by $\frac{25}{25} = 1$ .
Hence the final corrected average is $y = x + 4 - 1 = x + 3$ , giving $y - x = 3$ .