A student‘s marks were wrongly entered as 65 instead of 45. Due to this, the average marks for the class got increased by 1/3. The number of students in the class is:

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 08 Dec 2022 Shift 3)

Answer 1

Given:

Average with the marks were counted 45 = x

Average when the marks were counted 65 = x+\({1\over3}\)

Concept used:

x = x = \( {\sum y \over n}\)

Here n is the total number of students.

Let the sum of marks of rest of the students \(\sum z \: \)

Calculation:

x = \({\sum z+45\over n}\)

nx = \(\sum z \) +45 {equation 1}

x + \(1\over3\) = \({\sum z+65\over n}\)

nx + \(n\over3\) = +65

Putting the value of nx from equation 1

\(\sum z \) + 45 + \(n\over3\) = \(\sum z \) + 65

\(n\over3\) = 20

n = 60

∴ The number of students is 60.

Alternate Method

A student‘s marks were wrongly entered as 65 instead of 45, so 20 marks extra were distributed among students.

Due to this, the average marks for the class got increased by 1/3, so the number of students in the class = 20 × 3 = 60