The average marks of a class of 30 students are 52. One student whose marks are 82 left the class and two new students joined the class. The average of the class remains the same and the difference between the marks of new students is 4. What will be the marks of the student who scored greater marks between the two new students?

The average marks of a class of 30 students are 52. One student whose marks are 82 left the class and two new students joined the class. The average of the class remains the same and the difference between the marks of new students is 4. What will be the marks of the student who scored greater marks between the two new students? Correct Answer 69

Given:

The average marks of a class of 30 students is 52.

One student whose marks are 82 left the class and two new students joined the class.

The average of the class remains the same and the difference between the marks of new students is 4. 

Formula:

Average marks of students = Total marks/Total number of students

Calculation:

Average marks of 30 students = 52

⇒ Sum of marks of 30 student = 30 × 52 = 1560

Sum of marks after a student left the class = 1560 – 82 = 1478

Now, 2 students joined the class

⇒ Sum of marks of all students now = 31 × 52 = 1612

Sum of marks of two new students = 1612 - 1478 = 134

Let the marks of one student be x

⇒ Marks of 2^nd student = x + 4

Now, x + x + 4 = 134

⇒ x = 65

∴ Required marks = (x + 4) = 69