cat 2021 Question 7

Question

The arithmetic mean of scores of 25 students in an examination is 50. Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being 30, then the maximum possible score of the toppers is

Accepted Answer

Let sum of marks of students be x

Now therefore x = 25*50 =1250

Now to maximize the marks of the toppers

We will minimize the marks of 20 students

so their scores will be (30,31,32.....49 )

let score of toppers be y

so we get 5y + $\frac{20}2$(79) = 1250

we get 5y +790=1250

5y=460

y=92

So scores of toppers = 92

Question 7.

Question Explanation