CAT 2022 Slot 3 QA Question 9: In an examination, the average marks of students in sections A and B are 32 and 60, respectively. The number of students in section A is 10 less than that in section B. If the average marks of all the

Question

In an examination, the average marks of students in sections A and B are 32 and 60, respectively. The number of students in section A is 10 less than that in section B. If the average marks of all the

Accepted Answer

Let the number of students in section A be $a$. Then the number of students in section B is $a + 10$.
Combined average = $\dfrac{32a + 60(a + 10)}{a + (a + 10)}$
$= \dfrac{92a + 600}{2a + 10}$
$= \dfrac{46a + 300}{a + 5}$
$= 46 + \dfrac{70}{a + 5}$
For the combined average to be an integer, $a + 5$