CAT 2025 Slot 1 QA Question 3: In a class, there were more than 10 boys and a certain number of girls. After 40% of the girls and 60% of the boys left the class, the remaining number of girls was 8 more than the remaining number of

Question

In a class, there were more than 10 boys and a certain number of girls. After 40% of the girls and 60% of the boys left the class, the remaining number of girls was 8 more than the remaining number of

Accepted Answer

Let the initial number of boys be B and the initial number of girls be G.
Since 60% of the boys and 40% of the girls left, both B and G must be multiples of 5.
$0.6G = 0.4B + 8$
$\dfrac{3G}{5} = \dfrac{2B}{5} + 8$
$3G = 2B + 40$
$B = \dfrac{3G - 40}{2}$

To minimize the total, we try the smallest po

In a class, there were more than 10 boys and a certain number of girls. After 40% of the girls and 60% of the boys left the class, the remaining number of girls was 8 more than the remaining number of boys. Then, the minimum possible number of students initially in the class was