CAT 2023 Slot 1 QA Question 9: In an examination, the average marks of 4 girls and 6 boys is 24. Each of the girls has the same marks while each of the boys has the same marks. If the marks of any girl is at most double the marks o

Question

In an examination, the average marks of 4 girls and 6 boys is 24. Each of the girls has the same marks while each of the boys has the same marks. If the marks of any girl is at most double the marks o

Accepted Answer

Let each girl have g marks and each boy have b marks.

$4g + 6b = 10 	imes 24 = 240$
$2g + 3b = 120$

The given condition is $b \leq g \leq 2b$.

From $b \leq g$:
$b \leq \dfrac{120 - 3b}{2}$
$5b \leq 120$
$b \leq 24$

From $g \leq 2b$:
$\dfrac{120 - 3b}{2} \leq 2b$
$120 \leq 7b$
$b \geq \dfrac{120