CAT 2021 Slot 2 QA Question 2: A box has 450 balls, each either white or black, there being as many metallic white balls as metallic black balls. If 40% of the white balls and 50% of the black balls are metallic, then the number of

Question

A box has 450 balls, each either white or black, there being as many metallic white balls as metallic black balls. If 40% of the white balls and 50% of the black balls are metallic, then the number of

Accepted Answer

Let the number of white balls and black balls be W and B respectively.

$W+B=450$
$0.4W=0.5B$
$4W=5B$
$W:B=5:4$

Hence, $W = 250$ and $B = 200$.

$0.4 	imes 250 = 100$
$0.5 	imes 200 = 100$

$	ext{Total metallic balls} = 200$. Therefore, $	ext{non-metallic balls} = 450 - 200 = 250$.

Answer: 250

A box has 450 balls, each either white or black, there being as many metallic white balls as metallic black balls. If 40% of the white balls and 50% of the black balls are metallic, then the number of non-metallic balls in the box is