CAT 2024

Question

A certain amount of water was poured into a $300$ litre container and the remaining portion of the container was filled with milk. Then an amount of this solution was taken out from the container which was twice the volume of water that was earlier poured into it, and water was poured to refill the container again. If the resulting solution contains $72\%$ milk, then the amount of water, in litres, that was initially poured into the container was?

Answer 1

Let x be the volume of water poured initially.

Concentration of milk = $\frac{300-x}{300}$

Volume of solution removed = 2x

Volume of solution remaining = 300 - 2x

Remaining milk = (300 - 2x) x $\frac{300-x}{300}$

Final volume of milk = 0.72 x 300 = 216

Hence,

(300 - 2x) x $\frac{300-x}{300}$ = 216

This gives

$x^{2} - 450x + 12600 = 0$

x = 420 or 30

but since volume removed i.e. 2x can't be >300, therefore water poured initially was 30 litres.