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Question 1667 :
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

Video Explanation

Explanatory Answer

Initial quantity of water in the container $= x$
So, initial quantity of milk in the container $= 300 - x$
Part of mixture taken out $= \frac{2 x}{300}$
Part of mixture that is retained $= 1 - \frac{2 x}{300}$
So, part of milk that is retained $= (300 - x) (1 - \frac{2 x}{300})$
Also, quantity of milk that is retained after the iteration $= 72 %$ of $300 = 216$
Then,

(300 - x) (1 - 2 x 300) = 216 90000 - 300 x - 600 x + 2 x 2 = 216 \times 300 2 x 2 - 900 x + 25200 = 0 x 2 - 450 x + 12600 = 0 (x - 420) (x - 30) = 0 x = 420 (or) x = 30

The total content itself 300 litre. So, $x = 420$ is inadmissible.
Thus, amount of water that was initially poured = 30 litre

The question is "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"

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Video Explanation

Explanatory Answer

The answer is

Choice 30 is the correct answer.