Question

A vessel contain's mixture of 24 $l$ milk and 6 $l$ water and a second vessel contains a mixture of 15 $l$ milk and 10 $l$ water. How much mixture of milk and water should be taken from the first and the second vessel separately and kept in a third vessel so that the third vessel may contain a mixture of 25 $l$ milk and 10 $l$ water?

• A. $18,20$
• B. $16,18$
• C. $20,15$
• D. $25,20$

Answer 1

Answer: (C)

$20,15$

Let $x$ litre of mixture be taken from 1st vessel and $y$ litre of the mixture be taken from 2nd vessel and kept in 3rd vessel so that $(x+y)$ litre of the mixture in the third vessel may contain $225$ litre of milk and $10$ litre of water.
A mixture of $x$ litre from 1st vessel contains $\frac{24}{30}x=\frac{4}{5}x$ of mile and $\frac{x}{5}l$ of water. And a mixture of y$l$ from 2nd vessel contains $\frac{3y}{5}l$ of milk and $\frac{2y}{5}l$ of water.
$\therefore \frac{4}{5}x+\frac{3}{5}y=25$ ........ (1)
$\frac{x}{5}+\frac{2}{5}y=10$ ........ (2)
Solve it to get $x$ and $y$, i.e. $x=20l$, $y=15l$.