Question

Two vessels A and B contain milk and water mixed in the ratio $8:5$ and $5:2$. The ratio in which these two mixtures be mixed to get a new mixture containing $69\frac{3}{13}$% milk, is:

• A. $2:7$
• B. $3:5$
• C. $5:2$
• D. $5:7$

Answer 1

The correct option is A $2:7$

$A\to 8:5$

$\frac{8}{13}$ milk and $\frac{5}{13}$ water

$B\to 5:2$

$\frac{5}{7}$ milk and $\frac{2}{7}$ water

$69\frac{3}{13}\%=\frac{13\times 69+3}{13}=\frac{900}{13}\times \frac{1}{100}=\frac{9}{13}$

$\frac{9}{13}$ milk and $\frac{4}{13}$ water

Let $x:y$ be the ratio in which they are mixed

$\frac{8}{13}x+\frac{5}{7}y=\frac{9}{13}$

$\frac{5}{13}x+\frac{2}{7}y=\frac{4}{13}$

Solving for $x$ and $y$ we get $x=\frac{2}{9}$ and $y=\frac{7}{9}$

$x:y=2:7$