Question

Two vessels contain mixtures of milk and water in the ratio $4:9$ in the first vessel and in the ratio of $2:7$ in the secopnd vessel$.$ in what ratio should the contents be mixed such that the resultant mixture has milk and water in the ratio of $2:5$

• A. 26:9
• B. 15:7
• C. 5:2
• D. 7:5

Answer 1

Answer: (A)

26:9

Let $1st$ vessel contains $x$ liters of mixture of milk and water$.$
Milk in $1st$ vessel $=\frac{4}{13}x$
Water in $1st$ vessel$=\frac{9}{13}x$

Let $2nd$ vessel contains $Y$ liters of mixture of milk and water
Milk in $2nd$ vessel $=\frac{2}{9}y$
Water in $2nd$ vessel $=\frac{7}{9}y$

Let the two mixture combine such that the milk to water ratio is $2:5$
$\frac{\frac{4x}{13}+\frac{2y}{9}}{\frac{9x}{13}+\frac{7y}{9}}=\frac{2}{5}$
$\frac{36x+26y}{81x+91y}=\frac{2}{5}$
$180x+130y=162x+182y$
$18x=52y$
$\frac{x}{y}=\frac{26}{9}$

Hence mixture from vessel $1$ and vessel $2$ should be mixed in the ratio $26/9$ for milk and water to be in ratio $2:5$

Hence, option $\left(A\right)$ is correct answer.