Question

Vessels A and B contain mixture of milk and water in the ratio 4 : 5 and 5 : 1 respectively In what ratio should quantities of mixtures be taken from A to B to form a mixture in which milk to water is in the ratio 5 : 4?

• A. 2 : 5
• B. 2 : 3
• C. 4 : 3
• D. 5 : 2

Answer 1

The correct option is D 5 : 2

Let the required ratio be x : y Milk in x litres of 1st mixture $=(x\times \frac{4}{9})$ litres $=\frac{4x}{9}$ litres
Water in x litres of 1st mixture = $=(x-\frac{4x}{9})litres=\frac{5x}{9}litres$
Milk in y litres of 2nd mixture $=(y\times \frac{5}{6})litres=\frac{5y}{6}litres$
Water in y litres of 2nd mixture $=(y-\frac{5y}{6})litres=\frac{y}{6}litres$
$\therefore Milk:Water=(\frac{4x}{9}+\frac{5y}{6}):(\frac{5x}{9}+\frac{y}{6})$
$=\left(\frac{8x+15y}{18}\right):\left(\frac{10x+3y}{18}\right)=(8x+15y):(10x+3y)$
Given $=\frac{8x+15y}{10x+3y}=\frac{5}{4}\Rightarrow 32x+60y=50x+15y$
$\Rightarrow 18x=45y\Rightarrow \frac{x}{y}=\frac{45}{18}=\frac{5}{2}$
$\therefore$ Required ratio = 5 : 2