Two vessels A and B contain milk and water in the ratio 3 : 2 and 7 : 13 respectively. They are mixed in the ratio of 2 : 3. What us the ratio of milk  and water ?

9 : 11

The correct answer is option (4) : 9 : 11

Quantity of milk in mix. A $=\frac{3}{5}$ part

Quantity of milk in mix. B $=\frac{7}{20}$ part

Let the quantity of milk in final mixture be $\frac{x}{y}$ part

LCM of 5, 20 and y = 20y.

Quantity of milk in mix. A $=\frac{3}{5}×\frac{4y}{4y}=\frac{12y}{20y}$

Quantity of milk in mix. B $\frac{7}{20}×\frac{x}{y}=\frac{7y}{20y}$

So quantity of milk in final mixture $=\frac{x}{y}×\frac{20}{20}=\frac{20x}{20y}$

Acc to given $\frac{3}{2}=\frac{\frac{12y}{20y}-\frac{20x}{20y}}{\frac{20x}{20y}-\frac{7x}{20y}}$

$=\frac{3}{2}=\frac{12y-20x}{20x-7y}$

$60x-21y=24y-40x$

$100x= 45y$

$\frac{x}{y}=\frac{9}{20}$

So, the ratio of milk and water in final mixture is $\frac{9}{20-9}=\frac{9}{11}$ i.e 9 : 11