A sample of x litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x? 

 60 litre mixture of milk and water containing milk and water in the ratio 2:3

Let x litres is removed 

milk in remaining mixture=$\frac{\left(60-x\right)2}{5}$

Water in remaining mixture=$\frac{\left(60-x\right)3}{5}$

Let x litres of milk added such that milk and water are in equal proportion

$\frac{\left(60-x\right)2}{5}+x=\frac{\left(60-x\right)3}{5}\Rightarrow x=10$