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 is equal proportions. What is the value of X?

In the container of 60 litres, milk and water were in the proportion 2:3 which means
Milk = $$\frac{2}{5}\times\ 60=24$$ litres and Water = 36 litres.

If X litres of solution is removed and replaced with pure milk, water remaining in the solution = $$36-\frac{3}{5}X$$.
As proportion of milk and water is equal, water is exactly half of the total quantity i.e. half of (60 - X + X = 60 litres) = 30 litres.
$$36-\frac{3}{5}X=30$$
This gives X = 10 litres.