In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:

Quantity of milk
$$ = \left( {60 \times \frac{2}{3}} \right)\,{\text{litres}} = 40\,{\text{litres}}$$
Quantity of water in it = (60 - 40) litres = 20 litres
New ratio = 1 : 2
Let quantity of water to be added further be x litres
$$\eqalign{ & {\text{Then,}}\,{\text{milk : water}} = {\frac{{40}}{{20 + x}}} \cr & {\text{Now}},\, {\frac{{40}}{{20 + x}}} = \frac{1}{2} \cr & \Rightarrow 20 + x = 80 \cr & \Rightarrow x = 60 \cr & \therefore {\text{Quantity}}\,{\text{of}}\,{\text{water}}\,{\text{to}}\,{\text{be}}\,{\text{added = 60}}\,{\text{litres}}{\text{.}} \cr} $$