The respective ratio of milk and water in the mixture is 4 : 3. If 6 litres of water is added to this mixture, the respectively ratio of milk and water becomes 8 : 7. What is the quantity of milk in the original mixture ?

Let the quantity of milk and water in initial mixture be 4x and 3x litres.
Quantity of water = 3x litres
On adding 6 litres of water, we get
$$\eqalign{ & \Rightarrow \frac{{4x}}{{3x + 6}} = \frac{8}{7} \cr & \Rightarrow 28x = 24x + 48 \cr & \Rightarrow 28x - 24x = 48 \cr & \Rightarrow 4x = 48 \cr & \Rightarrow x = \frac{{48}}{4} \cr & \Rightarrow x = 12 \cr} $$
∴ Required quantity of milk
= 4x
= 4 × 12
= 48 litres