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 ?

Answer: Option C

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
$$\begin{array}{rl}& \Rightarrow \frac{4x}{3x+6}=\frac{8}{7}\\ & \Rightarrow 28x=24x+48\\ & \Rightarrow 28x-24x=48\\ & \Rightarrow 4x=48\\ & \Rightarrow x=\frac{48}{4}\\ & \Rightarrow x=12\end{array}$$
∴ Required quantity of milk
= 4x
= 4 × 12
= 48 litres