A vessel contains a mixture of milk and water in the ratio 3:2 respectively. If 20 liters of the mixture is removed and 4 liters of milk is added, the ratio of milk to water becomes 13:8 respectively. Find the initial quantity of the mixture (in liters). 

Correct option is A

Information Given:
A vessel contains a mixture of milk and water in the ratio 3:2 respectively.
20 liters of the mixture is removed.
4 liters of milk is added.
The ratio of milk to water becomes 13:8 respectively.
Basic Explanation:
Let the milk and water be 3a and 2a liters respectively
ATQ,
$$\frac{3a - 20 \times \frac{3}{5} + 4}{2a - 20 \times \frac{2}{5}} = \frac{13}{8}$$​
$$\frac{3a - 8}{2a - 8} = \frac{13}{8}$$​
24a - 64 = 26a - 104
40 = 2a
20 = a
Initial quantity of the mixture = 5a = 100 liters