A vessel contains 20 litres containing milk and water in the ratio 3 : 2. Ten litres of this milk is removed and replaced with equal amount of pure milk. If this process is repeated once again, find the final ratio of milk and water.

Correct option is C

Given:

Initial volume of the mixture = 20 litres
Ratio of milk to water = 3:2
Volume removed = 10 litres
We are to find the final ratio of milk to water after two replacements.

Concept Used:
This is a dilution and replacement problem. After each removal and replacement cycle, the amount of water in the mixture reduces due to the introduction of pure milk.

Solution:
Initial quantities of milk and water.
Initial milk = $$\frac{3}{5} \times 20 = 12 \text{ litres},$$​​
Initial water =$$\frac{2}{5} \times 20 = 8 \text{ litres}.$$​​
After the first removal and replacement.
When 10 litres is removed, it contains milk and water in the same 3:2 ratio.
Removed milk = $$\frac{3}{5} \times 10 = 6 \text{ litres},$$​​
Removed water = $$\frac{2}{5} \times 10 = 4 \text{ litres}.$$​​
Remaining milk = $$12 - 6 = 6 \text{ litres},$$​​
Remaining water = $$8 - 4 = 4 \text{ litres}.$$​​
After adding 10 litres of pure milk, new quantities are:
Milk =$$6 + 10 = 16 \text{ litres},$$​​
Water = $$4 \text{ litres}.$$​​
After the second removal and replacement.
Removed milk =$$\frac{16}{20} \times 10 = 8 \text{ litres}$$​,
Removed water = $$\frac{4}{20} \times 10 = 2 \text{ litres}.$$​​
Remaining milk =$$16 - 8 = 8 \text{ litres}$$​,
Remaining water = $$4 - 2 = 2 \text{ litres}.$$​​
After adding 10 litres of pure milk again, final quantities are:
Milk = $$8 + 10 = 18 \text{ litres},$$​​
Water = $$2 \text{ litres}.$$​​
Final ratio of milk to water.
Final ratio =$$\frac{18}{2} = 9:1.$$​​

The final ratio of milk to water is 9:1.