20 litres of a mixture contains milk and water in the ratio of 5 : 3. If four litres of this mixture is replaced by four litres of milk, then the ratio of the milk to that of the water in the new mixture will be

### Concept & Mixture Replacement When a portion of a mixture is removed, the remaining mixture retains the exact same ratio of ingredients. Replacements alter the total composition by adding pure quantities of one component. ### Step-by-Step Solution 1. Total initial volume = 20 litres. 4 litres of the mixture is removed, leaving $20 - 4 = 16$ litres of the original mixture. 2. In this remaining 16 litres, the ratio of milk to water is still $5 : 3$. 3. Calculate the quantity of milk in the remaining mixture: $$ \text{Milk} = 16 \times \frac{5}{5 + 3} = 16 \times \frac{5}{8} = 10 \text{ litres} $$ 4. Calculate the quantity of water in the remaining mixture: $$ \text{Water} = 16 \times \frac{3}{5 + 3} = 16 \times \frac{3}{8} = 6 \text{ litres} $$ 5. Now, 4 litres of pure milk is added to this remaining mixture. 6. New quantity of milk = $10 + 4 = 14$ litres. 7. The quantity of water remains unchanged at 6 litres. 8. The new ratio of milk to water is $14 : 6$, which simplifies to $7 : 3$. ### Exam Strategy & Shortcut Instead of calculating the initial quantities of the 20L mixture and then subtracting the fractions removed, immediately deduct the removed volume from the total (20L - 4L = 16L). Apportion this 16L into $5:3$ (giving 10L and 6L). Then just add the 4L of pure milk to the milk portion. This saves calculation steps. ### Common Pitfall Calculating the initial components of the 20L mixture first ($12.5$L milk, $7.5$L water) and then forgetting that removing 4L of the mixture removes *both* milk and water proportionally, not just one or the other. ### Final Answer Therefore, the correct answer is **7 : 3**.