16 litres of a mixture contains milk and water in the ratio 5 : 3. If 4 litres of milk is added to this mixture, the ratio of milk to water in the new mixture would be :

Question

Accepted Answer

To solve the problem and justify why Option 2 is correct, let's break down the steps:

1. **Initial Mixture Composition:**
   - The mixture contains milk and water in the ratio 5:3.
   - Total volume of the mixture = 16 litres.

2. **Calculating the Amount of Milk and Water:**
   - The ratio 5:3 means that out of every 8 parts of the mixture, 5 parts are milk and 3 parts are water.
   - Amount of milk = $\frac{5}{8} \times 16 = 10$ litres.
   - Amount of water = $\frac{3}{8} \times 16 = 6$ litres.

3. **Adding Milk to the Mixture:**
   - 4 litres of milk is added to the mixture.
   - New amount of milk = 10 + 4 = 14 litres.
   - Amount of water remains the same = 6 litres.

4. **Calculating the New Ratio:**
   - New ratio of milk to water = 14:6.
   - Simplifying this ratio by dividing both terms by 2 gives 7:3.

5. **Conclusion:**
   - The new ratio of milk to water is 7:3, which corresponds to Option 2.

**Explanation of Why Other Options are Incorrect:**

- **Option 1 (2:1):** 
  - This would imply that for every 2 parts of milk, there is 1 part of water. If the milk is 14 litres, the water would need to be 7 litres, which is incorrect as the water remains 6 litres.

- **Option 3 (4:3):**
  - This ratio suggests that for every 4 parts of milk, there are 3 parts of water. If the milk is 14 litres, the water would need to be 10.5 litres, which is incorrect as the water remains 6 litres.

- **Option 4 (8:3):**
  - This ratio implies that for every 8 parts of milk, there are 3 parts of water. If the milk is 14 litres, the water would need to be 5.25 litres, which is incorrect as the water remains 6 litres.

Thus, the correct answer is Option 2, with the new ratio of milk to water being 7:3.