A mixture of milk and water weighs 60 litres which contains 10% water. How much water should be added to it so that water may be 25% ?

Question

Accepted Answer

To solve the problem, we need to determine how much water should be added to a mixture of milk and water so that the water content becomes 25%.

### Initial Situation:
- The total weight of the mixture is 60 litres.
- The mixture contains 10% water.

### Calculation of Initial Water Content:
- 10% of 60 litres is water.
- Water content = $ \frac{10}{100} \times 60 = 6 $ litres.

### Calculation of Milk Content:
- Since the total mixture is 60 litres and it contains 6 litres of water, the milk content is $ 60 - 6 = 54 $ litres.

### Desired Situation:
- We want the water to be 25% of the total mixture.

### Let $ x $ be the amount of water to be added:
- New water content = $ 6 + x $ litres.
- New total mixture = $ 60 + x $ litres.

### Setting up the Equation:
- We want the water to be 25% of the new total mixture:
  $$
  \frac{6 + x}{60 + x} = \frac{25}{100}
  $$

### Solving the Equation:
1. Cross-multiply to solve for $ x $:
   $$
   100(6 + x) = 25(60 + x)
   $$
2. Expand both sides:
   $$
   600 + 100x = 1500 + 25x
   $$
3. Rearrange to isolate $ x $:
   $$
   100x - 25x = 1500 - 600
   $$
   $$
   75x = 900
   $$
4. Solve for $ x $:
   $$
   x = \frac{900}{75} = 12
   $$

### Conclusion:
- Therefore, 12 litres of water should be added to the mixture to make the water content 25% of the total mixture. This confirms that Option 3 is correct.

### Explanation of Incorrect Options:
- **Option 1 (10 litres):** Adding 10 litres would result in a water content of 16 litres in a total of 70 litres, which is approximately 22.86%, not 25%.
- **Option 2 (9 litres):** Adding 9 litres would result in a water content of 15 litres in a total of 69 litres, which is approximately 21.74%, not 25%.
- **Option 4 (15 litres):** Adding 15 litres would result in a water content of 21 litres in a total of 75 litres, which is 28%, not 25%.

Thus, Option 3 is the only correct choice that satisfies the condition of making the water content 25% of the total mixture.