How many litres of water should be added to a 30 litre mixture of milk and water containing milk and water in the ratio of 7:3 such that the resultant mixture has `40%` water in it?

Options

A. 5
B. 2
C. 3
D. 8

Answer

To solve the problem, we need to determine how many liters of water should be added to a 30-liter mixture of milk and water, which has a milk to water ratio of 7:3, so that the resultant mixture has 40% water.

### Step-by-Step Solution:

1. **Identify the initial quantities of milk and water:**
- The total volume of the mixture is 30 liters.
- The ratio of milk to water is 7:3.
- To find the quantities of milk and water, we can use the ratio:
- Total parts = 7 (milk) + 3 (water) = 10 parts.
- Quantity of milk = (7/10) * 30 = 21 liters.
- Quantity of water = (3/10) * 30 = 9 liters.

2. **Determine the desired percentage of water in the final mixture:**
- We want the final mixture to have 40% water.
- Let \( x \) be the amount of water to be added.
- After adding \( x \) liters of water, the total volume of the mixture becomes \( 30 + x \) liters.
- The quantity of water in the new mixture will be \( 9 + x \) liters.

3. **Set up the equation based on the desired percentage:**
- We want the water to be 40% of the total mixture:
\[ \frac{9 + x}{30 + x} = 0.4 \]

4. **Cross-multiply to solve for \( x \):**
\[ 9 + x = 0.4(30 + x) \]
\[ 9 + x = 12 + 0.4x \]

5. **Rearrange the equation:**
\[ x - 0.4x = 12 - 9 \]
\[ 0.6x = 3 \]

6. **Solve for \( x \):**
\[ x = \frac{3}{0.6} = 5 \]

Thus, the amount of water that should be added is **5 liters**.