How much water must be added to a cask contains 45 litres of milk at cost price of Rs 4 per litre so that cost of milk reduces to Rs 3 per litre?

Options

A. 8 litres
B. 10 litres
C. 12 litres
D. 15 litres

Answer

To solve the problem, we need to determine how much water must be added to a cask containing 45 liters of milk, which is priced at Rs 4 per liter, in order to reduce the cost of the milk to Rs 3 per liter.

### Step-by-Step Solution:

1. **Calculate the total cost of the milk:**
- The cost price of milk is Rs 4 per liter.
- The volume of milk is 45 liters.
- Total cost of milk = Cost per liter × Volume of milk
\[ \text{Total cost} = 4 \, \text{Rs/liter} \times 45 \, \text{liters} = 180 \, \text{Rs} \]

2. **Determine the desired cost price per liter:**
- We want the cost price to reduce to Rs 3 per liter.

3. **Let \( x \) be the amount of water to be added:**
- After adding \( x \) liters of water, the total volume of the mixture will be \( 45 + x \) liters.

4. **Set up the equation for the new cost price:**
- The total cost of the mixture remains Rs 180 (since water is free).
- The new cost price per liter can be expressed as:
\[ \text{New cost price} = \frac{\text{Total cost}}{\text{Total volume}} = \frac{180}{45 + x} \]
- We want this to equal Rs 3:
\[ \frac{180}{45 + x} = 3 \]

5. **Solve for \( x \):**
- Cross-multiply to eliminate the fraction:
\[ 180 = 3(45 + x) \]
- Distribute the 3:
\[ 180 = 135 + 3x \]
- Subtract 135 from both sides:
\[ 45 = 3x \]
- Divide by 3:
\[ x = 15 \]

6. **Conclusion:**
- Therefore, the amount of water that must be added is **15 liters**.