How much water must be added to a bucket which contains 40 L of milk at the cost price of Rs.3.50 per L, so that the cost of milk reduces to Rs.2 per L?

Options

A. 25 L
B. 28 L
C. 30 L
D. 35 L

Answer

To solve the problem of how much water must be added to 40 liters of milk at a cost price of Rs. 3.50 per liter to reduce the cost to Rs. 2 per liter, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the initial conditions**:
- Volume of milk = 40 liters
- Cost price of milk = Rs. 3.50 per liter
- Desired cost price after adding water = Rs. 2 per liter

2. **Calculate the total cost of the milk**:
- Total cost of 40 liters of milk = 40 liters × Rs. 3.50/liter = Rs. 140.

3. **Set up the equation for the new cost price**:
- Let the amount of water to be added be \( x \) liters.
- The total volume of the mixture after adding water = \( 40 + x \) liters.
- The new cost price should be Rs. 2 per liter, so:
\[ \text{New cost price} = \frac{\text{Total cost}}{\text{Total volume}} = \frac{140}{40 + x} \]
- We want this to equal Rs. 2, so we set up the equation:
\[ \frac{140}{40 + x} = 2 \]

4. **Solve the equation**:
- Cross-multiply to eliminate the fraction:
\[ 140 = 2(40 + x) \]
- Expand the right side:
\[ 140 = 80 + 2x \]
- Rearrange to isolate \( x \):
\[ 140 - 80 = 2x \\ 60 = 2x \\ x = \frac{60}{2} = 30 \]

5. **Conclusion**:
- The amount of water that must be added is **30 liters**.