How much water should be added to 60 litres of milk at 1 1/2 litres for Rs.10, so as to have a mixture worth Rs.5 1/3 per litre ?

Options

A. 16 litres
B. 15 litres
C. 18 litres
D. 20 litres

Answer

To solve the problem of how much water should be added to 60 liters of milk to achieve a desired mixture value, we can follow these steps:

### Step 1: Determine the Cost Price of Milk
The cost price of 1.5 liters of milk is given as Rs. 10.

To find the cost price of 60 liters of milk, we can use the following formula:

\[ \text{CP of 60 liters} = \left(\frac{60 \text{ liters}}{1.5 \text{ liters}}\right) \times 10 \text{ Rs.} \]

Calculating this gives:

\[ \text{CP of 60 liters} = \left(\frac{60}{1.5}\right) \times 10 = 40 \times 10 = 400 \text{ Rs.} \]

### Step 2: Assume the Cost Price of Water
We assume the cost price of water is Rs. 0 (since water is typically considered free in such problems).

### Step 3: Set Up the Equation for the Mixture
Let \( x \) be the amount of water (in liters) to be added. The total cost price of the mixture will then be:

\[ \text{Total CP} = 400 + 0 = 400 \text{ Rs.} \]

The total volume of the mixture will be:

\[ \text{Total Volume} = 60 + x \text{ liters.} \]

The desired cost price of the mixture is given as Rs. 5 1/3 per liter, which can be converted to an improper fraction:

\[ 5 \frac{1}{3} = \frac{16}{3} \text{ Rs.} \]

### Step 4: Set Up the Equation for the Average Cost Price
The average cost price of the mixture can be expressed as:

\[ \frac{\text{Total CP}}{\text{Total Volume}} = \frac{400}{60 + x} \]

Setting this equal to the desired cost price:

\[ \frac{400}{60 + x} = \frac{16}{3} \]

### Step 5: Cross-Multiply to Solve for \( x \)
Cross-multiplying gives:

\[ 400 \times 3 = 16 \times (60 + x) \]

This simplifies to:

\[ 1200 = 960 + 16x \]

### Step 6: Solve for \( x \)
Rearranging the equation to isolate \( x \):

\[ 1200 - 960 = 16x \]
\[ 240 = 16x \]
\[ x = \frac{240}{16} = 15 \]

### Conclusion
Thus, the amount of water that should be added is **15 liters**.

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