In what ratio two types of liquid costing Rs 52/litre and Rs 65/litre should be mixed to obtain a mixture of Rs 60/litre?

Options

A. `8 : 13`
B. `5 : 8`
C. `13 : 5`
D. `8 : 5`

Answer

To solve the problem of mixing two types of liquids costing Rs 52/litre and Rs 65/litre to obtain a mixture costing Rs 60/litre, we can use the method of alligation.

### Step-by-Step Solution:

1. **Identify the Costs**:
- Cost of Liquid 1 (CP1) = Rs 52/litre
- Cost of Liquid 2 (CP2) = Rs 65/litre
- Cost of Mixture (CP) = Rs 60/litre

2. **Apply the Alligation Formula**:
- The formula for alligation is:
\[ \text{Ratio} = \frac{CP2 - CP}{CP - CP1} \]

3. **Calculate the Differences**:
- Calculate \( CP2 - CP \):
\[ CP2 - CP = 65 - 60 = 5 \]
- Calculate \( CP - CP1 \):
\[ CP - CP1 = 60 - 52 = 8 \]

4. **Set Up the Ratio**:
- The ratio of the two liquids can now be expressed as:
\[ \text{Ratio} = \frac{5}{8} \]

5. **Conclusion**:
- Therefore, the two types of liquids should be mixed in the ratio of 5:8.

### Final Answer:
The required ratio of the two liquids is **5:8**.