In what ratio must a grocer mix tea at Rs 60 a kg and Rs 65 a kg, so that by selling the mixture at Rs 68.20 a kg, he may gain 10%?

Options

A. 3:2
B. 3:4
C. 3:5
D. 4:5

Answer

To solve the problem of mixing two types of tea at different prices to achieve a desired profit margin, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Selling Price (SP) and Gain Percentage**:
- Selling Price (SP) of the mixture = Rs. 68.20 per kg
- Gain Percentage = 10%

2. **Calculate the Cost Price (CP) of the Mixture**:
- The formula to calculate CP when SP and gain percentage are known is:
\[ CP = \frac{SP \times 100}{100 + \text{Gain Percentage}} \]
- Substituting the values:
\[ CP = \frac{68.20 \times 100}{100 + 10} = \frac{6820}{110} = 62 \text{ Rs. per kg} \]

3. **Set Up the Allegation Method**:
- Let the price of the first type of tea (A) = Rs. 60 per kg
- Let the price of the second type of tea (B) = Rs. 65 per kg
- Let the CP of the mixture = Rs. 62 per kg

4. **Apply the Allegation Formula**:
- The allegation method helps us find the ratio in which two items at different prices must be mixed to achieve a desired average price.
- The formula is:
\[ \text{Difference between A and CP} : \text{Difference between CP and B} \]
- Calculate the differences:
- Difference between A and CP = 62 - 60 = 2
- Difference between B and CP = 65 - 62 = 3

5. **Determine the Ratio**:
- The ratio of the two types of tea (A : B) is given by:
\[ \text{Ratio} = 2 : 3 \]

### Final Answer:
The grocer must mix the tea at Rs. 60 per kg and Rs. 65 per kg in the ratio of **2:3**.