By mixing two varieties of tea casting Rs. 65 and Rs. 115 per kg. and selling the mixture at the rate of Rs.100 kg., a seller made a profit of 25%. In what ratio did he mix the two varieties?

Options

A. `101:129`
B. `07:03`
C. `129:101`
D. `129:100`

Answer

To solve the problem of mixing two varieties of tea costing Rs. 65 and Rs. 115 per kg, and selling the mixture at Rs. 100 per kg with a profit of 25%, we can follow these steps:

### Step 1: Calculate the Cost Price of the Mixture
Given that the selling price (SP) is Rs. 100 per kg and the profit is 25%, we can find the cost price (CP) of the mixture using the formula:

\[ \text{SP} = \text{CP} + \text{Profit} \]

Since profit is 25% of CP, we can express this as:

\[ \text{SP} = \text{CP} + 0.25 \times \text{CP} = 1.25 \times \text{CP} \]

Rearranging gives us:

\[ \text{CP} = \frac{\text{SP}}{1.25} = \frac{100}{1.25} = 80 \text{ Rs. per kg} \]

### Step 2: Set Up the Alligation Formula
We have two varieties of tea:
- Variety 1: Rs. 65 per kg
- Variety 2: Rs. 115 per kg
- Mixture: Rs. 80 per kg

Using the alligation method, we can find the ratio in which the two varieties are mixed. The alligation formula is:

\[ \text{Difference between cost of variety 1 and mixture} = 80 - 65 = 15 \]
\[ \text{Difference between cost of variety 2 and mixture} = 115 - 80 = 35 \]

### Step 3: Calculate the Ratio
Now, we can set up the ratio of the two varieties:

\[ \text{Ratio} = \frac{\text{Difference of variety 2}}{\text{Difference of variety 1}} = \frac{35}{15} \]

To simplify this ratio:

\[ \text{Ratio} = \frac{35 \div 5}{15 \div 5} = \frac{7}{3} \]

### Conclusion
The two varieties of tea should be mixed in the ratio of **7:3**.

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