In what ratio should Darjeeling Tea costing Rs. 400 per kg be mixed with Assam Tea costing Rs. 300 per kg, so that by selling the mixture at Rs. 408 per kg, there is a gain of 20%?
A. 1:2
B. 2:3
C. 2:5
D. 1:6

Options

A. A
B. C
C. B
D. D

Answer

To solve the problem of mixing Darjeeling Tea and Assam Tea to achieve a specific selling price with a gain, we can follow these steps:

### Step 1: Determine the Cost Price of the Mixture
We know that selling the mixture at Rs. 408 per kg gives a gain of 20%. To find the cost price (CP) of the mixture, we can use the formula:

\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Gain} \]

Given that the gain is 20% of the CP, we can express this as:

\[ SP = CP + 0.2 \times CP = 1.2 \times CP \]

Setting SP to Rs. 408, we have:

\[ 408 = 1.2 \times CP \]

### Step 2: Calculate the Cost Price
Now, we can solve for CP:

\[ CP = \frac{408}{1.2} = 340 \]

### Step 3: Set Up the Allegation Method
Now we have the cost price of the mixture (Rs. 340). We will use the allegation method to find the ratio in which the two types of tea should be mixed.

- Cost of Darjeeling Tea = Rs. 400 per kg
- Cost of Assam Tea = Rs. 300 per kg
- Cost of Mixture = Rs. 340 per kg

### Step 4: Apply the Allegation Formula
Using the allegation method, we set it up as follows:

\[ \text{Cost of Darjeeling Tea} - \text{Cost of Mixture} = 400 - 340 = 60 \]
\[ \text{Cost of Mixture} - \text{Cost of Assam Tea} = 340 - 300 = 40 \]

### Step 5: Find the Ratio
The ratio of Darjeeling Tea to Assam Tea is given by the inverse of the differences calculated:

\[ \text{Ratio} = \frac{40}{60} = \frac{2}{3} \]

### Conclusion
Thus, the ratio in which Darjeeling Tea and Assam Tea should be mixed is **2:3**.