In what ratio should two varieties of tea at Rs.300 and Rs.400 per kg, respectively, be mixed so that the mixture is worth Rs.320 per kg?

Options

A. `1:5`
B. `1:4`
C. `5:1`
D. `4:1`

Answer

To solve the problem of mixing two varieties of tea priced at Rs. 300 and Rs. 400 per kg to achieve a mixture worth Rs. 320 per kg, we can use the method of allegation. Here’s a step-by-step solution:

### Step 1: Identify the prices of the two varieties of tea
- Price of the first variety (Tea A) = Rs. 300 per kg
- Price of the second variety (Tea B) = Rs. 400 per kg
- Price of the mixture = Rs. 320 per kg

### Step 2: Set up the allegation formula
According to the allegation method, we calculate the differences between the prices of the mixtures and the individual prices.

### Step 3: Calculate the differences
- Difference between the price of Tea A and the price of the mixture:
\[ 320 - 300 = 20 \]
- Difference between the price of Tea B and the price of the mixture:
\[ 400 - 320 = 80 \]

### Step 4: Set up the ratio
The ratio of the two varieties of tea can be determined by the differences calculated:
- The ratio of Tea A to Tea B is given by the differences:
\[ \text{Ratio of Tea A to Tea B} = \frac{80}{20} = 4:1 \]

### Step 5: Conclusion
Thus, the two varieties of tea should be mixed in the ratio of **4:1**.