In what proportion must tea at Rs. 14-per-kg-be mixed-with-tea at Rs. 18 per kg, so that the mixture be worth Rs. 17 a kg?

Answer

To solve the problem of mixing two types of tea at different prices to achieve a specific price for the mixture, we can use the method of allegation. Here’s the step-by-step solution:

### Step 1: Identify the prices of the teas
- Price of the first type of tea (Tea A) = Rs. 14 per kg
- Price of the second type of tea (Tea B) = Rs. 18 per kg
- Desired price of the mixture = Rs. 17 per kg

### Step 2: Set up the allegation
Using the allegation method, we will calculate the differences between the prices of the teas and the desired price of the mixture.

### Step 3: Calculate the differences
- Difference between the price of Tea B and the desired price:
\[ 18 - 17 = 1 \]
- Difference between the desired price and the price of Tea A:
\[ 17 - 14 = 3 \]

### Step 4: Set up the ratio
The ratio of the quantities of Tea A and Tea B can be represented as:
- Tea A : Tea B = Difference from Tea B : Difference from Tea A
- Therefore, the ratio is:
\[ \text{Tea A : Tea B} = 1 : 3 \]

### Step 5: Conclusion
Thus, the two types of tea must be mixed in the ratio of 1:3 to achieve a mixture worth Rs. 17 per kg.

### Final Answer:
The required proportion of tea at Rs. 14 per kg to tea at Rs. 18 per kg is **1:3**.

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