In what proportion must a grocer mix teas at Rs. 1.22/kg and Rs.1.94/kg so as to make a mixture worth Rs.1.66/kg.

Answer

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

### Step 1: Identify the Prices
Let:
- Price of tea A (Rs. 1.22/kg)
- Price of tea B (Rs. 1.94/kg)
- Price of the mixture (Rs. 1.66/kg)

### Step 2: Set Up the Alligation
Using the alligation method, we can find the proportions in which the two teas should be mixed. We set up the alligation as follows:

```
Price of tea A: Rs. 1.22
Price of the mixture: Rs. 1.66
Price of tea B: Rs. 1.94
```

### Step 3: Calculate the Differences
Now, we calculate the differences between the price of each tea and the price of the mixture:

- Difference for tea A:
\[ 1.66 - 1.22 = 0.44 \]

- Difference for tea B:
\[ 1.94 - 1.66 = 0.28 \]

### Step 4: Set Up the Ratio
The ratio of the quantities of tea A and tea B can be set up as the inverse of the differences calculated:

\[ \text{Ratio of tea A to tea B} = \frac{0.28}{0.44} \]

### Step 5: Simplify the Ratio
To simplify this ratio, we can divide both numbers by their greatest common divisor (GCD).

- The GCD of 28 and 44 is 4.

Now, divide both parts of the ratio:

\[ \frac{0.28 \div 0.04}{0.44 \div 0.04} = \frac{7}{11} \]

### Step 6: Final Ratio
Thus, the required ratio of tea A to tea B is:

\[ \text{Tea A : Tea B} = 7 : 11 \]

### Conclusion
The grocer must mix the two teas in the ratio of 7:11 to achieve a mixture worth Rs. 1.66/kg.

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