Meera bought two varieties of tea, first at Rs. 80 /kg and second at Rs. 120 /kg. She mixed both varieties and sold the mixture at Rs. 121 /kg making a profit of 10%. In what ratio did mix the two varieties of tea?

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Cost Price of the Mixture
We know that the selling price of the mixture is Rs. 121 per kg and Meera makes a profit of 10%.

Using the formula for selling price:
\[ \text{Selling Price} = \left(1 + \frac{\text{Profit Percentage}}{100}\right) \times \text{Cost Price} \]

Substituting the known values:
\[ 121 = \left(1 + \frac{10}{100}\right) \times \text{Cost Price} \]
\[ 121 = 1.1 \times \text{Cost Price} \]

To find the Cost Price:
\[ \text{Cost Price} = \frac{121}{1.1} = 110 \text{ Rs. per kg} \]

### Step 2: Set Up the Allegation Method
Now we have the cost prices:
- Cost Price of first variety (CP1) = Rs. 80 per kg
- Cost Price of second variety (CP2) = Rs. 120 per kg
- Cost Price of mixture (CPm) = Rs. 110 per kg

Using the allegation method, we set up the following:
- The difference between CP2 and CPm:
\[ CP2 - CPm = 120 - 110 = 10 \]
- The difference between CPm and CP1:
\[ CPm - CP1 = 110 - 80 = 30 \]

### Step 3: Calculate the Ratio
Now we can find the ratio of the two varieties using the differences calculated:
\[ \text{Ratio} = \frac{CP2 - CPm}{CPm - CP1} = \frac{10}{30} = \frac{1}{3} \]

### Conclusion
Thus, the ratio in which Meera mixed the two varieties of tea is **1:3**.

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