To determine the mixing ratio of two tea varieties priced at ₹60/kg and ₹65/kg to achieve a selling price of ₹68.20/kg with a 10% profit, the following steps are required:
1. Calculate the Cost Price (CP) of the mixture:
A 10% profit on the CP results in a SP of ₹68.20. The relationship is SP = 1.1 * CP.
\[ \text{CP} = \frac{\text{SP}}{1.1} = \frac{68.20}{1.1} = ₹62 \text{ per kg} \]
2. Employ the Rule of Alligation:
Using the CP of the cheaper variety (₹60), the dearer variety (₹65), and the mean CP of the mixture (₹62), we calculate the differences:
\[ \begin{align*} \text{CP of cheaper variety} & : ₹60 \\ \text{Mean CP of mixture} & : ₹62 \\ \text{CP of dearer variety} & : ₹65 \end{align*} \]
\[ \text{Difference (Dearer - Mean)} = 65 - 62 = 3 \]
\[ \text{Difference (Mean - Cheaper)} = 62 - 60 = 2 \]
3. Determine the Ratio:
The ratio of mixing the cheaper to the dearer variety is the inverse of these differences.
The required ratio is 3:2.
Thus, the grocer must mix the two tea varieties in a 3:2 ratio to sell the mixture at ₹68.20 per kg while making a 10% profit.