In what ratio should Assam tea at $\text{Rs. }40$ per kg and Darjeeling tea at $\text{Rs. }65$ per kg be mixed and sold at $\text{Rs. }60$ per kg to make an overall profit of $25\%$?

Given:
$$\text{Selling Price of mixture (SP)}=\text{Rs. }60\text{/kg}$$

$$\text{Profit}=25\%$$

First, find the mean Cost Price ($\text{CP}$) of the mixture:

$$\text{Mean CP}=\frac{\text{SP}}{1+\frac{\text{Profit}}{100}}=\frac{60}{1.25}=\text{Rs. }48\text{/kg}$$

Now, apply the rule of alligation:

* Cost of Cheaper Tea (Assam) = $\text{Rs. }40$
* Cost of Dearer Tea (Darjeeling) = $\text{Rs. }65$
* Mean Price = $\text{Rs. }48$

$$\text{Ratio of Cheaper to Dearer}=\frac{\text{Dearer Price}-\text{Mean Price}}{\text{Mean Price}-\text{Cheaper Price}}$$

$$\text{Ratio}=\frac{65-48}{48-40}=\frac{17}{8}$$

Therefore, the required mixing ratio is $17:8$.