While preparing a mixture of tea, $5\%$ of the tea is lost. In what ratio should a trader mix two kinds of tea costing $\text{Rs. }600/\text{kg}$ and $\text{Rs. }450/\text{kg}$ respectively so that he might gain $25\%$ by selling the mixed tea at $\text{Rs. }625/\text{kg}$?

Let the trader mix $a\text{kg}$ of the first tea and $b\text{kg}$ of the second tea.
$$\text{Total Cost Price (CP)}=600a+450b$$

The total initial weight is $(a+b)\text{kg}$. Since $5\%$ of the tea is lost during preparation, the remaining usable weight is:

$$\text{Remaining Weight}=0.95(a+b)\text{kg}$$

The remaining mixture is sold at $\text{Rs. }625/\text{kg}$.

$$\text{Total Selling Price (SP)}=625\times 0.95(a+b)=593.75(a+b)$$

To achieve a profit of $25\%$, we use the relation $\text{SP}=1.25\times \text{CP}$:

$$593.75(a+b)=1.25(600a+450b)$$

$$593.75a+593.75b=750a+562.5b$$

Rearranging terms to group $a$ and $b$:

$$593.75b-562.5b=750a-593.75a$$

$$31.25b=156.25a$$

$$\frac{a}{b}=\frac{31.25}{156.25}=\frac{1}{5}$$

Thus, the required ratio is $1:5$.