Sugar costing $\text{Rs. }40/\text{kg}$ and $\text{Rs. }30/\text{kg}$ are mixed together. In what ratio should both types of sugar be mixed so that there is no gain or loss when the mixture is sold at $\text{Rs. }32/\text{kg}$?

Since there is no profit or loss at a selling price of $\text{Rs. }32/\text{kg}$, the mean cost price ($\text{C.P.}$) of the mixture is also $\text{Rs. }32/\text{kg}$.
Using the rule of Alligation:
Cost of Type 1 sugar = $\text{Rs. }40$
Cost of Type 2 sugar = $\text{Rs. }30$
Mean Cost Price = $\text{Rs. }32$

Applying alligation:

$$\text{Ratio}=(32-30):(40-32)$$

$$=2:8=1:4$$