In what proportion must a grocer mix sugar at \ 48\text{ per kg}$and$ \$28\text{ per kg}$ so that he makes a mixture worth \ 40\text{ per kg}$?

We can solve this question using the rule of Alligation.
Let the price of the first variety of sugar be C_1 = \ 48\text{ per kg}$andthesecondvarietybe$ C_2 = \$28\text{ per kg}$.
The mean price required is M = \ 40\text{ per kg}$.Bythealligationformula:$$\frac{\text{Quantity of first variety}}{\text{Quantity of second variety}}=\frac{M-C_2}{C_1-M}$ $

$$\frac{\text{Quantity of }\$48\text{ sugar}}{\text{Quantity of }\$28\text{ sugar}}=\frac{40-28}{48-40}=\frac{12}{8}=\frac{3}{2}$$

Thus, the ratio of the dearer sugar to the cheaper sugar is $3:2$. If we express the ratio of cheaper sugar to dearer sugar, it is $2:3$, which corresponds to option C.