A grocer wishes to sell a mixture of two varieties of rice worth ₹56 per kg. In what ratio must he mix the rice to reach this selling price, when cost of one variety of rice is ₹54 per kg and the other is ₹64 per kg?

The correct option is 4 : 1.

We can solve this problem using the rule of alligation, which helps find the ratio in which two ingredients of known prices must be mixed to produce a mixture of a desired mean price.

Let the cost price of the cheaper variety of rice be:
$C_1=₹54$ per kg
Let the cost price of the dearer variety of rice be:
$C_2=₹64$ per kg
Let the target price of the mixture be:
$C_m=₹56$ per kg

According to the rule of alligation:
$\frac{\text{Quantity of cheaper rice}}{\text{Quantity of dearer rice}}=\frac{C_2-C_m}{C_m-C_1}$

Substituting the values into the formula:
$\frac{\text{Quantity of cheaper rice}}{\text{Quantity of dearer rice}}=\frac{64-56}{56-54}$

Simplifying the expression:
$\frac{\text{Quantity of cheaper rice}}{\text{Quantity of dearer rice}}=\frac{8}{2}=\frac{4}{1}$

Therefore, the grocer must mix the two varieties of rice in the ratio of 4 : 1.