In what ratio must a shopkeeper mix two varieties of rice costing ₹75 and ₹80 per kg, respectively, so as to get a mixture worth ₹76.5 per kg?

Given:

Cost of first variety of rice = ₹75 per kg

Cost of second variety of rice = ₹80 per kg

Cost of mixture = ₹76.5 per kg

Formula Used:

Alligation Rule: If two ingredients are mixed, then the ratio of the quantities of the two ingredients is given by:

Ratio = (C₂ - C_m) : (C_m - C₁)

where C₁ is the cost of the first ingredient, C₂ is the cost of the second ingredient, and C_m is the cost of the mixture.

Calculation:

Here,

C₁ = ₹75

C₂ = ₹80

C_m = ₹76.5

Using the Alligation Rule:

Ratio = (80 - 76.5) : (76.5 - 75)

⇒ Ratio = 3.5 : 1.5

⇒ Ratio = 7 : 3

The ratio in which the shopkeeper must mix the two varieties of rice is 7 : 3.