Question

The cost of Type I sugar is ₹ 25 per kg and Type II sugar is ₹ 35 per kg. If both Type I sugar and Type II sugar are mixed in the ratio 3:2, find the price per kg of the mixture.

Hint:

When quantities are mixed in a given ratio with different unit costs, use the weighted average formula: \[ \text{Average cost} = \frac{\text{Total Cost}}{\text{Total Quantity}} \]

Answer 1

Given a mixture of 3 kg of Type I sugar and 2 kg of Type II sugar in a 3:2 ratio.
The total weight of the mixture is $3 + 2 = 5$ kg.
Calculate the cost of 3 kg of Type I sugar. With Type I sugar costing ₹ 25 per kg, the cost for 3 kg is $3 \times 25 = ₹ 75$.
Similarly, the cost for 2 kg of Type II sugar is $2 \times 35 = ₹ 70$.
The total cost of the mixture is ₹ 75 + ₹ 70 = ₹ 145.
To determine the cost per kg of the mixture, divide the total cost by the total weight:
\[\text{Price per kg} = \frac{145}{5} = ₹ 29\]
Therefore, the final answer is ₹ 29 per kg.