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

Let us assume we are mixing 3 kg of Type I sugar and 2 kg of Type II sugar, as per the given ratio of 3:2.
The total quantity of the mixture becomes $3 + 2 = 5$ kg.
Now, compute the total cost of 3 kg of Type I sugar.
Cost of Type I sugar per kg is ₹ 25, so cost for 3 kg = $3 \times 25 = ₹ 75$.
Similarly, cost of 2 kg of Type II sugar = $2 \times 35 = ₹ 70$.
So, total cost of the mixture = ₹ 75 + ₹ 70 = ₹ 145.
Now, to find the cost per kg of the mixture, divide total cost by total weight:
\[ \text{Price per kg} = \frac{145}{5} = ₹ 29 \]
Hence, the final answer is ₹ 29 per kg.