Two varieties of sugar are mixed in the ratio 3 : 2 and sold for ₹80 per kg to make a profit of 25%. If the cost of the variety of sugar whose quantity is more is ₹40 per kg, what is the cost of the other variety of sugar?

Solution

Given:
– The mixture of two varieties of sugar is sold at ₹80 per kg for a profit of 25%.
– The cost of the variety of sugar in larger quantity is ₹40 per kg.
– The ratio of the two varieties of sugar is 3:2.

Step 1: Find the cost price of the mixture

The selling price of the mixture is ₹80 per kg, and the profit is 25%. Therefore, the cost price (CP) of the mixture is:
\[ CP = \frac{\text{Selling Price}}{1 + \text{Profit Percentage}} = \frac{80}{1 + 0.25} = \frac{80}{1.25} = ₹64 \text{ per kg} \]

Step 2: Calculate the cost of the other variety of sugar

Let the cost of the other variety of sugar be ₹\(x\) per kg. Using the weighted average formula for the cost price of the mixture:
\[ CP_{\text{mixture}} = \frac{(3 \times 40) + (2 \times x)}{3 + 2} \]
\[ 64 = \frac{120 + 2x}{5} \]
\[ 320 = 120 + 2x \]
\[ 2x = 200 \]
\[ x = ₹100 \text{ per kg} \]

Conclusion

The cost of the other variety of sugar is ₹100 per kg.