Target profit via cost-price averaging: How many kilograms of ₹ 10/kg rice must be mixed with 25 kg of ₹ 8/kg rice so that, when sold at ₹ 15/kg, the overall profit is 80%?

Introduction / Context:
We need to choose the mix so that the blended cost price is low enough to secure an 80% profit at the given selling price. This is a weighted-average cost problem solved by equating blend CP to SP / 1.8.

Given Data / Assumptions:

• Component A: ₹ 10/kg, unknown mass x kg.
• Component B: ₹ 8/kg, mass 25 kg.
• Selling price of mixture = ₹ 15/kg; target profit = 80%.

Concept / Approach:
If profit is 80%, mixture CP must be SP / 1.8 = 15 / 1.8 = ₹ 25/3 per kg. Set the weighted-average CP equal to 25/3 and solve for x.

Step-by-Step Solution:
Weighted CP = (10x + 8*25) / (x + 25).Set (10x + 200) / (x + 25) = 25/3.Cross-multiply: 30x + 600 = 25x + 625 ⇒ 5x = 25 ⇒ x = 5.

Verification / Alternative check:
Blend mass = 30 kg. Total CP = 10*5 + 8*25 = 50 + 200 = ₹ 250. CP/kg = 250/30 = 25/3. Selling at ₹ 15 gives profit% = (15 − 25/3) / (25/3) = 80%, as required.

Why Other Options Are Wrong:

• 3, 6, and 7 kg do not produce CP = ₹ 25/3 per kg when checked.

Common Pitfalls:

• Using 80% of ₹ 15 as CP (incorrect). The correct CP is SP / 1.8.

Final Answer:
5 kgs