Kantilal mixes 80 kg of sugar at Rs. 6.75/kg with 120 kg at Rs. 8/kg. At what selling price per kg should he sell to earn a 20% profit on the mixture?

Introduction / Context:
First compute the cost price (CP) per kg of the mixture using weighted average. Then apply the desired profit percentage to find the required selling price (SP) per kg that yields a 20% gain overall.

Given Data / Assumptions:

• Quantity 1 = 80 kg at Rs. 6.75/kg.
• Quantity 2 = 120 kg at Rs. 8.00/kg.
• Desired profit = 20% on mixture CP.

Concept / Approach:
Mixture CP per kg = (total cost) / (total kg). Then SP per kg = CP per kg * (1 + profit%). Profit% = 20% ⇒ multiplier 1.20.

Step-by-Step Solution:
Cost1 = 80 * 6.75 = Rs. 540. Cost2 = 120 * 8 = Rs. 960. Total cost = 540 + 960 = Rs. 1500; total quantity = 80 + 120 = 200 kg. Mixture CP/kg = 1500 / 200 = Rs. 7.50. Required SP/kg = 7.50 * 1.20 = Rs. 9.00.

Verification / Alternative check:
Selling 200 kg at Rs. 9 earns revenue Rs. 1800. Profit = 1800 − 1500 = Rs. 300, which is 20% of 1500, confirming correctness.

Why Other Options Are Wrong:
Rs. 7.50 is the CP, not SP. Rs. 8.20 and Rs. 8.85 yield profits lower than 20%.

Common Pitfalls:
Forgetting to compute weighted average CP or applying 20% to the wrong base (quantity instead of cost). Always apply percentage to CP amount.

Final Answer:
Rs. 9