Profit and Loss – Mixture price and target margin: At what price per kg must Kantilal sell a mixture made by combining 80 kg sugar at Rs 6.75 per kg with 120 kg at Rs 8 per kg to earn a 20% profit on the mixture?

Introduction / Context:
This problem combines weighted average cost with a target profit percentage. First compute the mixture cost per kg by averaging with weights 80 kg and 120 kg. Then apply the desired profit margin to obtain the selling price per kg.

Given Data / Assumptions:

• Quantity 1 = 80 kg at Rs 6.75 per kg
• Quantity 2 = 120 kg at Rs 8.00 per kg
• Target profit = 20%

Concept / Approach:
Mixture CP per kg = (80 * 6.75 + 120 * 8) / (80 + 120). Then SP for 20% gain = 1.20 * CP_mixture.

Step-by-Step Solution:
Total cost = 80 * 6.75 + 120 * 8 = 540 + 960 = Rs 1500Total weight = 80 + 120 = 200 kgCP per kg = 1500 / 200 = Rs 7.50Required SP per kg = 1.20 * 7.50 = Rs 9.00

Verification / Alternative check:
Profit per kg = 9.00 − 7.50 = 1.50 which is 20% of 7.50, confirming accuracy.

Why Other Options Are Wrong:
8.85 and 8.76 understate the 20% margin; 8.20 equals neither mixture CP nor a 20% markup; 7.50 is the CP, not the selling price.

Common Pitfalls:
Taking simple average of prices instead of weighted average, or applying 20% to the wrong base.

Final Answer:
Rs 9.00 per kg