Manideep purchases two lots of barley: 30 kg at ₹11.50 per kg and 20 kg at ₹14.25 per kg. He mixes both lots thoroughly and sells the entire mixture in his shop.\nAt what selling price per kg should he sell this barley mixture so that he earns exactly 30% profit on his total cost price?

Introduction:
This question tests the concept of weighted average cost (mixture cost price) and then applying a required profit percentage to find the selling price per unit. When different quantities are bought at different rates and mixed, the effective cost per kg is the total cost divided by the total quantity, not a simple average of the rates.

Given Data / Assumptions:

• Barley quantity 1 = 30 kg, rate = ₹11.50 per kg
• Barley quantity 2 = 20 kg, rate = ₹14.25 per kg
• Total quantity = 50 kg
• Required profit = 30% on cost

Concept / Approach:
First compute total cost, then compute cost price per kg (weighted average). Finally apply 30% profit using: SP = CP * (1 + profit%).

Step-by-Step Solution:
Cost of 30 kg = 30 * 11.50 = 345.00Cost of 20 kg = 20 * 14.25 = 285.00Total cost = 345.00 + 285.00 = 630.00Total quantity = 30 + 20 = 50 kgCost price per kg (CP) = 630.00 / 50 = 12.60Selling price per kg (SP) for 30% profit = 12.60 * (1 + 30/100)SP = 12.60 * 1.30 = 16.38

Verification / Alternative Check:
Profit per kg should be 30% of ₹12.60, which is 0.30 * 12.60 = ₹3.78. Adding to CP: 12.60 + 3.78 = ₹16.38, matching the computed SP.

Why Other Options Are Wrong:
₹15.84: corresponds to a smaller profit than 30%.₹14.92: too low; profit becomes much less than required.₹13.98: close to CP, nearly no profit.₹17.10: implies profit higher than 30%.

Common Pitfalls:
Taking the average of ₹11.50 and ₹14.25 without weighting by quantities.Applying 30% to the selling price instead of the cost price.Forgetting to divide total cost by total kilograms to get per-kg CP.

Final Answer:
₹16.38 per kg