Profit and Loss – Mixed purchase rates and a single selling rate: Raju buys equal numbers of eggs in two purchases: first at 3 eggs per rupee and next at 6 eggs per rupee. He later sells all the eggs at the rate of 9 eggs for Rs 2. What is his overall percentage profit or loss?

Introduction / Context:
When quantities are equal but rates differ, compute the average cost per egg weighted by the equal quantities. Then compare with the unified selling rate to evaluate overall profit or loss as a percentage of total cost.

Given Data / Assumptions:

• First buy rate = 3 eggs per rupee ⇒ cost per egg = 1/3 rupee
• Second buy rate = 6 eggs per rupee ⇒ cost per egg = 1/6 rupee
• Equal number of eggs in both purchases (say q eggs each)
• Selling rate = 9 eggs for Rs 2 ⇒ price per egg = 2/9 rupee

Concept / Approach:
Total cost = q * (1/3) + q * (1/6) = (1/2) * q rupee. Total eggs = 2q. Total revenue = 2q * (2/9) = (4/9) * q rupee. Percentage profit or loss = (Revenue − Cost) / Cost * 100.

Step-by-Step Solution:
Cost = 0.5 qRevenue = (4/9) q ≈ 0.444... qLoss = Cost − Revenue = (0.5 − 4/9) q = (1/18) qLoss% = ( (1/18) q ) / (0.5 q) * 100 = (1/18) / (1/2) * 100 = (2/18) * 100 = 11.11% loss

Verification / Alternative check:
Choose q = 18 eggs each (36 total): cost = 9; revenue = 8; loss = 1 ⇒ 1/9 of cost = 11.11%.

Why Other Options Are Wrong:
10% and 3% loss miscompute averages; 2.5% profit is wrong direction; no-profit is incorrect since revenue < cost.

Common Pitfalls:
Taking simple mean of rates or averaging rupee amounts without holding quantity fixed.

Final Answer:
11.11% loss