Profit and Loss — Ram buys 800 eggs at ₹ 3.75 per dozen. He sells 450 eggs at 2 for ₹ 1 and the remaining 350 eggs at 5 for ₹ 2. What is his overall percentage gain?

Introduction / Context:
Mixed-rate sales problems require converting all prices to per-unit values and then summing revenues across segments. The cost is based on a per-dozen rate and must be converted to per-egg to match selling units.

Given Data / Assumptions:

• Purchase: 800 eggs at ₹ 3.75 per dozen ⇒ CP per egg = 3.75 / 12.
• Sales: 450 eggs at 2 for ₹ 1; 350 eggs at 5 for ₹ 2.
• No wastage; all eggs are sold.

Concept / Approach:
Compute total cost and total revenue separately. Then percentage gain = (Revenue − Cost)/Cost * 100. Careful unit handling is essential: “per dozen” to “per egg”, and “k for ₹ m” to “per egg”.

Step-by-Step Solution:

Verification / Alternative check:
Compute per dozen equivalent revenues to cross-check; the ratio remains consistent at 46% gain.

Why Other Options Are Wrong:
28%, 36%, 14%, and 32% mismatch the exact arithmetic from the given rates and quantities.

Common Pitfalls:
Averaging selling rates without weighting by quantities; failing to convert per-dozen cost to per-egg cost before comparing to per-egg SPs.

Final Answer:
46%