Profit equals the selling price of some units — infer overall gain By selling 100 pens, a shopkeeper’s profit equals the selling price of 40 pens. What is his gain percentage on the entire lot?

Introduction / Context:
If a seller’s profit (in rupees) equals the selling price of a certain number of units, we can represent totals algebraically and cancel unknowns cleanly. This type of question emphasizes understanding the relationship between total selling price, total cost price, and profit.

Given Data / Assumptions:

• Total items sold: 100 pens.
• Profit amount = SP of 40 pens.
• Uniform unit price for all pens in the transaction.

Concept / Approach:
Let s be the SP per pen. Then total SP = 100s and profit = 40s. Hence total cost = total SP − profit = 60s. Profit% = profit / cost * 100 = (40s)/(60s) * 100.

Step-by-Step Solution:
Let SP per pen = s; Total SP = 100s.Profit = 40s.Total cost = 100s − 40s = 60s.Gain% = (40s / 60s) * 100 = 66.666...% = 66.67%.

Verification / Alternative check:
Assume s = ₹1 for simplicity. Then total SP = ₹100, profit = ₹40, cost = ₹60, which indeed gives a 40/60 = 2/3 = 66.67% gain.

Why Other Options Are Wrong:
6.67%, 8.8%, 5.59%, and 44.7% misinterpret the profit relation or the base used for the percentage.

Common Pitfalls:
Taking percentage on SP rather than on CP, or assuming profit equals the cost of 40 pens (the statement says selling price of 40 pens).

Final Answer:
66.67%