When CP of 16 equals SP of 12 — identify profit percentage If the cost price of 16 pens equals the selling price of 12 pens (same kind), what is the profit percentage?

Introduction / Context:
Comparing total cost for some units with total selling price for a different number of the same units reveals the SP-to-CP ratio per item. From this ratio we can read off the profit or loss percentage directly.

Given Data / Assumptions:

• Total CP of 16 items equals total SP of 12 items.
• All items identical; uniform per-unit CP and SP.

Concept / Approach:
Let CP per pen be C and SP per pen be S. Then 16C = 12S ⇒ S/C = 16/12 = 4/3. Since S > C, there is a profit. Profit% = (S − C)/C * 100 = (4/3 − 1) * 100 = 1/3 * 100.

Step-by-Step Solution:
From 16C = 12S, S/C = 4/3 ≈ 1.3333.Profit fraction = (4/3 − 1) = 1/3.Profit% = (1/3) * 100 = 33 1/3% gain.

Verification / Alternative check:
Assume C = ₹3 per pen ⇒ 16C = ₹48. Then S = 4/3 * 3 = ₹4 per pen; 12 pens at ₹4 gives ₹48, consistent. Profit per pen = ₹1 on ₹3 ⇒ 33 1/3%.

Why Other Options Are Wrong:
25% gain/loss and 33 1/3% loss contradict S/C = 4/3 > 1.

Common Pitfalls:
Inverting the ratio to 3/4 by mistake or labeling the outcome as loss instead of profit.

Final Answer:
33 1/3% gain