Profit and Loss — The cost price of 12 pencils equals the selling price of 10 pencils. What is the gain as a percentage of the cost price?

Introduction / Context:
Bundle comparisons are easiest when converted to per-unit prices. If the cost of 12 equals the selling revenue of 10, the selling price per unit must exceed the cost per unit, yielding a gain on the cost base.

Given Data / Assumptions:

• Total CP(12) = Total SP(10).
• Uniform unit cost and unit SP across pencils.

Concept / Approach:
Let CP per pencil = c and SP per pencil = s. Then 12c = 10s ⇒ s/c = 12/10 = 1.2. Thus, profit on cost = 20%. (Note: If asked as a percentage of SP, the profit would be (s − c)/s = 1/6 = 16 2/3%. This item asks on cost.)

Step-by-Step Solution:

Verification / Alternative check:
Assume c = ₹ 10 ⇒ CP(12) = 120. Then s = 12 ⇒ SP(10) = 120 (consistent). Profit per unit = 2 on a base of 10 ⇒ 20%.

Why Other Options Are Wrong:
16 2/3% gain is on the SP base, not the CP base; 25% and 10% gains are incorrect; 15% loss has wrong sign.

Common Pitfalls:
Reporting profit as a fraction of SP when the question asks for a percentage of cost; always check the required base.

Final Answer:
20% gain