If the cost price of 12 pens is equal to the selling price of 8 pens, the gain…

Concept — Profit per cent is always measured on the cost price: Gain% = (SP − CP) ÷ CP × 100. When a question fixes the prices by a statement of the form "the cost price of m articles equals the selling price of n articles", the two per-article prices are locked to each other, so the gain per cent follows from the ratio m : n alone and no actual money value is needed.

Application — Take the cost price of one pen as ₹1, since only a ratio is being asked for.

1. Cost price of 12 pens = 12 × ₹1 = ₹12.

2. The question states that the selling price of 8 pens is the same amount, so the selling price of 8 pens = ₹12.

3. Selling price of one pen = ₹12 ÷ 8 = ₹1.50.

4. Gain on one pen = ₹1.50 − ₹1 = ₹0.50.

5. Gain per cent = (₹0.50 ÷ ₹1) × 100 = 50%.

Cross-check — The same figure follows from the ratio shortcut: Gain% = (m − n) ÷ n × 100 = (12 − 8) ÷ 8 × 100 = 50%. A sanity check agrees — the money that buys 12 pens is collected by selling only 8 pens, so each pen must be sold above its cost, and ₹1.50 against ₹1 is one-and-a-half times the cost.