Pens bought and sold in packs — compute true gain percentage Pens are bought at 5 for ₹4 (purchase pack rate) and sold at 4 for ₹5 (selling pack rate). What is the gain percentage?

Introduction / Context:
When items are priced as “x for ₹y”, always convert to per-unit cost and per-unit selling price. The profit percentage is then computed on the cost price per unit, not the selling price.

Given Data / Assumptions:

• Buy 5 pens for ₹4 ⇒ CP per pen.
• Sell 4 pens for ₹5 ⇒ SP per pen.
• Find gain% on cost.

Concept / Approach:
CP per pen = 4/5. SP per pen = 5/4. Gain% = (SP − CP)/CP * 100.

Step-by-Step Solution:
CP per pen = ₹4/5 = ₹0.80.SP per pen = ₹5/4 = ₹1.25.Gain per pen = 1.25 − 0.80 = ₹0.45.Gain% = 0.45 / 0.80 * 100 = 56.25%.

Verification / Alternative check:
On 20 pens: cost = 4 packs of 5 → ₹16; sell as 5 packs of 4 → ₹25; profit = ₹9 on ₹16 = 56.25% (same result).

Why Other Options Are Wrong:
55% and 52% are close but not exact; 45.26% and 60% deviate further from the correct calculation.

Common Pitfalls:
Mixing the bases (computing percentage on SP), or averaging the pack rates instead of converting to per-unit prices first.

Final Answer:
56.25%