Find the gain percentage, given that Aditi sold her scooter for ₹40620 gaining 1⁄5th of the selling price.

Correct — A. The stem figure reads: find the gain percentage, given that Aditi sold her scooter for ₹40620 gaining 1⁄5 th of the selling price.

Gain = (1⁄5) × 40,620 = ₹8,124
Cost price = 40,620 − 8,124 = ₹32,496
Gain % = 8,124 ⁄ 32,496 × 100 = 25% → option (a)

The rupee figure never matters. If the gain is 1⁄5 of SP, the cost is 4⁄5 of SP, so gain ÷ cost = (1⁄5) ÷ (4⁄5) = 1⁄4 = 25%.

Why the others are wrong

• (b)
  20% — 20% is 1⁄5 quoted on the selling price, which is the datum, not the answer. Profit percentage is taken on cost, and a 20% gain on cost would make the gain 0.2⁄1.2 = 1⁄6 of the selling price, not 1⁄5.
• (c)
  35% — A 35% gain on cost puts the selling price at 1.35 × cost, so the gain would be 0.35⁄1.35 ≈ 25.9% of the selling price. The stem fixes that share at exactly 20%.
• (d)
  10% — A 10% gain on cost makes the gain 0.1⁄1.1 = 1⁄11 of the selling price. The stem says 1⁄5, more than twice that share.

Profit percentage has one base and it is the cost price. Every trap in this family comes from a question quoting the gain against the selling price instead.

Converting is one line. If the gain is a fraction k of SP, then CP = (1 − k)·SP, so the gain as a fraction of cost is k ⁄ (1 − k).

Here k = 1⁄5, giving (1⁄5) ⁄ (4⁄5) = 1⁄4 = 25%. The ₹40,620 is decoration — the ratio alone settles it.

Key facts

• Gain % = (SP − CP) ⁄ CP × 100, always on the cost price.
• A gain of 1⁄5 of the selling price leaves the cost at 4⁄5 of the selling price.
• A gain of 1⁄n of SP converts to a gain of 1⁄(n − 1) on CP, so 1⁄5 of SP is 1⁄4 = 25% of CP.
• Here CP = ₹32,496 and SP = ₹40,620, a gain of ₹8,124.

Common traps

• Reading 1⁄5 as 20% and answering straight from the fraction.
• Dividing the gain by the selling price instead of the cost price.
• Computing the cost as 40,620 × 5⁄4 instead of 40,620 × 4⁄5.

No directly related past PYQ was found.