Find the gain percentage, given that Priya sold her scooter for ₹42564 gaining 1⁄6 th of the selling price.

Correct — B. The gain is 1⁄6 of the selling price, not of the cost price. That single word decides the question.

SP = ₹42,564
Gain = SP⁄6 = 42564⁄6 = ₹7,094
CP = SP − Gain = 42564 − 7094 = ₹35,470

Gain% = 7094⁄35470 × 100 = 20% → option (b)

The rupee figure never mattered: CP is always 5⁄6 of SP here, so Gain% = (1⁄6)⁄(5⁄6) = 1⁄5 = 20%.

Why the others are wrong

• (a)
  15% — A gain of 15% would make the profit 15⁄115 = 3⁄23 of the selling price, about 13% of it — short of the 1⁄6 (≈16.7%) the question states.
• (c)
  30% — A gain of 30% would make the profit 30⁄130 = 3⁄13 of the selling price, roughly 23% of it, well above the stated 1⁄6.
• (d)
  40% — A gain of 40% would make the profit 40⁄140 = 2⁄7 of the selling price, about 28.6% of it, far more than the stated 1⁄6.

Profit percentage is always measured on the cost price, so a profit quoted as a fraction of the selling price has to be converted before you can use it.

If gain = k × SP, then CP = (1 − k) × SP and Gain% = k⁄(1 − k) × 100.

The reverse conversion is just as useful: a gain of g% means the profit is g⁄(100 + g) of the selling price. Here 20% ↔ 20⁄120 = 1⁄6, which closes the loop on the answer.

Key facts

• Profit percentage is computed on the cost price, never on the selling price.
• If the gain is a fraction k of SP, then Gain% = k⁄(1 − k) × 100.
• A gain of g% means the profit is g⁄(100 + g) of the selling price.
• A gain of 1⁄6 of SP is exactly a gain of 20% on cost.

Common traps

• Reading 1⁄6 th of the selling price as 1⁄6 of the cost price, which gives 16.67%.
• Dividing ₹42,564 by 6 and reporting the gain instead of the gain percentage.

No directly related past PYQ was found.