Find the gain percentage, given that Siddhi sold her scooter for ₹31902 gaining 1⁄6 th of the selling price.

Correct — A. The stem is a figure: Siddhi sold her scooter for ₹31902, gaining 1⁄6 th of the selling price.

Gain = SP ÷ 6 = 31902 ÷ 6 = ₹5317
CP = SP − gain = 31902 − 5317 = ₹26585

Gain% = 5317 ÷ 26585 × 100 = 20% → option (a)

The rupee figure never mattered. Gain = SP⁄6 makes CP = 5⁄6 of SP, so gain% = (1⁄6) ÷ (5⁄6) = 1⁄5 = 20% for any selling price at all.

Why the others are wrong

• (b)
  25% — 25% is the answer to a gain of 1⁄5 of the selling price: then CP is 4⁄5 of SP and the gain is a quarter of it. The stem says one sixth, not one fifth.
• (c)
  5% — 5% would need the gain to be 1⁄21 of the selling price — cost 20 parts, gain 1 part, selling price 21. That is nowhere near one sixth.
• (d)
  30% — 30% corresponds to a gain of 3⁄13 of the selling price — cost 10 parts, gain 3, selling price 13. It is the right method applied to the wrong fraction.

Profit percentage is always measured on the cost price, whatever base the question uses to state the profit itself. So the first job is to move the given fraction onto CP.

Do it in parts. Gain is 1⁄6 of SP, so let SP = 6 parts. Then gain = 1 part and CP = 6 − 1 = 5 parts.

Gain% = 1⁄5 × 100 = 20%. The rupee amount is never touched, which is the point of working in parts.

Key facts

• Profit percentage is computed on the cost price, not on the selling price.
• A gain of 1⁄6 of SP means SP = 6 parts, gain = 1 part and CP = 5 parts.
• A gain of one sixth of the selling price is a gain of 20% on cost.
• 31902 ÷ 6 = 5317, and 31902 − 5317 = 26585.

Common traps

• Dividing the gain by the selling price and answering about 16.67%, a figure the options do not even carry.
• Applying the one sixth to the cost price when the stem says selling price.
• Reaching for the calculator on 31902 when the fraction alone decides it.

No directly related past PYQ was found.