Find the gain percentage, given that Aditi sold her scooter for ₹25404 gaining 1⁄6 th of the selling price.

Correct — D. The stem is an image: Aditi sold her scooter for ₹25404, gaining 1⁄6 th of the selling price. Gain per cent, though, is always measured on the cost.

Gain = 25404 ⁄ 6 = ₹4,234
Cost price = 25404 − 4234 = ₹21,170

Gain% = 4234 ⁄ 21170 × 100 = 20% → option (d).

The rupee figure is decoration. Gain = SP ⁄ 6 makes CP : gain : SP = 5 : 1 : 6, so the gain on cost is 1⁄5 whatever the scooter sold for.

Why the others are wrong

• (a)
  30% — A 30% gain means CP 10, gain 3, SP 13, so the gain would be 3⁄13 of the selling price. The stem fixes that fraction at 1⁄6.
• (b)
  25% — A 25% gain means CP 4, gain 1, SP 5, putting the gain at 1⁄5 of the selling price. Close to 1⁄6, but the stem's fraction is smaller.
• (c)
  40% — A 40% gain means CP 5, gain 2, SP 7, so the gain is 2⁄7 of the selling price — well above the 1⁄6 the question states.

Profit percentage is gain ⁄ cost price × 100, always. A question that quotes the gain as a fraction of the selling price is testing whether you change the base before you divide.

Convert once and the arithmetic disappears. If gain = SP ⁄ 6 then CP = SP − SP ⁄ 6 = 5 SP ⁄ 6, so the three quantities stand as CP : gain : SP = 5 : 1 : 6.

Gain on cost is then 1 ⁄ 5, which is 20%, and ₹25,404 is never needed. The general form is worth memorising: a gain of x% on cost is a gain of x ⁄ (100 + x) of the selling price.

Key facts

• Gain% is computed on the cost price, never on the selling price.
• Gain = SP ⁄ 6 gives CP : gain : SP = 5 : 1 : 6, hence 20% on cost.
• A gain of x% on cost equals a gain of x ⁄ (100 + x) of the selling price.

Common traps

• Dividing the gain by the selling price and reporting 16.67%.
• Subtracting the wrong way and taking the cost as 25404 + 4234.
• Reaching for long division when the 5 : 1 : 6 split answers it in one line.

No directly related past PYQ was found.