Find the gain percentage, given that Anubha sold her scooter for ₹23358 gaining 1⁄6 th of the selling price.

Correct — A. The gain is one-sixth of the selling price, not of the cost price. That is the entire question.

Gain = SP ⁄ 6 = 23358 ⁄ 6 = ₹3,893
CP = SP − gain = 23358 − 3893 = ₹19,465

Gain % = 3893 ⁄ 19465 × 100 = 20% → option (a)

The ₹23,358 never actually matters: gain ⁄ CP = (SP⁄6) ÷ (5SP⁄6) = 1⁄5 for any selling price at all.

Why the others are wrong

• (b)
  35% — 35% would need a cost price of 23358 ⁄ 1.35 ≈ ₹17,302 and so a gain near ₹6,056, far above the ₹3,893 that one-sixth of the selling price comes to.
• (c)
  30% — 30% would need a cost price of 23358 ⁄ 1.3 ≈ ₹17,968 and a gain near ₹5,390, where the stated gain is ₹3,893.
• (d)
  25% — 25% is the answer when the gain is one-fifth of the selling price, which leaves CP = 4SP⁄5. Here it is one-sixth, so CP = 5SP⁄6 and the gain works out at 20%.

Gain percentage is always measured on the cost price: gain % = (gain ⁄ CP) × 100. A question that states the gain as a fraction of the selling price is testing precisely that reflex.

So translate before you calculate. Gain = SP⁄6 means CP = SP − SP⁄6 = 5SP⁄6, and gain ⁄ CP = (SP⁄6) ÷ (5SP⁄6) = 1⁄5.

The general result is worth memorising. If the gain is 1⁄n of the selling price, the gain percentage is 100 ⁄ (n − 1). Here n = 6, so it is 100⁄5 = 20%.

Key facts

• Gain percentage is computed on the cost price, never on the selling price.
• If the gain is 1⁄n of the selling price, the gain percentage is 100 ⁄ (n − 1).
• Here SP = ₹23,358, gain = ₹3,893 and CP = ₹19,465.
• A gain of one-fifth of the selling price would instead give 25%.

Common traps

• Dividing the gain by the selling price and answering 16⅔%.
• Reading 'one-sixth of the selling price' as one-sixth of the cost price.
• Using ₹23,358 as the cost price, which makes every later step wrong.

No directly related past PYQ was found.