SSC CGL 2024 Tier-I · 12 September 2024, Shift 2 · Quantitative Aptitude · Question 9 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

Find the gain percentage, given that Siddhi sold her scooter for ₹24318 gaining 1⁄6 th of the selling price.

(a)25%
(b)35%
(c)5%
(d)20%

Answer

Why

Correct — D. The gain is given as a fraction of the selling price, but gain per cent is always reckoned on the cost price.

Gain = SP⁄6
CP = SP − gain = SP − SP⁄6 = 5SP⁄6

Gain% = (gain ⁄ CP) × 100
= (SP⁄6) ÷ (5SP⁄6) × 100
= (1⁄5) × 100 = 20% → option (d)

The SP cancels out of that ratio, which is why the ₹24318 never has to be used.

Why the others are wrong

(a)
25% — A 25% gain makes the profit 25⁄125 = 1⁄5 of the selling price. The stem says 1⁄6, and 1⁄6 of the SP belongs to a 20% gain.
(b)
35% — A 35% gain puts the profit at 35⁄135 = 7⁄27 of the selling price, nowhere near 1⁄6. The check to carry is gain% ⁄ (100 + gain%) = the profit's share of the SP.
(c)
5% — A 5% gain is only 5⁄105 = 1⁄21 of the selling price. The stem's 1⁄6 is more than three times that share.

Concept

Profit and loss percentages are always taken on the cost price unless a stem says otherwise — and this stem says otherwise.

Gain as a fraction of SP: gain = SP⁄6, so CP = 5SP⁄6 and gain% = (SP⁄6) ⁄ (5SP⁄6) = 20%.
Gain as a fraction of CP: gain = CP⁄6 would instead give 100⁄6 ≈ 16.67%.

The conversion generalises. If the gain is 1⁄n of the SP it is 1⁄(n − 1) of the CP, so the percentage is 100⁄(n − 1) — here n = 6 and the answer is 100⁄5.

The ₹24318 is there to be ignored: the selling price cancels out of the ratio, so the answer would be 20% for any price at all. No cost price is given anywhere, and none is needed.

Key facts

Gain per cent is computed on the cost price, not on the selling price.
If the gain is 1⁄n of the SP, then CP = (n − 1)SP⁄n and the gain is 100⁄(n − 1) per cent.
Here n = 6, so the gain is 1⁄5 of the CP, which is 20%.
A gain of 1⁄6 of the cost price would instead be about 16.67%.

Study next

Converting between profit on cost and profit on selling price in both directionsThe CP : SP ratio implied by a stated profit percentageChains of transactions where one person's selling price is the next person's cost price

Common traps

Computing (1⁄6) × 100 = 16.67% by treating the fraction as a share of the cost price.
Insisting on using the ₹24318, then rounding somewhere and losing the exact 20%.
Taking CP = SP + SP⁄6 instead of SP − SP⁄6, which turns the gain into a loss.

SSC likes making you switch bases. At 12 Sep 2024, 16:00, Quant Q.19 the profit starts at 320% of the cost, the cost then rises 10% with the selling price held constant, and the profit is wanted as a percentage of the SP.

At 13 Sep 2024, 09:00, Quant Q.2 a 250% profit has to be turned into the cost price to selling price ratio.

Related PYQs

No directly related past PYQ was found.