SSC CGL 2024 Tier-I · 18 September 2024, Shift 2 · Quantitative Aptitude · Question 24 of 99

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 10 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 ₹71785 gaining 1⁄5th of the selling price.

(a)20%
(b)15%
(c)10%
(d)25%

Answer

Why

Correct — D. The stem is an image: Siddhi sold her scooter for ₹71,785, gaining 1⁄5th of the selling price. Gain per cent is measured on cost, so the base has to be moved.

Gain = SP ÷ 5 = 71,785 ÷ 5 = ₹14,357
CP = SP − gain = 71,785 − 14,357 = ₹57,428

Gain% = 14,357 ÷ 57,428 × 100 = 25% → option (d)

Faster, without touching the rupees: a gain of SP⁄5 leaves CP = 4SP⁄5, so gain ÷ CP = (SP⁄5) ÷ (4SP⁄5) = 1⁄4, which is 25%.

Why the others are wrong

(a)
20% — Option (a), 20%, is the gain measured on the selling price — 1⁄5 rewritten as a percentage. It is the figure the question hands you before the base is shifted to cost.
(b)
15% — Option (b), 15%, would put the cost at 71,785 ÷ 1.15 = ₹62,421.74 and the gain at ₹9,363.26, well short of the ₹14,357 that a fifth of the selling price requires.
(c)
10% — Option (c), 10%, implies a cost of 71,785 ÷ 1.1 = ₹65,259.09 and a gain of ₹6,525.91, under half the gain the question states.

Concept

Profit and loss percentages are quoted on the cost price unless a question names another base. This question names another base, and everything follows from that.

If the gain is a fraction g of the selling price, then CP = SP(1 − g), and the gain measured on cost is

g ⁄ (1 − g)

With g = 1⁄5 that is (1⁄5) ÷ (4⁄5) = 1⁄4, or 25%. The mirror statement is worth memorising: a gain of 25% on cost is always 20% of the selling price.

The ₹71,785 never reaches the answer. It happens to divide by 5 cleanly, which makes the long route safe, but the fractions settle the question on their own.

Key facts

Profit per cent is computed on cost price unless the question names a different base.
A gain of g times the selling price equals g ⁄ (1 − g) of the cost price.
A gain of 1⁄5 of the selling price is a gain of 1⁄4, that is 25%, of the cost price.
Here SP = ₹71,785, gain = ₹14,357 and CP = ₹57,428.

Study next

Converting a percentage quoted on selling price into one quoted on cost priceMark-up and discount chains in which MP, CP and SP all appearSuccessive changes to cost while the selling price is held fixed

Common traps

Reading 1⁄5 as 20% and stopping there.
Dividing the gain by the selling price instead of by the cost price.
Assuming the rupee figure must be used, when the fractions alone decide it.

SSC swaps the base in both directions. 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 fixed, and the new profit is wanted as a percentage of the selling price.

At 24 Sep 2024, 16:00, Quant Q.19 a 25% mark-up followed by an 18% discount has to be turned into a gain per cent on cost.

Related PYQs

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