SSC CGL 2024 Tier-I · 23 September 2024, Shift 2 · Quantitative Aptitude · Question 22 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 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.

The marked price of 55 items was equal to the cost price of 99 items. The selling price of 56 items was equal to the marked price of 35 items. Calculate the profit or loss percentage from the sale of each item.

(a)12.5% profit
(b)15% profit
(c)12.25% profit
(d)12.5% loss

Answer

Why

Correct — A. Each statement is a price ratio in disguise, and the counts swap sides.

55 marked prices = 99 cost prices:
MP ⁄ CP = 99 ⁄ 55 = 9 ⁄ 5

56 selling prices = 35 marked prices:
SP ⁄ MP = 35 ⁄ 56 = 5 ⁄ 8

Chain them:
SP ⁄ CP = (5 ⁄ 8) × (9 ⁄ 5) = 9 ⁄ 8
Profit = (9 ⁄ 8 − 1) × 100 = 100 ⁄ 8 = 12.5% profit → option (a)

Why the others are wrong

(b)
15% profit — 15% profit needs SP ⁄ CP = 23 ⁄ 20 = 1.15. The two equalities force (35 ⁄ 56) × (99 ⁄ 55), which is exactly 9 ⁄ 8 = 1.125.
(c)
12.25% profit — 12.25% would make SP ⁄ CP = 1.1225. The working gives 9 ⁄ 8 = 1.125 exactly, so this is a near-miss on the second decimal rather than a different method.
(d)
12.5% loss — The direction is wrong: SP ⁄ CP = 9 ⁄ 8 is greater than 1, so the selling price beats the cost price. A 12.5% loss would need SP ⁄ CP = 7 ⁄ 8.

Concept

'The marked price of 55 items was equal to the cost price of 99 items' is not a counting problem. It is 55 × MP = 99 × CP, so MP ⁄ CP = 99 ⁄ 55 — the counts land on the opposite side from where they were written.

The logic is worth holding on to: if it takes more items at the cost price to match the marked price of fewer, then each marked price is the larger figure.

Two such ratios chain by multiplication, because SP ⁄ CP = (SP ⁄ MP) × (MP ⁄ CP). The marked price cancels and never needs a number.

No rupee figure is given anywhere, and none is needed — profit percentage depends only on the ratio SP ⁄ CP.

Set CP = ₹5 per item if a concrete number helps: then MP = ₹9, SP = ₹45 ⁄ 8 = ₹5.625, and the gain is ₹0.625 on ₹5, which is 12.5%.

Key facts

If the MP of m articles equals the CP of n articles, then MP ⁄ CP = n ⁄ m.
Here MP ⁄ CP = 99 ⁄ 55 = 9 ⁄ 5 and SP ⁄ MP = 35 ⁄ 56 = 5 ⁄ 8.
Multiplying the two gives SP ⁄ CP = 9 ⁄ 8.
SP ⁄ CP = 9 ⁄ 8 is a gain of one-eighth of the cost price, which is 12.5%.

Study next

Chaining profit and discount through the marked price as SP ⁄ CP = (SP ⁄ MP) × (MP ⁄ CP)Turning 'cost price of x items = selling price of y items' into a single gain percentageSuccessive discounts collapsed into one equivalent multiplier

Common traps

Writing MP ⁄ CP = 55 ⁄ 99 by leaving each count on its own side.
Answering with the discount instead: SP is 5 ⁄ 8 of MP, a 37.5% reduction on the marked price.
Reporting SP ⁄ CP itself as 112.5% when the question asks for the 12.5% gain.

SSC states the same profit chain either as a count equality, as here, or as a direct percentage link between the three prices.

11 Sep 2024, 12:30, Quant Q.19 fixes the cost price at 75% of the marked price and then allows a 15% discount. 10 Sep 2024, 16:00, Quant Q.23 runs it backwards, from a 20% discount and a 10% gain to the CP : MP ratio.

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