SSC CGL 2025 Tier-I · 13 September 2025, Shift 2 · Quantitative Aptitude · Question 13 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

An antique dealer sold three items, A, B, and C, with their selling prices in the ratio 4:5:6. He suffered a loss of 10% on item A, made a profit of 50% on item B, and broke even (no profit, no loss) on item C. What was his approximate percentage gain or loss in the overall deal?

(a)loss of 8.88%
(b)profit of 8.88%
(c)profit of 10.88%
(d)loss of 10.88%

Answer

Why

Correct — B. Give the selling prices numbers that divide cleanly: 36, 45, 54 (4 : 5 : 6 × 9).

A, 10% loss: CP = 36 ÷ 0.9 = 40
B, 50% profit: CP = 45 ÷ 1.5 = 30
C, break-even: CP = 54

Total CP = 124, total SP = 135
Profit = 11, and 11 ÷ 124 × 100 = 8.87%
Nearest option: profit of 8.88% → option (b)

Why the others are wrong

(a)
loss of 8.88% — Right size, wrong direction. The total selling price of 135 exceeds the total cost of 124, so the dealer gained on the whole deal.
(c)
profit of 10.88% — That rate on a cost of 124 would need a profit of about 13.5. The actual profit is 135 − 124 = 11, which is 8.87%.
(d)
loss of 10.88% — Wrong on both counts: the deal ends in profit (135 against 124), and its size is 8.87%, not 10.88%.

Concept

When selling prices come in a ratio, recover each item's cost separately: CP = SP ÷ (1 + profit%) or SP ÷ (1 − loss%).

The overall figure is total profit over total cost, not an average of the three percentages. Scaling the ratio by 9 makes both divisions exact: 36 ÷ 0.9 = 40 and 45 ÷ 1.5 = 30.

The exact figure is 11⁄124 = 8.8709…%, which rounds to 8.87%. The option prints 8.88%, and the stem asks for the approximate figure, so the key's profit of 8.88% is the match.

Key facts

CP = SP ÷ (1 + p⁄100) for a profit of p%, and SP ÷ (1 − l⁄100) for a loss of l%.
Overall profit % = (total SP − total CP) ÷ total CP × 100.
With selling prices of 36, 45 and 54, the costs are 40, 30 and 54, totalling 124.

Study next

Overall profit when cost prices, not selling prices, are in a ratioTwo items sold at the same price, one at a profit and one at a lossWeighted averages of percentages

Common traps

Averaging the three percentages: (−10 + 50 + 0) ÷ 3 = 13.33%, which matches no option.
Weighting the percentages by the selling-price ratio: (4 × −10 + 5 × 50) ÷ 15 = 14%. Percentages must be weighted by cost.
Dropping C because it broke even: its cost of 54 still belongs in the total.

15 Sep 2025, 16:00, Quant Q.12 uses the same frame with mobile covers: selling prices 3 : 4 : 5, profits of 25% and 10% and a 20% loss, so costs of 2.4 + 3.636 + 6.25 = 12.286 against sales of 12, keyed a loss of 2.33%.

Related PYQs

No directly related past PYQ was found.

Topic: Profit and Loss — all 87 SSC CGL questions on it, every solved shift.