SSC CGL 2024 Tier-I · 24 September 2024, Shift 1 · Quantitative Aptitude · Question 21 of 98

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.

Samreen sells a keyboard for ₹1,260 at a profit of 25%, and another keyboard for ₹1,440 at a loss of 10%. What is her total gain or loss percentage?

Answer

Why

Correct — C. Two independent sales, so recover each cost price and then compare totals. Percentages on different cost prices cannot be added or averaged.

First keyboard: CP = 1260 ÷ 1.25 = ₹1,008
Second keyboard: CP = 1440 ÷ 0.90 = ₹1,600

Total CP = 1008 + 1600 = ₹2,608
Total SP = 1260 + 1440 = ₹2,700
Gain = 2700 − 2608 = ₹92

Gain % = (92 ÷ 2608) × 100
= 9200⁄2608
= 575⁄163
= 3 86⁄163 % gain → option (c), the image reading 3 86⁄163 % Gain.

Why the others are wrong

(a)
Two errors at once. The total selling price ₹2,700 beats the total cost ₹2,608, so this is a gain, and 11⁄27 comes from dividing the ₹92 by the selling price instead of the cost.
(b)
The right fraction with the wrong direction. ₹92 more came in than went out, so 86⁄163 belongs to a gain and not to a loss.
(d)
3 11⁄27 % is the gain taken on the selling price: 92⁄2700 × 100 = 92⁄27. Profit percentage is measured on cost price unless the stem says otherwise, giving 92⁄2608 × 100.

Concept

Profit and loss percentages are measured on cost price unless the question says otherwise, so a question that hands you selling prices is really asking you to run the formula backwards.

CP = SP ÷ (1 + profit) and CP = SP ÷ (1 − loss). Here 1260 ÷ 1.25 = 1008 and 1440 ÷ 0.90 = 1600.

Once both cost prices exist, two separate deals become one: add the costs, add the receipts, and take the difference as a percentage of the total cost.

The familiar shortcut — equal selling prices at +x% and −x% always leave a net loss of x²⁄100 % — does not apply here. The selling prices differ (₹1,260 and ₹1,440) and so do the percentages, so the long route is the only route.

Key facts

CP = SP ÷ (1 + profit%) and CP = SP ÷ (1 − loss%).
Profit or loss percentage is calculated on cost price unless the question states otherwise.
Here CP₁ = ₹1,008 and CP₂ = ₹1,600, against receipts of ₹1,260 and ₹1,440.
9200⁄2608 reduces to 575⁄163, which is 3 86⁄163.

Study next

Recovering cost price from selling price at a stated profit or lossThe equal-selling-price rule, where a gain of x% and a loss of x% give a net loss of x²⁄100 %Successive transactions, where the proceeds of one sale fund the next purchase

Common traps

Averaging +25% and −10% into a net 7.5%, which ignores the unequal cost prices.
Dividing the ₹92 gain by the total selling price ₹2,700 rather than the total cost ₹2,608.
Multiplying by 1.25 and 0.90 to find the cost prices instead of dividing.

Recovering a cost price from a selling price is asked on its own at 25 Sep 2024, 12:30, Quant Q.10: a 28% loss at ₹144 puts the cost at ₹200, so a sale at ₹288 is a 44% gain.

Related PYQs

No directly related past PYQ was found.

Topic: Profit and Loss — all 38 SSC CGL questions on it, every solved shift.