SSC CGL 2025 Tier-I · 13 September 2025, Shift 2 · Quantitative Aptitude · Question 12 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.

A tea seller bought 15 kg of Darjeeling tea at ₹300 per kg and 25 kg of Assam tea at ₹240 per kg. He mixed them together. Due to a slight drop in market prices, he had to sell the entire mixture at ₹260 per kg. Calculate his total profit or loss.

(a)Loss of ₹100
(b)Profit of ₹100
(c)Profit of ₹200
(d)Profit of ₹200

Answer

Why

Correct — A. Compare the total cost with the total sale.

Darjeeling: 15 × 300 = ₹4,500
Assam: 25 × 240 = ₹6,000
Total cost = ₹10,500 for 40 kg

Sale: 40 × 260 = ₹10,400
10,400 − 10,500 = −₹100, a loss of ₹100 → option (a)

Why the others are wrong

(b)
Profit of ₹100 — Right amount, wrong direction. The mixture costs 10,500 ÷ 40 = ₹262.50 a kg and sells at ₹260, so every kilogram loses money.
(c)
Profit of ₹200 — No profit is possible: the mixture sells at ₹260 a kg against an average cost of ₹262.50. The deal loses ₹2.50 on each of the 40 kg.
(d)
Profit of ₹200 — Printed with the same text as option (c), and wrong for the same reason: ₹260 a kg is below the ₹262.50 average cost, so the deal is a loss.

Concept

When two lots are mixed, the mixture's cost is the total cost divided by the total weight, not the plain average of the two rates.

The plain average, (300 + 240) ÷ 2 = ₹270, overstates the cost because more of the cheaper Assam tea went in. The weighted cost is 10,500 ÷ 40 = ₹262.50 a kg.

Profit or loss is then selling price minus cost: (260 − 262.50) × 40 = −₹100.

On the response sheet, options (c) and (d) are both printed as Profit of ₹200. Neither is correct, so the duplicate does not change the answer.

Key facts

Mixture cost per kg = (q₁ × c₁ + q₂ × c₂) ÷ (q₁ + q₂).
(15 × 300 + 25 × 240) ÷ 40 = ₹262.50 a kg.
A selling price below the cost per kg means a loss on every kilogram sold.

Study next

Alligation: finding the mixing ratio from a target average priceMixture profit percentage when the selling price carries a markupWeighted averages with unequal quantities

Common traps

Averaging ₹300 and ₹240 to ₹270: that ignores the 15 kg against 25 kg split and inflates the loss to ₹400.
Getting the size right and the sign wrong: ₹100 is offered as both a loss and a profit.

15 Sep 2025, 16:00, Quant Q.15 runs this backwards: tea at ₹150 mixed 4 : 5 with a second quality sells at ₹130 with no profit or loss, so 4 × 150 + 5x = 9 × 130 and x = ₹114.

15 Sep 2025, 16:00, Quant Q.11 weights three notebook costs 3 : 4 : 3 the same way before comparing with the sale price, keyed a profit of 9.2%.

Related PYQs

No directly related past PYQ was found.

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