SSC CGL 2025 Tier-I · 15 September 2025, Shift 3 · Quantitative Aptitude · Question 15 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 11 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 shopkeeper mixes two qualities of tea. The first quality costs ₹150 per kg and is mixed with the second quality in the ratio 4 : 5. If the mixture is sold at ₹130 per kg (at no profit, no loss), what is the cost per kg of the second quality of tea?

(a)₹100
(b)₹110
(c)₹114
(d)₹120

Answer

Why

Correct — C.
No profit, no loss, so the mixture costs ₹130 per kg.
Take 4 kg of the first and 5 kg of the second: 9 kg in all.
Cost of 9 kg: 9 × 130 = ₹1,170

First quality: 4 × 150 = ₹600
Second quality, 5 kg: 1,170 − 600 = ₹570
Per kg: 570 ÷ 5 = ₹114 → option (c)

Why the others are wrong

(a)
₹100 — ₹100 makes 9 kg cost 600 + 500 = ₹1,100, only ₹122.22 a kg. Selling at ₹130 would then earn a profit, but the stem says no profit, no loss.
(b)
₹110 — ₹110 is the price a 1 : 1 mix would need, since (150 + 110) ÷ 2 = 130. In 4 : 5 the cheaper tea weighs more: 600 + 550 = ₹1,150 for 9 kg, ₹127.78 a kg.
(d)
₹120 — ₹120 makes 9 kg cost 600 + 600 = ₹1,200, or ₹133.33 a kg. Selling at ₹130 would then be a loss, not the no profit, no loss the stem states.

Concept

A mixture's cost per kg is a weighted average of its ingredients' costs, weighted by quantity.

Here 'no profit, no loss' makes the ₹130 selling price equal to that average. So 4 kg at ₹150 and 5 kg at the unknown price must together cost 9 × ₹130.

Alligation gives the same answer: first : second = (130 − x) : (150 − 130). Setting (130 − x) : 20 = 4 : 5 gives 130 − x = 16, so x = ₹114.

Check forwards: (130 − 114) : (150 − 130) = 16 : 20 = 4 : 5.

Key facts

Mixture cost per kg = total cost ÷ total quantity.
Alligation: dearer quantity : cheaper quantity = (mean − cheaper price) : (dearer price − mean).
No profit, no loss means the selling price equals the cost price.

Study next

Alligation when the mixture is sold at a profit, so its cost must be backed out firstFinding the quantity of one ingredient mixed with a fixed quantity of anotherMixtures of three ingredients at different prices

Common traps

Assuming the mean sits halfway and answering ₹110, which holds only for a 1 : 1 mix.
Reversing the ratio, 5 kg at ₹150 with 4 kg of the unknown: 750 + 4x = 1,170 gives ₹105.

15 Sep 2025, 12:30, Quant Q.11 asks for the ratio instead of a price: pulses at ₹60 and ₹90, sold at ₹84 for a 20% profit, cost ₹70 a kg, and (90 − 70) : (70 − 60) gives the keyed 2 : 1.

12 Sep 2025, 09:00, Quant Q.17 does the same with oils at ₹90 and ₹150 sold at ₹144 for a 20% profit: cost ₹120, keyed 1 : 1.

Related PYQs

No directly related past PYQ was found.

Topic: Profit and Loss — all 56 SSC CGL questions on it, every solved shift.