SSC CGL 2025 Tier-I · 16 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.

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Two distinct grades of rice, one priced at ₹80 per kilogram and the other at ₹120 per kilogram, are amalgamated in an undisclosed proportion. The resultant blend is retailed at ₹132 per kilogram, securing a profit margin of 20% on the overall cost price. Determine the precise ratio in which the two rice varieties were intermingled.

(a)1 : 3
(b)2 : 1
(c)3 : 2
(d)4 : 1

Answer

Why

Correct — A. Remove the profit first, then apply alligation to the cost price.

Cost of the blend = 132 ÷ 1.20 = ₹110 per kg

Alligation around ₹110:
₹80 grade: 120 − 110 = 10
₹120 grade: 110 − 80 = 30

Ratio ₹80 : ₹120 = 10 : 30 = 1 : 3 → option (a)
Check: (1 × 80 + 3 × 120) ÷ 4 = 440 ÷ 4 = ₹110

Why the others are wrong

(b)
2 : 1 — 2 : 1 gives a cost of (2 × 80 + 120) ÷ 3 ≈ ₹93.33 per kg. With 20% profit that sells at ₹112, not ₹132.
(c)
3 : 2 — 3 : 2 gives a cost of (3 × 80 + 2 × 120) ÷ 5 = ₹96 per kg, which sells at ₹115.20 with 20% profit, well short of ₹132.
(d)
4 : 1 — 4 : 1 gives a cost of (4 × 80 + 120) ÷ 5 = ₹88 per kg. More of the cheap grade pulls the cost down, and 88 × 1.2 = ₹105.60, not ₹132.

Concept

Alligation finds the ratio in which two prices mix to give a mean price. Each grade's share is the gap between the other grade's price and the mean: cheaper : dearer = (dearer − mean) : (mean − cheaper).

The mean must be a cost price. The ₹132 in the question is a selling price with 20% profit on it, so divide by 1.2 to reach the ₹110 cost first.

The ₹132 selling price is above both grade prices. Fed straight into alligation it gives 120 − 132 = −12, a negative share, which is the signal that the profit has not been removed.

Key facts

Cost price = selling price ÷ (1 + profit %): 132 ÷ 1.2 = ₹110.
Cheaper : dearer = (dearer − mean) : (mean − cheaper).
₹110 is 30 away from ₹80 but only 10 away from ₹120, so the mix leans 1 : 3 towards the ₹120 grade.

Study next

Alligation with a free ingredient, such as water added to milkFinding the quantity of one grade to add to a fixed amount of the otherMixtures of three varieties where the ratio is given and one price is unknown

Common traps

Using ₹132 as the mean price without first removing the 20% profit.
Writing the ratio the wrong way round, 3 : 1, by setting each difference against its own price.

12 Sep 2025, 09:00, Quant Q.17 is the same frame: oils at ₹90 and ₹150 sold at ₹144 with 20% profit give a cost of ₹120, and (150 − 120) : (120 − 90) = 1 : 1.

24 Sep 2024, 09:00, Quant Q.18 does it with sugar: ₹75 at a 20% gain means a cost of ₹62.50, so ₹78 and ₹46 sugar mix as (62.5 − 46) : (78 − 62.5) = 16.5 : 15.5 = 33 : 31.

Related PYQs

No directly related past PYQ was found.

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