SSC CGL 2025 Tier-I · 15 September 2025, Shift 2 · Quantitative Aptitude · Question 11 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.

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A shopkeeper has two types of pulses: one costing ₹60/kg and the other costing ₹90/kg. He mixes them in a specific ratio and sells the mixture at ₹84/kg, thereby earning a 20% profit. In what ratio did he mix the two types of pulses?

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

Answer

Why

Correct — B.
Undo the 20% profit: mixture cost = 84 ÷ 1.2 = ₹70/kg
Alligation, share of the ₹60 pulse: 90 − 70 = 20
Share of the ₹90 pulse: 70 − 60 = 10

Ratio ₹60 pulse : ₹90 pulse = 20 : 10 = 2 : 1 → option (b)

Why the others are wrong

(a)
1 : 3 — 1 : 3 leans on the dearer pulse: cost = (60 + 270) ÷ 4 = ₹82.50/kg. Selling at ₹84 then earns under 2%, not 20%.
(c)
3 : 2 — 3 : 2 gives a cost of (180 + 180) ÷ 5 = ₹72/kg. At ₹84 that is a 16.7% profit, short of the 20% stated.
(d)
4 : 1 — 4 : 1 gives a cost of (240 + 90) ÷ 5 = ₹66/kg. At ₹84 that is about a 27% profit, above the 20% stated.

Concept

Two steps. First strip the profit to get the cost price of the mixture: selling price ÷ (1 + profit rate) = 84 ÷ 1.2 = ₹70.

Then alligation: the mixture's cost sits between the two prices, and each pulse's share equals the gap between the mixture cost and the other pulse's price. ₹70 is 20 below ₹90 and 10 above ₹60, so the cheaper pulse gets the larger share.

Check the ratio forwards: 2 kg at ₹60 plus 1 kg at ₹90 costs ₹210 for 3 kg, which is ₹70/kg. Sold at ₹84, each kg earns ₹14, and 14 ÷ 70 = 20%.

Key facts

Cost of the mixture = selling price ÷ (1 + profit %): 84 ÷ 1.2 = ₹70.
Alligation: cheaper : dearer = (dearer price − mixture cost) : (mixture cost − cheaper price).
The mixture cost lies nearer the ingredient used in the larger quantity: ₹70 is nearer ₹60.

Study next

Alligation when the profit or loss on the mixture's selling price is givenReplacement problems: part of a mixture drawn off and replacedProfit percentage on a mixture when the mixing ratio is given

Common traps

Putting the selling price ₹84 in the alligation cross instead of the cost ₹70
Taking 20% off ₹84 (₹67.20) instead of dividing ₹84 by 1.2 (₹70)
Writing the ratio the wrong way round, 1 : 2, which puts more of the ₹90 pulse in

12 Sep 2025, 09:00, Quant Q.17 is the same two-step problem with oils: sold at ₹144/kg for a 20% profit, the blend costs ₹120/kg, and alligation between ₹90 and ₹150 gives 30 : 30 = 1 : 1.

14 Sep 2025, 09:00, Quant Q.11 runs it forwards: two pulses whose costs you back out of their own profit rates (₹60 and ₹48), mixed 2 : 1 to cost ₹56/kg and sold at ₹70, a 25% profit.

Related PYQs

No directly related past PYQ was found.

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