Two oils priced at ₹90 per kg and ₹150 per kg are blended and sold at ₹144 per kg, achieving a profit margin of 20%. What is the ratio of the two oils in the mixture?

Correct — A. The ₹144 includes profit, so first find the cost price of the blend.

Cost price = 144 ÷ 1.2 = ₹120 per kg

Alligation, cheaper : dearer
= (150 − 120) : (120 − 90)
= 30 : 30 = 1 : 1 → option (a).

Check: equal amounts average (90 + 150) ÷ 2 = ₹120.

Why the others are wrong

• (b)
  2 : 1 — Either way round it misses ₹120. Two parts ₹90 oil to one of ₹150 costs (180 + 150) ÷ 3 = ₹110 a kg. The reverse costs ₹130.
• (c)
  3 : 2 — 3 : 2 costs ₹114 or ₹126 a kg, depending on which oil takes the 3. Neither is the ₹120 cost price that a 20% profit at ₹144 requires.
• (d)
  4 : 1 — 4 : 1 costs ₹102 or ₹138 a kg. Both miss ₹120, which sits exactly midway between ₹90 and ₹150 and so needs equal amounts.

Alligation needs the mean cost price, never the selling price. A 20% profit means SP = 1.2 × CP, so the blend costs 144 ÷ 1.2 = ₹120 a kg.

The rule: cheaper : dearer = (dearer − mean) : (mean − cheaper). Each oil's share is the distance of the other price from the mean.

Here ₹120 is exactly halfway between ₹90 and ₹150, so the two distances match and the ratio is 1 : 1.

Key facts

• Selling price = cost price × (1 + profit %⁄100), so ₹144 at 20% profit means a cost of ₹120.
• Alligation: cheaper : dearer = (dearer − mean) : (mean − cheaper).
• A mean price exactly midway between two prices means equal quantities.

Common traps

• Using ₹144 as the mean price, which gives (150 − 144) : (144 − 90) = 1 : 9.
• Pairing each oil with its own distance from the mean, which reverses the ratio — harmless at 1 : 1, wrong whenever the parts differ.

No directly related past PYQ was found.