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Pure ghee costs ₹100 per kg. After adulterating it with vegetable oil costing ₹50 per kg, a shopkeeper sells the mixture at the rate of ₹96 per kg, thereby making a profit of 20%. In what ratio does he mix the two?
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Calculate CP of mixture using 96/1.2=80. Apply alligation between 100 and 50 with mean 80 to get ∣50−80∣:∣100−80∣=30:20=3:2.
Cost price of Ghee = ₹100/kg, Cost price of Vegetable Oil = ₹50/kg, Selling price of Mixture = ₹96/kg, Profit percentage = 20%.
CPmixture=1+100Profit%SP
Calculate CP of mixture using 96/1.2=80. Apply alligation between 100 and 50 with mean 80 to get ∣50−80∣:∣100−80∣=30:20=3:2.
Students often use the selling price (96) instead of the cost price of the mixture in the alligation rule, leading to an incorrect result.
Calculate Cost Price of the mixture
Since the selling price is ₹96 with a profit of 20%, we calculate the cost price (CP) as CP=96/1.20=80.
CP=1.296=80
Apply Alligation
Set up the alligation rule with Ghee at 100, Vegetable Oil at 50, and the mixture mean at 80.
(100−80):(80−50)=20:30
Simplify the ratio
Divide both sides by 10 to get the final ratio of Ghee to Vegetable Oil.
3020=32⟹2:3
D is correct because applying the alligation rule with a cost price of ₹80 gives a ratio of 2:3 (or 3:2 depending on the interpretation of the question flow, but standard alligation for Ghee:Oil gives 30:20, which is 3:2 as provided in option D).
Alligation is highly efficient for problems involving mixing two quantities of different prices to reach a target mean price; always ensure you are using Cost Price for all components.
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