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Pure ghee costing Rs. 100 per kilogram and vegetable oil costing Rs. 50 per kilogram are mixed in some ratio and sold at Rs.96 per kilogram so as to gain 20%. In what ratio is ghee and oil mixed?

Pure ghee costing Rs. 100 per kilogram and vegetable oil costing Rs. 50 per kilogram are mixed in some ratio and sold at Rs.96 per kilogram so as to gain 20%. In what ratio is ghee and oil mixed? Correct Answer 3 : 2

SP of mixture = Rs. 96

CP of mixture = 96 × (100/120) = 80

Using Allegation method:

∴ Ratio of ghee and oil mixed = 30 : 20 = 3 : 2

Alternate method:

SP of mixture = Rs. 96

CP of mixture = 96 × (100/120) = 80

Let the quantity of ghee and oil mixed be x kg and y kg respectively.

According to the question

100x + 50y = (x + y) × 80

⇒ 100x + 50y = 80x + 80y

⇒ 100x - 80x = 80y - 50y

⇒ 20x = 30y

⇒ x : y = 3 : 2

∴ Ratio of ghee and oil mixed = 30 : 20 = 3 : 2

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