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If a dairy mixes cow’s milk which contains 10% fat with buffalo’s milk which contains 20% fat, then the resulting mixture has fat (120/7) % of fat. In what ratio was the cow’s milk mixed with buffalo’s milk?

If a dairy mixes cow’s milk which contains 10% fat with buffalo’s milk which contains 20% fat, then the resulting mixture has fat (120/7) % of fat. In what ratio was the cow’s milk mixed with buffalo’s milk? Correct Answer 2 : 5

Let the amount of cow milk be x and buffalo milk be 1.

⇒ Amount of fat added = 10% of x + 20% of 1 = 0.1x + 0.2

⇒ Total amount of milk = 1 + x

⇒ Net fat % = {(0.1x + 0.2) / (1 + x)} × 100 = 120/7

⇒ (0.1x + 0.2) / (1 + x) = 6/35

⇒ 3.5x + 7 = 6 + 6x

⇒ x = 1/2.5 = 2/5

∴ Required ratio = 2 : 5

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