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Two glasses A and B of quantity 200 ml contains milk-water mixture in the ratio 3 ∶ 2 and 3 ∶ 7 respectively. From glass A, 50 ml of the mixture is removed and replaced with water. From glass B, 100 ml of mixture is removed and replaced with milk. If the mixture of the two glasses is mixed, what is the ratio of milk and water in the final mixture?

Two glasses A and B of quantity 200 ml contains milk-water mixture in the ratio 3 ∶ 2 and 3 ∶ 7 respectively. From glass A, 50 ml of the mixture is removed and replaced with water. From glass B, 100 ml of mixture is removed and replaced with milk. If the mixture of the two glasses is mixed, what is the ratio of milk and water in the final mixture? Correct Answer 11 ∶ 9

Considering glass A,

Initial ratio of milk-water mixture = 3 ∶ 2

∵ 50 ml of mixture is removed and replaced with water

⇒ Quantity of milk in glass A = 3/5 × (200 - 50) = 3/5 × 150 = 90 ml

⇒ Quantity of water in glass A = + 50 = (2/5 × 150) + 50 = 60 + 50 = 110 ml

Considering glass B,

Initial ratio of milk-water mixture = 3 ∶ 7

∵ 100 ml of mixture is removed and replaced with milk

⇒ Quantity of milk in glass B = + 100 = (3/10 × 100) + 100 = 30 + 100 = 130 ml

⇒ Quantity of water in glass B = 7/10 × (200 - 100) = 7/10 × 100 = 70 ml

Now, if the mixtures of the two glasses are mixed,

⇒ Quantity of milk in final mixture = 90 + 130 = 220 ml

⇒ Quantity of water in final mixture = 110 + 70 = 180 ml

∴ Ratio of milk and water in final mixture = 220 ∶ 180 = 11 ∶ 9

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