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In a vessel, milk and water are in a ratio of 3 : 5. In the second vessel, the milk and water are in the ratio of 3 : 2. In what ratio should these two mixtures be mixed to form a new mixture in which the milk and water are in the ratio 2 : 3?1. 1 : 82. 6 : 13. 7 : 14. 8 : 15. None of these |
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Answer» Correct Answer - Option 4 : 8 : 1 Given: The ratio of milk and water in the first vessel = 3 : 5 The ratio of milk and water in the second vessel = 3 : 2 The ratio of milk and water in the final mixture = 2 : 3 Concept used: (New quantity of milk/New quantity of water) = (Quantity of milk taken from first vessel + Quantity of milk taken from the second vessel)/(Quantity of water taken from first vessel + Quantity of water taken from the second vessel) Calculation: Let the mixture from the two-vessel be mixed in the ratio x : y. Quantity of milk taken from the first vessel = 3x/8 Quantity of water taken from the first vessel = 5x/8 Quantity of milk taken from the second vessel = 3y/5 Quantity of water taken from the second vessel = 2y/5 Then, {(3x/8) + (3y/5}/{(5x/8) + (2y/5)} = 2/3 ⇒ {(15x + 24y)/40}/{(25x + 16y)/40} = 2/3 ⇒ 3(15x + 24y) = 2(25x + 16y) ⇒ 45x + 72y = 50x + 32y ⇒ 50x – 45x = 72y – 32y ⇒ 5x = 40y ⇒ x/y = 8/1 ∴ The first and second ratio is mixed in the ratio 8 : 1. |
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