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In a mixture of 30 litres, alcohol and water are in the ratio of 3 : 2. If 20 litres of mixture is removed and then 15 litres of alcohol and 10 litres of water is added to the mixture. What is the ratio of alcohol and water in the new mixture?1. 2 : 32. 3 : 23. 3 : 54. 5 : 35. None of these |
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Answer» Correct Answer - Option 2 : 3 : 2 Given: Initial quantity of mixture = 30 litres Initial ratio of alcohol and water = 3 : 2 Amount of mixture removed = 20 litres Amount of alcohol added = 15 litres Amount of water added = 10 litres Calculations: Let the initial quantity of alcohol and water be 3x and 2x respectively. After removal of 20 litres of mixture, Remaining quantity of mixture = 30 – 20 ⇒ 10 litres ∵ Ratio of alcohol and water will remain same after removal of mixture, 3x + 2x = 10 ⇒ 5x = 10 ⇒ x = 2 Now, remaining amount of alcohol in the mixture = 3x ⇒ 3 × 2 ⇒ 6 litres Remaining amount of water in the mixture = 2x ⇒ 2 × 2 ⇒ 4 litres After addition of 15 litres of alcohol and 10 litres of water, New amount of alcohol = 6 + 15 ⇒ 21 litres New amount of water = 4 + 10 ⇒ 14 litres Ratio of new amount of alcohol to new amount of water = 21 : 14 ⇒ 3 : 2 ∴ The ratio of alcohol and water in the new mixture = 3 : 2 |
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