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Directions: The following question is accompanied by two statements (I), (II). You have to determine which statements(s) is/are sufficient/necessary to answer the questions.What is the quantity of alcohol in 120 liters of a mixture of alcohol and water?Statement I: If 12 liters of water is poured into the mixture, then the ratio of alcohol and water would be 8 : 3.Statement II: If 20 liters of the solution is taken out and replaced with pure alcohol, then the ratio of the quantity of alcohol to that of water in the solution will be 5 : 1.1.Statement I alone is sufficient to answer the question but statement II alone is not sufficient. 2.Statement II alone is sufficient to answer the question but statement I alone is not sufficient. 3.Both statement I and statement II together is needed to answer the question.4.Neither statement I and nor statement II is sufficient to answer the question. 5. Either statement I alone or statement II alone is sufficient to answer the question. |
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Answer» Correct Answer - Option 5 : Either statement I alone or statement II alone is sufficient to answer the question. Statement I: Given: Added quantity of water = 20 l Ratio of alcohol and water after addition of water = 8 : 3 Calculation: Let x be the initial quantity of water Equating the quantity of water {(x + 12)/(120 + 12)} = 3/(8 + 3) ⇒ (x + 12)/132 = 3/11 ⇒ (x + 12)/12 = 3 ⇒ x + 12 = 36 ⇒ x = 36 – 12 = 24 Quantity of water in 120 liters mixture is 24 l Quantity of alcohol in 120 liters mixture is 120 – 24 = 96 l ∴ Statement I alone is sufficient to answer the question. Statement II: Given: Quantity of mixture replaced with alcohol = 20 l The ratio of alcohol and water after replacement = 5 : 1 Calculation: Let the quantity of alcohol be x ⇒ Quantity of alcohol after replacement = (x/120) × 100 = 5x/6 ⇒ Quantity of water after replacement = 100 – (5x/6) Equating with given ratio {(5x/6) + 20}/{100 – (5x/6)} = 5/1 ⇒ {(5x/6) + 20} = 500 – (25x/6) ⇒ (30x/6) = 480 ⇒ x = 480/5 = 96 Quantity of alcohol in 120 liters mixture is 120 – 24 = 96 l The quantity of water in 120 liters mixture is 24 l ∴ Statement II alone is sufficient to answer the question. ∴ Either statement I alone or statement II alone is sufficient to answer the question. |
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