Question
The current ages of 'Armaan' and 'Bhanu' are in the
ratio 3:5. 'Chetna' is presently 8 years older than 'Armaan.' Determine the current age of 'Armaan.' Statement I: The gap between the present ages of 'Bhanu' and 'Chetna' is 4 years. Statement II: In 10 years, the ratio of ages between 'Bhanu' and 'Chetna' will be 10:9, respectively. The question consists of two statements numbered "I and II" given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. A) The data in statement I alone are sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. B) The data in statement II alone are sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. C) The data either in statement I alone or in statement II alone is sufficient to answer the question. D) The data given in both statements I and II together is not sufficient to answer the question. E) The data in both statements I and II together is necessary to answer the question.Solution
ATQ, Let the present ages of 'Armaan' and 'Bhanu' be '3a' years and '5a' years, respectively. So, present age of 'Chetna' = '3a + 8' years Statement l: There are two possible cases, Case a: Age of Bhanu > Age of Chetna So, 5a = 3a +8+4 or, 2a = 12 a = 6 So, present age of 'Armaan' = 6 × 3 = 18 years Case b: Age of Bhanu < Age of Chetna So, 5a + 4 = 3a + 8 Or, 2a = 4 So, a = 2 So, present age of 'Armaan' = 2 × 3 = 6 years Both cases are possible. So, data in statement I alone is not sufficient to answer the question. Statement II: According to the statement: {(5a + 10) /(3a + 8 + 10) } = (10/9) Or, 9 × (5a + 10) = 10 × (3a + 18) Or, 45a + 90 = 30a + 180 Or, 15a = 90 So, a = 6 So, present age of 'Armaan' = 6 × 3 = 18 years So, data in statement II alone is sufficient to answer the question.
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