Question
'Anoop, Bittu, Chetan, and Danny' are the four staff
members. Find "Danny's" current age. Statement I: The ratio of Anoop's current age to Bittu's is 3:5, and the ratio of Bittu's current age to Danny is 5:7. In five years, Danny and Bittu will be three times older than each other. Statement II: The average age of "Bittu" and "Chetan" is currently 23 years, while the average age of "Anoop," "Bittu," "Chetan," and "Danny" is currently 24 years. Statement III: "Anoop" is ten years younger than "Bittu," who is fifteen years younger than "Chetan," who is five years older than "Danny." The age difference between Danny and Anoop is currently 3:7. Statement IV: The current ages of "Anoop," "Bittu," "Chetan," and "Danny" are 3:5:8:7, in that order. The total age of "Bittu" and "Chetan" will be 73 years in four years. The question consists of four statements numbered “I, II, III and IV” given below it. You have to decide that the data provided in which of the following statement alone is not sufficient to answer the question.Solution
ATQ, Statement I: Let present age of ‘Anoop’ and ‘Bittu’ is ‘3x’ years and ‘5x’ years, respectively. Present age of ‘Danny’ = ‘7x’ years According to statement, (5x + 5)/(7x + 5) = 3/4 Or, 20x + 20 = 21x + 15 Or, x = 5 Therefore, present age of ‘Danny’ = 7 × 5 = 35 years So, data in statement I alone is sufficient to answer the question. Statement II: Sum of present age of ‘Anoop’, ‘Bittu’, ‘Chetan’ and ‘Danny’ = 24 × 4 = 96 years Sum of present age of ‘Bittu’ and ‘Chetan’ = 23 × 2 = 46 years Since, we cannot find the present age of ‘Danny’. So, data in statement II alone is not sufficient to answer the question. Statement III: Let present age of ‘Danny’ be ‘x’ years. So, Present age of ‘Chetan’ = ‘x + 5’ years And, Present age of ‘Bittu’ = x + 5 – 15 = ‘x – 10’ years And, Present age of ‘Anoop’ = x – 10 – 10 = ‘x – 20’ years According to statement, (x – 20)/x = 3/7 Or, 7x – 140 = 3x Or, x = 35 Therefore, present age of ‘Danny’ = 35 years Statement IV: Let present age of ‘Anoop’, ‘Bittu’, ‘Chetan’ and ‘Danny’ be ‘3x’ years, ‘5x’ years, ‘8x’ years and ‘7x’ years, respectively. Present age of ‘Bittu’ and ‘Chetan’ = 73 – 8 = 65 years So, 5x + 8x = 65 Or, x = 5 Therefore, present age of ‘Danny’ = 7 × 5 = 35 years So, data in statement IV alone is sufficient to answer the question.
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