Question
There are four friends in a group: A, B, C, and D. What
is the present average age of the friends? Statement I: The present age of D is one-third the age of A, and the present age of B is 4 years less than the age of A. The average age of D and C is 16 years, and D is 24 years younger than B. Statement II: Seven years ago, D was one-fifth the age of A. The difference between the age of B and the age of D is the same as the difference between the age of A and the age of C. The average age of C and B is 28 years. 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.Solution
ATQ, Let, age of 'D' = 'd' years Present age of 'A' = 'f' years Present age of 'B' = 'm' years Present age of 'C' = 's' years Statement-I: So, 3d = f f – m = 4 f = 4 + m d + s = 32 m – d = 24 m = d + 24 Since 3d = 4 + m 3d = 4 + d + 24 2d = 28 d = 14 years f = 3d = 42 years m = 14 + 24 = 38 years s = 32 – 14 = 18 years Average age of friends = (14 + 18 + 42 + 38)/4 = 28 years So, data in statement-I alone is sufficient to answer the question. Statement-II: So, 5 × (d – 7) = (f – 7) 5d – 35 = f – 7 5d – 28 = f And, f – s = m – d f + d = m + s m + s = 28 × 2 = 56 m + s + f + d = 56 + 56 = 112 Average age of friends = 112/4 = 28 years So, data in statement-II alone is sufficient to answer the question.
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