Question
‘B’ is 14 years older than ‘A’, and ‘A’ is
24 years younger than ‘C’. Twelve years from now, the age of ‘C’ will be 25% more than the age of ‘A’. If the average of the present ages of ‘A’ and ‘D’ is 85 years, find the ratio of the ages of ‘B’ to ‘D’, 6 years ago.Solution
ATQ,
Let present age of ‘C’ be ‘x’ years. Present age of ‘A’ = x – 24 Present age of ‘B’ = (x – 24) + 14 = x – 10 Twelve years hence: 1.25 × [(x – 24) + 12] = x + 12 ⇒ 1.25 × (x – 12) = x + 12 ⇒ 1.25x – 15 = x + 12 ⇒ 0.25x = 27 ⇒ x = 108 Present age of ‘B’ = 108 – 10 = 98 years Present age of ‘A’ = 108 – 24 = 84 years Average(A, D) = 85 ⇒ (A + D)/2 = 85 ⇒ D = 170 – 84 = 86 years Required ratio (6 years ago) = (98 – 6) : (86 – 6) = 92 : 80 = 23 : 20
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