Question
Five years ago, the ratio of ages of 'X' and 'Y' was 2:3,
respectively. Seven years from now, the ratio of their ages will be 4:5, respectively. If 'Z' is eight years elder than Y, then find the average present age (in years) of 'X' and 'Z'.Solution
ATQ,
Let the age of 'X' and 'Y' five years ago be '2n' and '3n' years, respectively.
So, (2n + 5 + 7) : (3n + 5 + 7) = 4:5
Or, 5 × (2n + 12) = 4 × (3n + 12)
Or, 10n + 60 = 12n + 48
Or, 2n = 12
Or, n = 6
Present age of 'X' = 2 × 6 + 5 = 17 years
Present age of 'Y' = 3 × 6 + 5 = 23 years
Present age of 'Z' = 23 + 8 = 31 years
Required average = (17 + 31) ÷ 2 = 24 years
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