Question
Four years ago, the ratio of ages of 'X' and 'Y' was 2:3
respectively. Six years from now, the ratio of their ages will become 4:5 respectively. If 'Z' is 7 years older than 'Y', then what is the average current age (in years) of 'X' and 'Z'?Solution
ATQ,
Let the age of 'X' and 'Y' four years ago be '2n' and '3n' years respectively.
So, (2n + 4 + 6) : (3n + 4 + 6) = 4:5
Or, 5 × (2n + 10) = 4 × (3n + 10)
Or, 10n + 50 = 12n + 40
Or, 2n = 10
Or, 'n' = 5
Present age of 'X' = 2 × 5 + 4 = 14 years
Present age of 'Y' = 3 × 5 + 4 = 19 years
Present age of 'Z' = 19 + 7 = 26 years
Required average = (14 + 26) ÷ 2 = 20 years
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