Question
Ratio of age of 'X' three years hence to the age of 'Y'
five years ago is 7:9. Ratio of age of 'X' four years ago to the age of 'Y' two years hence is 3:5. Find the present age (in years) of 'X'.Solution
ATQ, Let the present age of 'X' and 'Y' be 'm' years and 'n' years respectively.
ATQ;
(m + 3) : (n − 5) = 7 : 9
Or, 9 × (m + 3) = 7 × (n − 5)
Or, 9m + 27 = 7n − 35
Or, 7n − 9m = 62 -------- (I) (m − 4) : (n + 2) = 3 : 5
Or, 5 × (m − 4) = 3 × (n + 2)
Or, 5m − 20 = 3n + 6
Or, 5m − 3n = 26 -------- (II) Multiply (I) by 3:
21n − 27m = 186
Multiply (II) by 7:
35m − 21n = 182
Add:
8m = 368
Or, m = 46 years
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