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Question
The sum of the ages of Anup and his father is 100. When Anup is as old as his father now, he will be five times as old as his son Anuj is now. Anuj will be eight years older than Anup is now, when Anup is as old as his father. What are their ages now?
Solution
When Anup is as old as his father now, i.e.,
After (100 – x) – x years Anuj’s age is equal to his fathers present age + 8
⇒ Present age of Anuj + (100 – 2x) = Present age of Anup + 8
= 100 – x + 5(100 – 2x) = 5(x + 8)
= 100 – x + 500 – 10x = 5x + 40
= –11x – 5x = 40 – 600
= x = `(-560)/(-16)`
= 35
∴ Anup’s present age is 35 years
Father’s present age = 100 – 35 = 65 years
Anuj’s present age = `(100 - 35)/5`
= 13 years
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