Question

The sum of the ages of Anup and his father is 100 . Anup is as old as his father now , he will be 5 times as old as his son Anuj is now . Anuj will be 8 years older than Anup is now , when Anup is as old as his father . What are their ages now ?

I think in this line , "Anuj will be 8 years older than Anup is now . " In place of Anup it should be Anuj and vice versa .

If it's correct please answer the question .

Answer 1

Let Anup's age be A and Anup's father's age = F. Then A + F = 100.
Father's age F = 100 - A.
When Anup is as old as his father, his age will be (100 - A).
Difference between Anup's age now and then = (100 - A) - A = (100 - 2A).
Hence Anup will reach his father's age after (100 - 2A) years.
Anuj's age now = (1/5) of Anup's age when his age equals his father's age = (100 - A)/5.

Anuj's age when Anup attains his father's age,i.e., after (100 - 2A) Years = [(100 - A)/5] + (100 - 2A).
This age is 8 years more than Anup's age now,i.e., 8 more than A = A + 8.
Hence [(100 - A)/5] + (100 - 2A) = A + 8
Solving, Anup's age A = 35, Anup's father's age F = 65, Anuj's age = (100 - 35)/5 = 13

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