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 father 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?
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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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