# `the sum of the ages of anup and his father is 100. when 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?

1
by kevinbansal11

• Brainly User
2014-09-02T18:21:12+05:30
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.
hanks a ton!!!