Question

The sum of present ages of a father and son is 99 yrs. When the father was as old as his son is now ,his age is 4 times age of the son at that time . The ratio of the present ages of father and son is __

Answer 1

Let the present age of father be 'f' and son be 's'
Given, f + s = 99.............(i)
Let the father was as old as his son now ('s' years) before X years.
father's age = f - X........(a)
son's age = s - X...........(b)
Given f - X = s ...[father's age b4 X years =son's present age]....(ii)
Father's age at that time = 4 times son's age
f - X = 4*(s - X)
s = 4s - 4X
4X = 3s
X = 3s/4......(c)
(c) in (ii)
f - 3s/4 = s
f = 7s/4.....(d)
(d) in (i)
7s/4 + s = 99
7s + 4s = 99*4
11s = 99*4
s = 36
f = 63
So son's present age = 36 & father's present age = 63
Ratio of present ages of father and son = 63 : 36 = 7:4
Hope it helps