Question

Five years ago, a man was seven times as old as his son, while five year hence, the man will be four times as old as his son. Find their present age

Answer 1

suppose age of father or a man=x
age of his son=y
A.TQ
5 years ago age of father=x-5
and 5 years ago age of his son=y-5
so x-5=7(y-5)
x-5=7y-35
x-7y=-35+5
x-7y=-30........1
after 5 years age of father=x+5
after 5 years age of his son=y+5
so x+5=4 (y+5)
x+5=4y+20
x-4y=20-5
x-4y=15.......2
by elimination method
x-7y=-30
x-4y=15
subtract equation 2 from 1
sign will change due to substation
x-7y=-30
x-4y= 15
- + -
-3y=-45
y=-45/-3
y=15

put value of y in equation 1 or 2
x-7y=-30
x-7(15)=-30
x-105=-30
x=-30+105
x=75

so age of father=x=75
and age of his son=y=15