Question 638661
Father's age =x
son's age = y

x+y = 100
x= 100-y

According to the second condition

(1/10) xy = x+180
xy= 10(x+180)
xy = 10x+1800
xy-10x=1800
x(y-10)=1800
x= 1800/(y-10)

100-y= 1800/(y-10)

(100-y)(y-10)=1800
100y-1000-y^2+10y=1800

y^2-110y+2800 =0

y^2-70y-40y+2800=0
y(y-70)-40(y-70)=0
(y-70)(y-40)=0

y= 70 OR 40

x+y = 100
son's age cannot be more than father's age
so y = 40 
Son's age = 40 years
Fathers age = 60 years