Question

The sum of a fathers age and his son son's age is 100 years. Also, one-tenth of the product of their ages, in years exceeds the father's age by 180. How old is the son ?

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Answer 1

Here you go...

Solving:

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

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