**7. The sum of the ages of father and his son is 42 years. The product of their ages is 185, find their ages.**

**Sol.**Sum of ages of father and son = 42 years

**= 185**

^{2}**– 42x + 185**

^{2}**– 42x + 185 = 0**

^{2}**– 5x – 37x + 185 = 0**

^{2}
Let father’s age be x years

Son’s
age = (42 – x) years

∴ The
age of his son is (42 – x) years.

As per the given condition,

x (42 – x) = 185

∴ 42x
– x^{2} = 185

∴ 0
= x^{2} – 42x + 185

∴ x^{2}
– 42x + 185 = 0

∴ x^{2}
– 5x – 37x + 185 = 0

∴ x
(x – 5) – 37 (x – 5) = 0

∴ (x
– 5) (x – 37) = 0

∴ x
– 5 = 0 or x – 37 = 0

∴ x
= 5 or x = 37

∵ 5 years cannot be the age of Father.

∴ It is unacceptable,

∴ x
= 37

And 42 – x = 42 – 37 = 5

The
father’s age is 37 years and son’s age 5 years.