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
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
– x2 = 185
∴ 0
= x2 – 42x + 185
∴ x2
– 42x + 185 = 0
∴ x2
– 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.
