Question

the sum of the ages of father and his son is 42 years. the product of the number the denoting in their ages is 185 find their ages.​

Answer 1

Answer:

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.

Answer 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 – 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.