Question

‘The sum of the ages of a boy and his sister (in years) is 25 and product of their ages is 150. Find their present ages.

Answer 1

Let the boy and his sister's ages be ‘x’ years and ‘y’ years, respectively

According to the question,

x + y = 25  ...(i)

and xy = 150

or, y = `150/x`  ...(ii)

Using equation (ii) in equation (i), we get

`x + 150/x` = 25

⇒ x² – 25x + 150 = 0

⇒ x² – 15x – 10x + 150 = 0

⇒ x(x – 15) – 10(x – 15) = 0

⇒ (x – 15)(x – 10) = 0

⇒ x – 15 = 0 or x – 10 = 0

⇒ x = 15 or x = 10

When x = 15 i.e., boy's age is 15 years.

Then, sister's age, y = `150/15` = 10 years

When x = 10 i.e, boy's age is 10 years

Then, sister's age, y = `150/10` = 15 years