Question

The sum of the ages of Vivek and his younger brother Amit is 47 years. The product of their ages in years is 550. Find their ages.

Answer 1

Let Vivek’s present age be x years.

His brother’s age = (47 – x) years

According to question,

x(47 – x) = 550

⇒ 47x – x² = 550

⇒ x² – 47x + 550 = 0

⇒ x² – 25x – 22x + 550 = 0

⇒ x(x – 25) – 22(x – 25) – 0

⇒ (x – 25)(x – 22) = 0

⇒ x – 25 = 0 or x – 22 = 0

⇒ x = 25 or x = 22

When x = 25, then 47 – x = 47 – 25 = 22

When x = 22, then 47 – x = 47 – 22 = 25      ...(Does not satisfy the given condition)

∴ Vivek's age = x = 25 years.

His younger brother's age = 22 years.