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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.
Solution
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.
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