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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.
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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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