Father’s age is 3 more than four times the age of his son and the product of their ages is 162. Find the father’s age.
Explanation:
Let the son’s present age be x years.
So, father’s present age = (4x + 3) years
Also, product of their ages i.e., x(4x + 3) = 162
⇒ 4x2 + 3x – 162 = 0
⇒ 4x2 + 27x - 24x – 162 = 0
⇒ x(4x + 27) - 6(4x – 27) = 0
⇒ (4x + 27)(x - 6) = 0
∴ Either x = 6 or -27/4
Since, x can not be negative, x = 6 is the only solution.
∴ Son’s age = 6 years and Father’s age = 4x + 3 = 27 years.
Hence, option (b).
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