The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 34. The age of the father is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 39 years
Five years ago each of the two was 5 years younger, so the sum of their ages then was 10 less. Knowing that sum and the product of the two ages fixes both ages.
Ages five years ago (father \(a\), son \(b\)):
\(a+b=45-10=35\) (1)
\(ab=34\) (2)
Two numbers with sum 35 and product 34 (from (1) and (2)):
The factor pairs of 34 are 1 × 34 and 2 × 17; only 34 and 1 add up to 35
The father is the elder, so \(a=34\) and \(b=1\)
Father’s age now \(=34+5=\) 39 years (the son is \(1+5=6\) years)