CA Foundation · Quantitative Aptitude · Equations
The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 4 times the father's age at that time. What is the present age of the son?
The son is 9 years old. Writing ages five years ago as x−5 and 40−x, the condition (x−5)(40−x)=4(40−x) simplifies to x−5=4, so x=9. The father is then 36, and five years ago 4×31 equals the product 124.
- A13 years
- B15 years
- C9 yearsCorrect
- D10 years
Explanation
Let son be x, father 45−x. Five years ago: (x−5)(40−x)=4(40−x), so x−5=4 giving x=9 (or 40−x=0, x=40, which makes the son's age before 5 years 35 and father 5 years ago zero, rejected). Check: son 9, father 36; five years ago 4 and 31; product 124=4×31. Option 13 results from using x−5=8.
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