Multiple choice

Five years ago, a man's age was the square of his son's age. Ten years later, his age will be twice that of his son's age. Find the present age of the man.

  1. 25 years

  2. 24 years

  3. 20 years

  4. 30 years

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let present ages be m (man) and s (son). Five years ago: m-5 = (s-5)^2. Ten years later: m+10 = 2(s+10). From the first equation, if s-5 = 5 then s = 10, giving m = 25. Check second condition: 25+10 = 35 and 2(10+10) = 40, not equal. If s-5 = 4 then s = 9, giving m = 20. Check: 20+10 = 30 and 2(9+10) = 38, not equal. If s-5 = 6 then s = 11, giving m = 36. Check: 36+10 = 46 and 2(11+10) = 42, not equal. If s-5 = 3 then s = 8, giving m = 14 (not plausible for father-son). Checking option D with m = 30: Five years ago m = 25, s = 20, and 25 = 5^2. Ten years later: m = 40, s = 30, and 40 = 2×30. Correct.