Multiple choice

The age of a son, who is more than two years old, is equal to the units digit of the age of his father. After ten years, the age of the father will be thrice the age of the son. What is the sum of the present ages of the son and the father?

  1. 30 years

  2. 36 years

  3. 40 years

  4. Cannot be determined
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C Correct answer
Explanation

Let son's age be S, father's age be F. S = units digit of F. F + 10 = 3(S + 10). F + 10 = 3S + 30, so F = 3S + 20. Since S is the units digit of F, F must end in S. If S=5, F=35 (ends in 5). If S=6, F=38 (ends in 8). If S=5, F=35, sum = 40.

AI explanation

Let the son's age be the single digit x, making the father's age a number ending in x, such as 10a plus x. The condition that after ten years the father's age will be thrice the son's age translates to 10a plus x plus 10 equals 3 times (x plus 10). This simplifies to 10a minus 2x equals 20, or 5a minus x equals 10. Since the son is more than two years old, testing x equals 5 yields a equals 3, meaning the father is 35 and the son is 5; after ten years, their ages are 45 and 15, which properly satisfies the three times condition. Adding their present ages of 35 and 5 gives a total of 40 years.

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