Multiple choice

B is 8 years older than A and 8 years younger than C. 12 years hence, respective ratio of the ages of A and C will be 5 : 9. What is the sum of present ages of A, B and C?

  1. 58 years

  2. 46 years

  3. 48 years

  4. 60 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A's age be x. Then B is x+8 and C is x+16. In 12 years, A will be x+12 and C will be x+28. Given (x+12)/(x+28) = 5/9, we get 9x + 108 = 5x + 140, so 4x = 32, x = 8. Present ages: A=8, B=16, C=24. Sum = 8+16+24 = 48.

AI explanation

Let the present age of A be x years, which makes B's age x plus 8 and C's age x plus 16. Twelve years hence, the ratio of A's age to C's age will be 5 to 9, giving the equation x plus 12 over x plus 28 equals 5 over 9. Cross multiplying yields 9x plus 108 equals 5x plus 140, so 4x equals 32 and x equals 8. The sum of their present ages is x plus x plus 8 plus x plus 16, which equals 3x plus 24; substituting x equals 8 gives a total of 48 years.

Keep practicing — related questions