Multiple choice

The average of the ages of A, B and C at present is 28 years. 7 years ago the ratio of ages of A and C was 1 : 4 and the age of B was 90% more than the age of C. After 8 years the age of C will be what percentage of the present age of A?

  1. 290.55%

  2. 299.9%

  3. 291.66%

  4. 298.67%

  5. None of these

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

Let present ages of A, B, C be a, b, c. Their average is 28, so a + b + c = 84. Seven years ago: (a-7)/(c-7) = 1/4, giving c = 4a - 21. Also, (b-7) = 1.9(c-7), so b = 1.9c - 6.3. Substituting c: b = 1.9(4a-21) - 6.3 = 7.6a - 46.2. Solving a + (7.6a-46.2) + (4a-21) = 84 gives 12.6a = 151.2, so a = 12. Then c = 27, b = 45. After 8 years, C's age = 35. Required percentage = (35/12) × 100 = 291.67%.