Multiple choice

The sum of ages of a group of teachers, doctors and lawyers is 2160 years and their average age is 36 years. If each teacher had been older by 1 year, each doctor by 6 years and each lawyer by 7 years, their average age would have increased by 5 years. Find the minimum possible number of doctors in the group.

  1. 6

  2. 8

  3. 10

  4. 12

  5. 15
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let T, D, L be the number of teachers, doctors, and lawyers. Total = T+D+L. Average increase = (T*1 + D*6 + L*7) / (T+D+L) = 5. T + 6D + 7L = 5T + 5D + 5L. D + 2L = 4T. To minimize D, we need to balance the variables; solving under constraints leads to D=6.

Keep practicing — related questions