Multiple choice

In a group of 12 students, the average age is increased by 2 years when three of them are replaced by 5 students, and the total age increased by 50 years. Then what is the sum of their ages?

  1. 132

  2. 154

  3. 172

  4. 182

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

Original: 12 students, total age = 12A. New: 14 students (3 replaced by 5), total age = 12A + 50, average = A + 2. So (12A + 50)/14 = A + 2, giving 12A + 50 = 14A + 28, so 2A = 22 and A = 11. New total sum = 12(11) + 50 = 182. Option D is correct.