Multiple choice

In a class of 84 students, the average age of students is 17 years 6 months. Some new students take admission in the class whose average age was 19 years 9 months. As a result, the new average age of students becomes 18 years and 3 months. Find the number of new admitted students.

  1. 36

  2. 48

  3. 24

  4. 42

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x be new students. Original total age = 84 × 17.5 = 1470 years. New students' total age = x × 19.75. Combined average = (1470 + 19.75x) / (84 + x) = 18.25. Solving: 1470 + 19.75x = 18.25(84 + x) = 1533 + 18.25x. 1.5x = 63. x = 42. Verification: (1470 + 829.5) / 126 = 2299.5 / 126 = 18.25. Correct.

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