The average age of students in a class was 15 years. When 5 new boys whose average age was 12 years 6 months were admitted, the average age was reduced by 6 months. How many students were there in the class originally?

The class originally had 20 students.

The new boys average 12 years 6 months = 12.5, and the new class average is 15 - 0.5 = 14.5.

With n original students, total age = 15n and new total = 15n + 5(12.5).

So (15n + 62.5)/(n + 5) = 14.5.

15n + 62.5 = 14.5n + 72.5 gives 0.5n = 10.

Thus n = 20.