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

The correct answer is (b).

Let $x$ be the number of students in the class originally. The total age of the students in the class originally is $15x$ years. When 5 boys whose average age is 12 years and 6 months are admitted in the class, the total age of the students in the class is $15x + 5 \times 12.5 = 162.5$ years. The average age of the students in the class is now 15 years and 6 months, which is 6 months less than the original average age. This means that the total number of students in the class has increased by 5. Therefore, $x = \frac{162.5 – 15 \times 6}{6} = 24$.

Option (a) is incorrect because 20 students would give an average age of 15 years and 3 months, which is not 6 months less than the original average age. Option (c) is incorrect because 25 students would give an average age of 15 years and 1 month, which is not 6 months less than the original average age. Option (d) is incorrect because 30 students would give an average age of 15 years, which is not 6 months less than the original average age.