A school had 120 students with an average age of 20 years. Later, a new batch of students joined. After their inclusion, the average age dropped to 19.5 years, even though the newcomers had an average age of 18 years. Find the number of students in the new batch.
Show answer & explanation
Correct answer: C
Explanation
Given:
Number of initial students = 120
Initial average age = 20 years
Average age of new students = 18 years
New average = 19.5 years
Initial total age = 120 × 20 = 2400
Let the number of new students = x
Total age of new students = 18x
New total average
(2400 + 18x) / (120 + x) = 19.5
2400 + 18x = 19.5(120 + x)
2400 + 18x = 2340 + 19.5x
60 = 1.5x
x = 40