Question

The average weight of students in a class is 49kg. Five new students are admitted in the class whose weights are 45 kg, 46.8 kg, 47.4 kg, 54.2 kg and 63.6 kg. Now, the average weight of all the students in the class is 50 kg. The number of students in the class in the beginning was:
1. 10
2. 12
3. 8
4. 7

Answer 1

Correct Answer - Option 4 : 7

Given:

Average weight of class = 49kg

New average weight of all students in a class = 50kg

Formula:

Average weight of n students = Total weight of n students/n

Calculation:

Let original number of students in a class be n.

Original total weight of a class = n × 49 = 49n kg

New total weight of a class = 49n + 45 + 46.8 + 47.4 + 54.2 + 63.6 = 49n + 257

Total new number of students in a class = n + 5

New total weight of a class = 50(n + 5) = 50n + 250

Then,

⇒ 49n + 257 = 50n + 250

⇒ n = 7

∴ There are 7 students in a class in the beginning.