The average weight of some students in a class was 62.5 kg. When 12 students whose average weight was 66 kg joined the class, the average weight of all the students increased by 0.7 kg. How many students were in the class initially?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 48
The total weight of a group is the average multiplied by the number of members. The total before the 12 students joined, plus their total, must equal the new total.
Let the class initially have \(n\) students; their total weight \(=62.5n\) kg
Total weight of the 12 new students \(=12\times66=792\) kg
New average \(=62.5+0.7=63.2\) kg for \(n+12\) students
\(62.5n+792=63.2(n+12)=63.2n+758.4\)
\(792-758.4=63.2n-62.5n\), so \(33.6=0.7n\)
\(\displaystyle n=\frac{33.6}{0.7}=48\)
The class initially had 48 students.