The average weight of some students of a class is 55.5 kg. If 4 students with an average weight of 60 kg join the class, the average weight of all the students increases by 360 g. How many students were there in the class initially?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 46
Each new student is heavier than the old average, and this extra weight is shared by everyone to raise the average by 360 g \(=0.36\) kg.
Let the class have \(n\) students at first; the new average is \(55.5+0.36=55.86\) kg
Extra weight brought by the 4 new students \(=4\times(60-55.5)=18\) kg
This extra raises the average of all \(n+4\) students by 0.36 kg: \(0.36\,(n+4)=18\)
\(\displaystyle n+4=\frac{18}{0.36}=50\), so \(n=46\)
There were 46 students in the class initially.