The average weight of a certain number of students in a class is 67.9 kg. When 4 new students weighing 69.5 kg, 69.3 kg, 73.5 kg and 68.5 kg join the class, the average weight of all the students increases by 400 g. How many students were in the class initially?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 19
The total weight is the average multiplied by the number of students. The old total plus the weights of the newcomers must equal the new total.
Let there be \(n\) students initially; their total weight \(=67.9n\) kg
Weight of the 4 new students \(=69.5+69.3+73.5+68.5=280.8\) kg
Rise in the average \(=400\) g \(=0.4\) kg, so the new average \(=67.9+0.4=68.3\) kg
\(67.9n+280.8=68.3(n+4)=68.3n+273.2\)
\(280.8-273.2=0.4n\), so \(7.6=0.4n\)
\(\displaystyle n=\frac{7.6}{0.4}=19\)
The class initially had 19 students.