Question

The average weight of a class of 20 students is 45kgs. A new student whose weight is 40kg replaces an old student of this class. Hence, the average weight of the whole class decreases by 1kg. The weight of the replaced student is:
A. 55 kg
B. 50kg
C. 60kg
D. None of these

Answer 1

Hint: To solve this question we will first calculate the total weight of 20 boys by using the formula, $\text{average weight=}\dfrac{\text{total weight}}{\text{number of boys}}$. After calculating the weight of those 20 students, we will again calculate the new weight of the students of the class. And then by subtracting, we will find the weight of that student.

Complete step by step answer:
Given that the average weight of a class of 20 students is 45kg. A new student whose weight is 40kg replaces an old student of this class. Hence, the average weight of the whole class decreases by 1kg and we have to find the weight of that student. As we know that we can calculate the average weight of the class by the formula:
$\text{average weight=}\dfrac{\text{total weight}}{\text{number of boys}}$
Total number of students = 20
Their average weight first = 45kg
Hence, $45=\dfrac{\text{total weight}}{20}$
So, the total weight of the class = 900kg.
Now if the weight of the new student who joined the class = 40kg,
Let us consider the weight of the student who left the class = $xkg$ .
So, now the new total net weight = $900+40-xkg=940-xkg$.
And the average weight is now 44kg, so,
$\begin{align}
  & 44=\dfrac{940-x}{20} \\
 & \Rightarrow 940-x=880 \\
 & \Rightarrow x=940-880 \\
 & \Rightarrow x=60 \\
\end{align}$
So, the weight of that student was 60kg.

So, the correct answer is “Option C”.

Note: While solving this type of questions, you have to be careful about the total weight and all the other calculations. And if it is asked to find the average weight or total number of students, then we can calculate all that without using another formula, we will use this same formula for calculating them too.