Question

There are 50 boys in a class. One boy weighing 40 kg goes away and at the same time another boy joins the class. If the average weight of the class is thus decreased by 100 g find the weight of the new boy.
A. 32 kg
B. 40 kg
C. 35 kg
D. 37 kg

Answer 1

Hint: First we will assume a variable for the average weight and then apply the formula: $\text{Average}=\dfrac{\text{Sum of units}}{\text{Number of units}}$ , then we will use the condition given in the question that is once a boy leaves of 40 kg and a new boy joins of y kg then there will be a new average weight which would be 100g less and we will again apply the formula and get the answer.

Complete step by step answer:
Now, we know that according to the formula of average:
 $\text{Average}=\dfrac{\text{Sum of units}}{\text{Number of units}}$
Now, here total numbers of students are 50 and let the average weight of the class be m kg , therefore:
$\Rightarrow m=\dfrac{\text{Total weight of the class}}{50}\Rightarrow \text{Total weight of the class}=50m\text{ kg}$
Now, it is given that one boy leaves the class weighing 40 kg and a new boy joins some weight, now let the weight of the new boy be y kg.
Therefore, the total weight of the class will become: $50m-40+y$ kg $\text{ }.......\left( 1 \right)$
It is also given that the average weight of the class is decreased by 100 g or $\dfrac{100}{1000}=0.1\text{ kg}$ , Therefore, the new average weight will be: $m-0.1$ kg $\text{ }.......\left( 2 \right)$
Now, we will again apply the formula of the average: $\text{Average weight }=\dfrac{\text{Total weight}}{\text{Number of boys}}$
We will now put the values from equation 1 and two: $\left( m-0.1 \right)=\dfrac{50m-40+y}{50}$
Now, we will solve this equation to get the value of y , first of all take 50 from the denominator of RHS to the left hand side, then we will be getting: $50\left( m-0.1 \right)=50m-40+y$
Now, multiply 50 into the bracket on the LHS :
 $\begin{align}
  & \Rightarrow 50m-5=50m-40+y\Rightarrow 50m-50m-5=-40+y \\
 & \Rightarrow -5=-40+y\Rightarrow -5+40=y \\
 & \Rightarrow y=35 \\
\end{align}$
Therefore, the weight of the new boy is 35 kg.
Hence, the correct option is C.
Note:
Common mistake that can be made is with the signs in the equation for example in equation 1 if we write $50m-40-y$ then the value of y would be negative as shown below: $\Rightarrow \left( m-0.1 \right)=\dfrac{50m-40-y}{50}\Rightarrow y=-35$ and we know that weight can’t be negative therefore we should be careful with the signs.