Question

The weighted average marks of $170$ students who appeared in an exam is $55$. It is also known that the average marks of failed students is $23$ and that of passed students is $63$. Find the number of students who passed the exam.

• A. $34$
• B. $62$
• C. $106$
• D. $136$

Answer 1

The correct option is D $136$

The formula to calculate the weighted average is,

$\text{Weighted Average}=\frac{(w_1\times n_1)+(w_2\times n_2)+\dots +(w_l\times n_l)}{w_1+w_2+\dots +w_l}$,

where $w_1,w_2,\dots w_l$ are the weighted factors and $n_1,n_2,\dots n_l$ are the data points.

Let the number of failed students be $x$, then the number of passed students will be $170-x$.

Thus, the given information will be depicted as,


Here, the weighted factors are the number of students with $w_1=x$ and $w_2=170-x$ and their corresponding average marks are the data points denoted by $n_1=23$ and $n_2=63$.

It is given that the weighted average marks is $55$ and the total number of students is $170$, i.e., $w_1+w_2=170$.

Substitute the required values in the formula of weighted average to calculate the value of $x$.

$\begin{array}{cc}55& =\frac{(x\times 23)+\left(\right(170-x)\times 63)}{170}\\ 55\times 170& =23x+10710-63x\\ 9350& =10710-40x\\ 40x& =10710-9350\\ x=\frac{1360}{40}& \\ x& =34\end{array}$

Thus, the number of failed students is $x=34$ and the number of passed students is calculated as,

$\begin{array}{cc}\text{Passed students}& =170-x\\ & =136\end{array}$

Hence, $136$ students passed the exam.

So, option (d) is correct.