Question

Rachna had an average score of $45$ from $6$ test. Her teacher dropped her lowest score, which is $30$ and calculated the average of the remaining scores to decide her grade. Which of the following gives her a new average score?
A. $\dfrac{\left( 45\times 5-30 \right)}{5}$
B. $\dfrac{\left( 45\times 5-30 \right)}{6}$
C. $\dfrac{\left( 45\times 6-30 \right)}{5}$
D. $\dfrac{\left( 45\times 6-30 \right)}{6}$

Answer 1

Hint: Here we will calculate the total score gained by the Rachana in $6$ subjects by using the relation between the total score and number of subjects and average score. Now the teacher revealed the lowest score as $30$ and he dropped that score. So, we will subtract it from the total score gained by Rachana in $6$ subjects, then we will get the total score gained by Rachana in $5$ subjects. Now we will calculate the average score of the Rachana for the $5$ subjects.

Complete step-by-step answer:
Given that,
The average score of Rachana in $6$ subjects is $45$, here
Number of observations is $n=6$
The average of the $n=6$ observations is $\text{Avg}=45$
We know that Average of $n$ observations is
$\text{Avg}=\dfrac{\text{Sum of the all the Observations}}{\text{Total Number of Observations}}$
From the above formula and given data, the sum of the scores in $6$ subjects is
$\begin{align}
  & \text{Sum}=\text{Avg}\times \text{Number of Observations} \\
 & \text{=Avg}\times n \\
 & =45\times 6
\end{align}$
Now the teacher dropped the lowest score $30$ from the sum of the scores in $6$ subjects, then
$\begin{align}
  & \text{Sum of }\left( 6-1 \right)\text{ subjects}=45\times 6-30 \\
 & \text{Sum of 5 subjects}=45\times 6-30
\end{align}$
Here the total number subjects is also reduced to $5$ since the teacher removed the subject score and subject as well.
Now the average is
$\begin{align}
  & \text{Av}{{\text{g}}_{1}}=\dfrac{\text{Sum of the subjects after dropping the lowest score}}{\text{Total number subjects after dropping the lowest score}} \\
 & =\dfrac{45\times 6-30}{5}
\end{align}$
So, the new average is $\dfrac{45\times 6-30}{5}$

So, the correct answer is “Option C”.

Note: Most of the students will forget to subtract one from the total number of subjects when the teacher dropped the lowest score. So please remember that when we remove the lowest score, the number of subjects is also automatically decreasing.