Question

The mean of the five numbers is $30$. If one number is excluded, their mean becomes $28$. The excluded number is:

• A. $28$
• B. $30$
• C. $35$
• D. $38$

Answer 1

The correct option is D

$38$

The explanation for the correct option.

Mean of the numbers:

Let the five numbers are $l,m,n,o,\mathrm{and}p$.

$\mathbf{mean}\mathbf{=}\frac{\mathbf{sum}\mathbf{}\mathbf{of}\mathbf{}\mathbf{observations}}{\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{oberservations}}$

Since the mean of the five numbers is $30$.

$$\begin{gathered} \therefore \frac{l+m+n+o+p}{5}=30 \\ \Rightarrow l+m+n+o+p=150...\left(1\right) \end{gathered}$$

Let the excluded number be $p$.

Since If one number is excluded, their mean becomes $28$.

$$\begin{gathered} \therefore \frac{l+m+n+o}{4}=28 \\ \Rightarrow l+m+n+o=112...\left(2\right) \end{gathered}$$

Substitute the value of equation $\left(2\right)$ into equation $\left(1\right)$.

$$\begin{gathered} \therefore 112+p=150 \\ \Rightarrow p=150-112 \\ \Rightarrow p=38 \end{gathered}$$

Thus, the excluded number is $38$.

Hence, the option D is correct.