Question

Question 11
The mean of 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 answer is D.
Let the numbers be $x_1,x_2,x_3,x_4$ and $x_5$.
Given, mean of the five numbers = 30
$\Rightarrow \frac{x_1+x_2+x_3+x_4+x_5}{5}=30$
$\Rightarrow x_1+x_2+x_3+x_4+x_5=150$
$\Rightarrow x_1+x_2+x_3+x_4=150-x_5$
On dividing both sides by 4, we get,
$\frac{x_1+x_2+x_3+x_4}{5}=\frac{150-x_5}{4}\dots \dots \left(i\right)$
Given, mean of the four numbers = 28
$\therefore \frac{150-x_5}{4}=28$ [from Eq. (i)]
$\Rightarrow 150-x_5=112$
$\Rightarrow x_5=150-112$
$\Rightarrow x_5=38$
Hence, the excluded number is 38.