The mean of five numbers is `30.` If one number is excluded, their mean becomes . The excluded number is

Options

A. `28`
B. `30`
C. `35`
D. `38`

Answer

D

Explanation

Let `x_(1), x_(2), x_(3), x_(4)` and `x_(5)` be five numbers and one of the exluded number is `x_(5)`.
Given, mean of the five numbers `= 30`
`rArr (x_(1)+x_(2)+x_(3)+x_(4) + x_(5))/(5)=30`
`rArr x_(1) + x_(2) + x_(3) + x_(4)=150`
`rArr x_(1)+x_(2)+x_(3)+x_(4)=150 - x_(5)`
On dividing both sides by 4, we get
`(x_(1)+x_(2)+x_(3)+x_(4))/(4)=(150-x_(5))/4`..........(i)
Given, mean of the four numbers =28
`therefore (150-x^(5))/4=28` (from Eq. (i))
`rArr 150-x_(5)=112`
`rArr x_(5)=150-112`
`rArr x_(5)=38`
Hence, the exluded number is `38.`