Question

The mean of the numbers $a,b,c,d$ and $e$ is $23$. The mean of the numbers $a,b,c,d,e$ and $f$ is $22$. What is the value of $f$?

• A. $23$
• B. $17$
• C. $22$
• D. $22.5$
• E. $20$

Answer 1

The correct option is B $17$

Since the mean of the numbers $a,b,c,d$ and $e$ is $23$.

Therefore, $\frac{a+b+c+d+e}{5}=23$

$\Rightarrow a+b+c+d+e=115$ ............(1)

Also, the mean of the numbers $a,b,c,d,e$ and $f$ is $22$, therefore,

$\frac{a+b+c+d+e+f}{6}=22$

$\Rightarrow a+b+c+d+e+f=132$ .............(2)

Put the value of equation (1) in equation (2) as follows:

$115+f=132$ that is

$f=132-115=17$

Hence, $f=17$