Question

The mean of $10,6,13,x+3,2$and $2x-1$is $9$. The value of $x$is-

• A. $7$
• B. $8$
• C. $9$
• D. $6$

Answer 1

The correct option is A

$7$

The numbers are $10,6,13,x+3,2,2x-1$

Sum of numbers $=10+6+13+x+3+2+2x-1$

$=3x+33$

Number of terms$=6$

The mean of the given numbers $=9$

We know that,

Mean $=\frac{\mathbf{S}\mathbf{u}\mathbf{m}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{n}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{s}\mathbf{}}{\mathbf{N}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{t}\mathbf{e}\mathbf{r}\mathbf{m}\mathbf{s}}$

$\begin{array}{rcl}& \Rightarrow & 9=\frac{3x+33}{6}\\ & \Rightarrow & 9\times 6=3x+33\\ & \Rightarrow & 54=3x+33\\ & \Rightarrow & 54-33=3x\\ & \Rightarrow & 3x=21\\ & \Rightarrow & x=\frac{21}{3}\\ & \Rightarrow & x=7\end{array}$

So, the value of $x=7$

Hence, option A is correct