Question

The average of $12$ numbers is $9$. If each number is multiplied by $2$ and added to $3$, the average of the new set of numbers is

• A. $9$
• B. $18$
• C. $21$
• D. $27$

Answer 1

The correct option is C $21$

Let the sum of 12 no. be $x=x_1+x_2+........x_{12}$

$average=\frac{\text{sum of no.}}{\text{total no.}}$

$\Rightarrow 9=\frac{x}{12}$

$sum=108$

let sum of new numbers is

according to question

$(x_1\times 2+3)+(x_2\times 2+3)+......(x_{12}\times 2+3)$

$\Rightarrow 2\times (x_1+x_2+.....x_{12})+12\times 3$

$sum=2\times 108+12\times 3=216+36=252$

$average=252/12=21$

$\therefore \text{correct option is C.}$