Question

The average of n numbers $x_1,x_2,x_3$,..... $x_n$ is A. If $x_1$ is replaced by $(x+a)x_1,x_2$ is replaced by $(x+a)x_2$......, then the new average is ___________.

• A. $(x+a)A$
• B. $\frac{(x-1)A+n{x}_n}{n}$
• C. $\frac{nA+(n+1)x_n}{n}$
• D. $\frac{(n+1)A+x_n}{n}$

Answer 1

The correct option is A $(x+a)A$

If the average of $n$ numbers is $A$, then $x_1+x_2+\dots x_n=An$ ....(q)

Average of $x_1(x+a),x_2(x+a)+\cdots +x_n(x+a)$ is given as

$\Rightarrow \frac{x_1(x+a)+x_2(x+a)+\cdots +x_n(x+a)}{n}=\frac{(x+a)(x_1+x_2+\cdots +x_n)}{n}$

$=\frac{(x+a)An}{n}$ .....(From equation (1))

$=(x+a)A$