Average of ten positive numbers is $$\overline x $$. If each number is increased by 10%, then $$\overline x $$ -

$$\eqalign{ & \Rightarrow \frac{{{x_1} + {x_2} + ..... + {x_{10}}}}{{10}} = \overline x \cr & \Rightarrow {x_1} + {x_2} + ..... + {x_{10}} = 10\overline x \cr & \Rightarrow \frac{{110}}{{100}}{x_1} + \frac{{110}}{{100}}{x_2} + ..... + \frac{{110}}{{100}}{x_{10}} = \frac{{110}}{{100}} \times 10\overline x \cr & \Rightarrow \frac{{\frac{{110}}{{100}}{x_1} + \frac{{110}}{{100}}{x_2} + ..... + \frac{{110}}{{100}}{x_{10}}}}{{10}} = \frac{{11}}{{10}}\overline x \cr} $$
⇒ Average is increased by 10%