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

Answer: Option D

$$\begin{array}{rl}& \Rightarrow \frac{x_1+x_2+.....+x_{10}}{10}=\overline{x}\\ & \Rightarrow x_1+x_2+.....+x_{10}=10\overline{x}\\ & \Rightarrow \frac{110}{100}{x}_1+\frac{110}{100}{x}_2+.....+\frac{110}{100}{x}_{10}=\frac{110}{100}\times 10\overline{x}\\ & \Rightarrow \frac{\frac{110}{100}{x}_1+\frac{110}{100}{x}_2+.....+\frac{110}{100}{x}_{10}}{10}=\frac{11}{10}\overline{x}\end{array}$$
⇒ Average is increased by 10%