### Average of ten positive numbers is $\bar{x}$. If each number is increased by 10%, then $\bar{x}$.

A. Remains unchanged B. May decrease C. May increase D. Is increased by 10% Answer: Option D

### Solution(By Apex Team)

\begin{aligned}&\Rightarrow\frac{x_1+x_2+\ldots.+x_{10}}{10}=\overline{x}\\ &\Rightarrow x_1+x_2+\ldots+x_{10}=10\overline{x}\\ &\Rightarrow\frac{110}{100}x_1+\frac{110}{100}x_2+\ldots.+\frac{110}{100}x_{10}=\frac{110}{100}\times10\overline{x}\\ &\Rightarrow\frac{\frac{110}{100}x_1+\frac{110}{100}x_2+\ldots\ldots+\frac{110}{100}x_{10}}{10}=\frac{11}{10}\overline{x}\\ &\text{⇒ Average is increased by 10%}\end{aligned}

A. 20
B. 21
C. 28
D. 32

A. 18
B. 20
C. 24
D. 30

A. 10 years
B. 10.5 years
C. 11 years
D. 12 years