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 DShow Answer
Solution(By Apex Team)
$\begin{aligned}&\Rightarrow\frac{x_1+x_2+\ldots.+x_{10}}{10}=\overline{x}\\
&\Rightarrow x_1+x_2+\ldots+x_{10}=10\overline{x}\\
&\Rightarrow\frac{110}{100}x_1+\frac{110}{100}x_2+\ldots.+\frac{110}{100}x_{10}=\frac{110}{100}\times10\overline{x}\\
&\Rightarrow\frac{\frac{110}{100}x_1+\frac{110}{100}x_2+\ldots\ldots+\frac{110}{100}x_{10}}{10}=\frac{11}{10}\overline{x}\\
&\text{⇒ Average is increased by 10%}\end{aligned}$
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