Average of ten positive numbers is $$\overline x $$. If each number is increased by 10%, then $$\overline x $$ -
A. Remains unchanged
B. May decrease
C. May increase
D. Is increased by 10%
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & \Rightarrow \frac{{{x_1} + {x_2} + ..... + {x_{10}}}}{{10}} = \overline x \cr & \Rightarrow {x_1} + {x_2} + ..... + {x_{10}} = 10\overline x \cr & \Rightarrow \frac{{110}}{{100}}{x_1} + \frac{{110}}{{100}}{x_2} + ..... + \frac{{110}}{{100}}{x_{10}} = \frac{{110}}{{100}} \times 10\overline x \cr & \Rightarrow \frac{{\frac{{110}}{{100}}{x_1} + \frac{{110}}{{100}}{x_2} + ..... + \frac{{110}}{{100}}{x_{10}}}}{{10}} = \frac{{11}}{{10}}\overline x \cr} $$⇒ Average is increased by 10%
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