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

A. remains unchanged

B. may decrease

C. may increase

D. is increased by 10%

Solution:

Let 10 numbers be x1, x2, x3, . . . . . . . x10
According to question average of these 10 numbers is 10

\Rightarrow \frac{x 1 + x 2 + x 3 + . . . . + x 10}{10} = x

Now if each number is increased by 10%,
then new average, say y.

y = \frac{1.1 x 1 + 1.1 x 2 + 1.1 x 3 + . . . . + 1.1 x 10}{10}

\Rightarrow y = 1.1 \times \frac{x 1 + x 2 + x 3 + . . . . + x 10}{10}

\begin{aligned} \Rightarrow y = 1.1 x \\ \Rightarrow y is 10 % increased \end{aligned}

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