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

Let 10 numbers be x1, x2, x3, . . . . . . . x10
According to question average of these 10 numbers is 10
$$ \Rightarrow \frac{{ {x1 + x2 + x3 + .... + x10} }}{{10}} = x$$
Now if each number is increased by 10%,
then new average, say y.
$$y = \frac{{ {1.1x1 + 1.1x2 + 1.1x3 + .... + 1.1x10} }}{{10}}$$
$${\kern 1pt} \Rightarrow y = 1.1 \times {\frac{{ {x1 + x2 + x3 + .... + x10} }}{{10}}} $$
$$\eqalign{ & \Rightarrow y = 1.1x \cr & \Rightarrow y\,{\text{is }}10\% \,{\text{increased}} \cr} $$