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

Explanation:-

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