A number x is mistakenly divided by 10 instead of being multiplied by 10. what is the percentage error in the result?

1-99%
2-100%
3+99%
4+100%

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Actual result = 10 x \\ By mistake it has been divided by \\ 10 = \frac{x}{10} \\ % change = [\frac{10 x - (\frac{10}{x})}{10 x}] \times 100 = 99 \\ = - 99 % \\ Since, actual value is greater than the wrong value . \\ Alternatively, \\ Let, x = 10 \\ Actual result = 10 \times 10 = 100 \\ Wrong result = \frac{10}{10} = 1 \\ Change = (1 - 100) = - 99 \\ % change = - 99 % \end{aligned}

$\eqalign{ & {\text{Actual}}\,{\text{result}} = 10x \cr & {\text{By}}\,{\text{mistake}}\,{\text{it}}\,{\text{has}}\,{\text{been}}\,{\text{divided}}\,{\text{by}} \cr & 10 = \frac{x}{{10}} \cr & \% \,{\text{change}} = \left[ {\frac{{10x - \left( {\frac{{10}}{x}} \right)}}{{10x}}} \right] \times 100 = 99 \cr & = - 99\% \cr & {\text{Since, actual value is greater than the wrong value}}{\text{.}} \cr & \cr & {\text{Alternatively,}} \cr & {\text{Let}},\,x = 10 \cr & {\text{Actual}}\,{\text{result}} = 10 \times 10 = 100 \cr & {\text{Wrong}}\,{\text{result}} = \frac{{10}}{{10}} = 1 \cr & {\text{Change}} = \left( {1 - 100} \right) = - 99 \cr & \% \,{\text{change}} = - 99\% \cr}$