Question

Tick (✓) the correct answer:
A number is first increased by 10% and then reduced by 10%. The number
(a) does not change
(b) decrease by 1 %
(c) increases by 1 %
(d) none of these

Answer 1

(b) decrease by 1 %

$$\begin{gathered} \mathrm{Let}x\mathrm{be}\mathrm{the}\mathrm{number}. \\ \mathrm{A}10\%\mathrm{increase}\mathrm{will}\mathrm{give}\mathrm{a}\mathrm{new}\mathrm{number},\frac{110}{100}x=\frac{11}{10}x \\ \mathrm{The}\mathrm{number}\mathrm{is}\mathrm{then}\mathrm{reduced}\mathrm{by}10\%. \\ \mathrm{The}\mathrm{new}\mathrm{number}\mathrm{will}\mathrm{be}\frac{90}{100}\left(\frac{11}{10}\mathrm{x}\right)=\frac{990}{1000}x=\frac{99}{100}x \\ \mathrm{Difference}=\mathrm{x}-\frac{99}{100}\mathrm{x}=\frac{1}{100}\mathrm{x} \\ \mathrm{Percentage}\mathrm{of}\mathrm{decrease}=\frac{1}{100}x\times \frac{1}{\mathrm{x}}\times 100=1\% \end{gathered}$$