Question

Two numbers are respectively 20% and 50% more than a third number. What percentage is the first of the third?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{third}\mathrm{number}=\mathrm{x} \\ \mathrm{Now},\mathrm{first}\mathrm{number}=\mathrm{x}+20\%\mathrm{of}\mathrm{x}=\mathrm{x}+\frac{\mathrm{x}}{5}=\frac{6\mathrm{x}}{5} \\ \mathrm{Second}\mathrm{number}=\mathrm{x}+50\%\mathrm{of}\mathrm{x}=\mathrm{x}+\frac{\mathrm{x}}{2}=\frac{3\mathrm{x}}{2} \\ \mathrm{Now},\mathrm{let}\mathrm{y}\%\mathrm{of}\mathrm{x}=\frac{6\mathrm{x}}{5} \\ \Rightarrow \frac{\mathrm{xy}}{100}=\frac{6\mathrm{x}}{5} \\ \Rightarrow \mathrm{y}=120 \\ \mathrm{So},\mathrm{first}\mathrm{number}\mathrm{is}120\%\mathrm{of}\mathrm{the}\mathrm{third}\mathrm{number}. \end{gathered}$$