Question Number 42479 by mondodotto@gmail.com last updated on 26/Aug/18
$$\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{digit}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{seven}}\:\boldsymbol{\mathrm{times}}\: \\ $$$$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{digits}}.\boldsymbol{\mathrm{if}}\:\mathrm{27}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{substracted}}\: \\ $$$$\boldsymbol{\mathrm{from}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{digits}}\:\boldsymbol{\mathrm{get}}\:\boldsymbol{\mathrm{interchanged}}. \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}} \\ $$$$ \\ $$
Answered by $@ty@m last updated on 26/Aug/18
$$\mathrm{10}{y}+{x}=\mathrm{7}\left({x}+{y}\right)\Rightarrow{y}=\mathrm{2}{x}\:…\left(\mathrm{1}\right) \\ $$$$\mathrm{10}{y}+{x}=\mathrm{10}{x}+{y}+\mathrm{27} \\ $$$$\mathrm{9}{y}=\mathrm{9}{x}+\mathrm{27} \\ $$$$\Rightarrow{y}={x}+\mathrm{3}\:…\left(\mathrm{2}\right) \\ $$$${From}\left(\mathrm{1}\right)\&\left(\mathrm{2}\right) \\ $$$$\mathrm{2}{x}={x}+\mathrm{3}\Rightarrow{x}=\mathrm{3} \\ $$$$\Rightarrow{y}=\mathrm{6} \\ $$$$\therefore\:{the}\:{no}.\:{is}\:\mathrm{63} \\ $$