Question Number 26156 by bbbbbb last updated on 21/Dec/17
$${a}\:{two}\:{digit}\:{number}\:{is}\:\mathrm{3}\:{more}\:{than} \\ $$$$\mathrm{4}\:{times}\:{the}\:{sum}\:{of}\:{its}\:{digits}.\:{if} \\ $$$$\mathrm{18}\:{is}\:{added}\:{to}\:{this}\:{number}\:.{the}\: \\ $$$${sum}\:{is}\:{equal}\:{to}\:{number}\:{obtained} \\ $$$${by}\:{interchanging}\:{the}\:{digits}.{find}\:{the}\:{number} \\ $$
Answered by mrW1 last updated on 22/Dec/17
$${let}'{s}\:{say}\:{the}\:{number}\:{is}\:\boldsymbol{{ab}}. \\ $$$$\mathrm{10}{a}+{b}=\mathrm{4}\left({a}+{b}\right)+\mathrm{3}\:\:\:...\left({i}\right) \\ $$$$\mathrm{10}{a}+{b}+\mathrm{18}=\mathrm{10}{b}+{a}\:\:...\left({ii}\right) \\ $$$$\left({i}\right)\Rightarrow\mathrm{2}{a}−{b}=\mathrm{1} \\ $$$$\left({ii}\right)\Rightarrow{a}−{b}=−\mathrm{2} \\ $$$$\Rightarrow{a}=\mathrm{3} \\ $$$$\Rightarrow{b}=\mathrm{5} \\ $$$${The}\:{number}\:{is}\:\mathrm{35}. \\ $$