Question Number 118825 by bramlexs22 last updated on 20/Oct/20
$${I}\:{am}\:{thinking}\:{of}\:{a}\:{two}−{digit}\:{number} \\ $$$$.{If}\:{i}\:{write}\:\mathrm{3}\:{to}\:{the}\:{left}\:{of}\:{my}\:{number} \\ $$$${and}\:{double}\:{this}\:{three}\:{digit}\:{number}\:{the} \\ $$$${result}\:{is}\:\mathrm{27}\:{times}\:{my}\:{original}\:{number}. \\ $$$${what}\:{is}\:{my}\:{number}\:? \\ $$
Answered by benjo_mathlover last updated on 20/Oct/20
$${let}\:{original}\:{your}\:{number}\:{is}\:{AB}\: \\ $$$${then}\:\mathrm{2}×\mathrm{3}{AB}\:=\:\mathrm{27}×{AB} \\ $$$$\Rightarrow\mathrm{2}\left(\mathrm{300}+\mathrm{10}{A}+{B}\right)=\mathrm{27}\left(\mathrm{10}{A}+{B}\right) \\ $$$$\Rightarrow\mathrm{600}+\mathrm{20}{A}+\mathrm{2}{B}=\mathrm{270}{A}+\mathrm{27}{B} \\ $$$$\Rightarrow\mathrm{600}=\mathrm{250}{A}+\mathrm{25}{B}\: \\ $$$$\Rightarrow\mathrm{24}\:=\:\mathrm{10}{A}+{B}\:.\:{Thus}\:{your}\:{number}\:{is}\:\mathrm{24} \\ $$
Answered by MJS_new last updated on 20/Oct/20
$$\mathrm{2}×\left(\mathrm{300}+{x}\right)=\mathrm{27}{x} \\ $$$$\mathrm{600}=\mathrm{25}{x} \\ $$$${x}=\mathrm{24} \\ $$
Commented by PRITHWISH SEN 2 last updated on 20/Oct/20
$$\mathrm{simple}\:\mathrm{and}\:\mathrm{beautiful} \\ $$