Question Number 192047 by sciencestudentW last updated on 06/May/23
$${we}\:{have}\:{three}\:{digit}\:{number}\:{like}\:{XYZ} \\ $$$${that}\:{X}+{Y}+{Z}=\mathrm{16},\:{if}\:{we}\:{replace}\:{X}\:{by}\:{Z} \\ $$$${then}\:{it}\:{will}\:{be}\:{changed}\:{to}\:{ZYX}\:{number}\: \\ $$$${that}\:{ZYX}={XYZ}−\mathrm{594} \\ $$$${find}\:{XYZ}\:{number}. \\ $$
Answered by AST last updated on 08/May/23
$$\mathrm{100}{Z}+\mathrm{10}{Y}+{X}−\mathrm{100}{X}−\mathrm{10}{Y}−{Z}=−\mathrm{594} \\ $$$$\Rightarrow\mathrm{99}{Z}−\mathrm{99}{X}=−\mathrm{594}\Rightarrow{Z}−{X}=−\mathrm{6}\Rightarrow{X}−{Z}=\mathrm{6} \\ $$$$\Rightarrow\left({X},{Z}\right)=\left(\mathrm{9},\mathrm{3}\right),\left(\mathrm{8},\mathrm{2}\right),\left(\mathrm{7},\mathrm{1}\right) \\ $$$$\Rightarrow{Y}=\mathrm{4},\mathrm{6}\:{or}\:\mathrm{8} \\ $$$$\Rightarrow{XYZ}=\mathrm{943},\:\mathrm{862}\:{or}\:\mathrm{781} \\ $$
Commented by sciencestudentW last updated on 07/May/23
$${great}\: \\ $$