Question Number 17961 by ketto last updated on 13/Jul/17
Answered by alex041103 last updated on 13/Jul/17
$${Let}\:{the}\:{total}\:{amount}\:{of}\:{money}\:{be}\:{M}. \\ $$$${And}\:{the}\:{money}\:{Lightness}\:{got}\:−\:{x} \\ $$$${Then} \\ $$$${M}=\frac{\mathrm{5}}{\mathrm{11}}{M}\:+\:\left(\mathrm{1}−\frac{\mathrm{5}}{\mathrm{11}}\right)\frac{\mathrm{7}}{\mathrm{12}}{M}\:+\:{x} \\ $$$$\Rightarrow{M}=\frac{\mathrm{5}}{\mathrm{11}}{M}+\frac{\mathrm{7}}{\mathrm{22}}{M}+{x} \\ $$$${x}={M}\left(\mathrm{1}−\frac{\mathrm{5}}{\mathrm{11}}−\frac{\mathrm{7}}{\mathrm{22}}\right) \\ $$$${x}=\frac{\mathrm{5}}{\mathrm{22}}{M} \\ $$$${Ans}.\:\frac{\mathrm{5}}{\mathrm{22}} \\ $$