Question

a man donated 1/10 of his money to a school, 1/6 of the remaining to a church and the remaining money he distributed equally among his 3 children. If each child gets Rs.50000, how much money the man originally have?

Answer 1

Dear student,

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{man}\mathrm{originally}\mathrm{have}=\mathrm{Rs}.\mathrm{x} \\ \mathrm{Therefore},\mathrm{money}\mathrm{donated}\mathrm{to}\mathrm{school}=\frac{\mathrm{x}}{10} \\ \mathrm{remaining}\mathrm{money}=\mathrm{x}-\frac{\mathrm{x}}{10}=\frac{9\mathrm{x}}{10} \\ \mathrm{money}\mathrm{donated}\mathrm{to}\mathrm{church}=\frac{1}{6}\left(\frac{9\mathrm{x}}{10}\right)=\frac{3\mathrm{x}}{20} \\ \mathrm{remaining}\mathrm{money}=\frac{9\mathrm{x}}{10}-\frac{3\mathrm{x}}{20}=\frac{18\mathrm{x}-3\mathrm{x}}{20}=\frac{15\mathrm{x}}{20} \\ \mathrm{He}\mathrm{distributes}\mathrm{this}\mathrm{money}\mathrm{equally}\mathrm{into}\mathrm{his}\mathrm{three}\mathrm{children}, \\ \mathrm{Therefore},\mathrm{each}\mathrm{child}\mathrm{get}=\frac{1}{3}\left(\frac{15\mathrm{x}}{20}\right) \\ \mathrm{According}\mathrm{to}\mathrm{question},\mathrm{each}\mathrm{child}\mathrm{get}\mathrm{Rs}.50000 \\ \mathrm{therefore}, \\ \frac{1}{3}\left(\frac{15\mathrm{x}}{20}\right)=50000 \\ \left(\frac{15\mathrm{x}}{20}\right)=50000\times 3 \\ \mathrm{x}=\frac{50000\times 3\times 20}{15} \\ \mathrm{x}=200000 \\ \mathrm{So},\mathrm{the}\mathrm{man}\mathrm{originally}\mathrm{have}\mathrm{Rs}.2,00,000 \end{gathered}$$
Regards