Question

A man's property was distributed among his wife and three sons.If the wife got half the share and the remaining was distributed equally among his three children such that each child gets $50,000. What was the worth of the property and how much did the wife get?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{total}\mathrm{property}\mathrm{of}\mathrm{man}=\mathrm{x}\mathrm{dollars} \\ \mathrm{Now},\mathrm{share}\mathrm{of}\mathrm{wife}=\left(\frac{\mathrm{x}}{2}\right)\mathrm{dollars} \\ \mathrm{Money}\mathrm{left}=\mathrm{x}-\frac{\mathrm{x}}{2}=\left(\frac{\mathrm{x}}{2}\right)\mathrm{dollars} \\ \mathrm{Now},\mathrm{it}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the}\mathrm{remaining}\mathrm{money}\mathrm{is}\mathrm{distributed}\mathrm{equally}\mathrm{among}\mathrm{his}3\mathrm{children},\mathrm{so} \\ \mathrm{share}\mathrm{of}\mathrm{each}\mathrm{child}=\frac{1}{3}\mathrm{of}\left(\frac{\mathrm{x}}{2}\right)=\left(\frac{\mathrm{x}}{6}\right)\mathrm{dollars} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}, \\ \frac{\mathrm{x}}{6}=50000 \\ \Rightarrow \mathrm{x}=300000 \\ \mathrm{So},\mathrm{total}\mathrm{property}=300000\mathrm{dollars} \\ \mathrm{Share}\mathrm{of}\mathrm{wife}=\mathrm{Rs}\left(\frac{300000}{2}\right)=150000\mathrm{dollars} \end{gathered}$$