Question

Richa spent 1/2 of her salary paying installments, 1/3 on conveyance, and gave the remaining money as donation. If she donated Rs.500, how much money did she get as salary and how much did she spend on installments?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{total}\mathrm{salary}\mathrm{of}\mathrm{Richa}=\mathrm{Rs}\mathrm{x} \\ \mathrm{Money}\mathrm{spent}\mathrm{on}\mathrm{paying}\mathrm{installments}=\mathrm{Rs}\left(\frac{\mathrm{x}}{2}\right) \\ \mathrm{Money}\mathrm{spent}\mathrm{on}\mathrm{conveyance}=\mathrm{Rs}\left(\frac{\mathrm{x}}{3}\right) \\ \mathrm{Remaning}\mathrm{money}=\mathrm{x}-\left(\frac{\mathrm{x}}{2}+\frac{\mathrm{x}}{3}\right)=\mathrm{x}-\left[\frac{3\mathrm{x}+2\mathrm{x}}{6}\right]=\mathrm{x}-\frac{5\mathrm{x}}{6}=\mathrm{Rs}\left(\frac{\mathrm{x}}{6}\right) \\ \mathrm{So},\mathrm{money}\mathrm{donated}=\mathrm{Rs}\left(\frac{\mathrm{x}}{6}\right) \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}: \\ \frac{\mathrm{x}}{6}=500 \\ \Rightarrow \mathrm{x}=3000 \\ \mathrm{So},\mathrm{salary}\mathrm{of}\mathrm{Richa}=\mathrm{Rs}3000 \\ \mathrm{Money}\mathrm{spent}\mathrm{on}\mathrm{paying}\mathrm{installments}=\mathrm{Rs}\left(\frac{\mathrm{x}}{2}\right)=\mathrm{Rs}\left(\frac{3000}{2}\right)=\mathrm{Rs}15000 \end{gathered}$$