Question

I have Rs 1000 in ten and five rupee notes. If the number of ten rupee notes that I have is ten more than the number of five rupee notes, how many notes do I have in each denomination?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{five}-\mathrm{rupee}\mathrm{notes}\mathrm{be}\mathrm{x}. \\ \mathrm{Therefore},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{ten}-\mathrm{rupee}\mathrm{notes}\mathrm{will}\mathrm{be}(\mathrm{x}+10). \\ \mathrm{Now}, \\ \mathrm{Value}\mathrm{of}\mathrm{five}-\mathrm{rupee}\mathrm{notes}=\mathrm{Rs}.5\mathrm{x} \\ \mathrm{Value}\mathrm{of}\mathrm{ten}-\mathrm{rupee}\mathrm{notes}=\mathrm{Rs}.10(\mathrm{x}+10) \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question}, \\ 5\mathrm{x}+10(\mathrm{x}+10)=1000 \\ \mathrm{or}15\mathrm{x}=1000-100 \\ \mathrm{or}\mathrm{x}=\frac{900}{15}=60 \\ \therefore \mathrm{Number}\mathrm{of}\mathrm{five}-\mathrm{rupee}\mathrm{notes}=60. \\ \mathrm{Number}\mathrm{of}\mathrm{ten}-\mathrm{rupee}\mathrm{notes}=60+10=70. \end{gathered}$$