Question

anuj has an equal number of two-rupee and five rupee coins. he has also some one-rupee coins.if the total number of coins is 40 and their values is Rs 120 , how many five rupee and two-rupee coins does he have .

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}2-\mathrm{rupee}\mathrm{coins}=x \\ \mathrm{then}\mathrm{the}\mathrm{number}\mathrm{of}5-\mathrm{rupee}\mathrm{coins}=x \\ \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{coins}=40 \\ \mathrm{Now}\mathrm{the}\mathrm{number}\mathrm{of}1-\mathrm{rupee}\mathrm{coins}=40-2x \\ \mathrm{Amount}\mathrm{with}2-\mathrm{rupee}\mathrm{coins}=\mathrm{Rs}2x \\ \mathrm{Amount}\mathrm{with}5-\mathrm{rupee}\mathrm{coins}=\mathrm{Rs}5x \\ \mathrm{Amount}\mathrm{with}1-\mathrm{rupee}\mathrm{coins}=\mathrm{Rs}\left(40-2x\right) \\ \mathrm{Now}, \\ 2x+5x+\left(40-2x\right)=120 \\ \Rightarrow 5x+40=120 \\ \Rightarrow 5x=80 \\ \Rightarrow x=16 \\ \mathrm{So},\mathrm{the}\mathrm{number}\mathrm{of}2-\mathrm{rupee}\mathrm{coins}=16 \\ \mathrm{number}\mathrm{of}5-\mathrm{rupee}\mathrm{coins}=16 \end{gathered}$$