Question

A BAG CONTAINS 25 PAISE AND 50 PAISE CONS WHOSE TOTAL VALUE IS RS. 200IF EACH NUMBER OF 25 PAISE COINS IS 6 TIMES THAT OF 50 PAISE COINS, FIND THE NUMBER OF EACH TYPE OF COINS.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}50\mathrm{paise}\mathrm{coins}=x \\ \mathrm{so},\mathrm{the}\mathrm{number}\mathrm{of}25\mathrm{paise}\mathrm{coins}=6x \\ \mathrm{total}\mathrm{amount}\mathrm{with}50\mathrm{paise}\mathrm{coins}=\mathrm{Rs}.\left(0.5\times x\right)=\mathrm{Rs}.0.5x \\ \mathrm{total}\mathrm{amount}\mathrm{with}25\mathrm{paise}\mathrm{coins}=\mathrm{Rs}.\left(0.25\times 6x\right)=\mathrm{Rs}.1.5x \end{gathered}$$

$$\begin{gathered} \mathrm{Total}\mathrm{amount}\mathrm{inside}\mathrm{the}\mathrm{bag}=\mathrm{Rs}.200 \\ \Rightarrow 0.5x+1.5x=200 \\ \Rightarrow 2x=200 \\ \Rightarrow x=100 \\ \mathrm{so},\mathrm{number}\mathrm{of}50\mathrm{paise}\mathrm{coins}=100 \\ \mathrm{and}\mathrm{number}\mathrm{of}25\mathrm{paise}\mathrm{coins}=6\times 100=600 \end{gathered}$$