Question

A sum of 500 is in the form of denominations of 5 and 10. If the total number of notes is 90, find the number of notes of each type.

Answer 1

$\begin{array}{l}\text{Let the number of five rupee notes be}x.\\ \text{Then, the number of ten rupee notes will be}(90-x).\\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question},\mathrm{we}\mathrm{have}:\\ \begin{array}{l}\text{5}x+10(90-x)=500\\ \text{⇒5}x+900-10x=500\\ \Rightarrow -5x=-400\\ \Rightarrow x=80\\ \mathrm{Number}\mathrm{of}\mathrm{ten}\mathrm{rupee}\mathrm{notes}=90-80=10\\ \therefore \mathrm{There}\mathrm{are}80\mathrm{five}\mathrm{rupee}\mathrm{notes}\mathrm{and}10\mathrm{ten}\mathrm{rupee}\mathrm{notes}.\end{array}\end{array}$