Question

The cost of Mathematics book is Rs $25\frac{3}{4}$ and that of Science book is Rs $20\frac{1}{2}$. Which costs more and by how much?

Answer 1

$$\begin{gathered} \mathrm{Cost}\mathrm{of}\mathrm{mathematics}\mathrm{book}=\mathrm{Rs}25\frac{3}{4}=\frac{(25\times 4)+3}{4}=\mathrm{Rs}\frac{103}{4} \\ \mathrm{Cost}\mathrm{of}\mathrm{Science}\mathrm{book}=\mathrm{Rs}20\frac{1}{2}=\frac{(20\times 2)+1}{2}=\frac{41}{2}=\frac{41}{2}\times \frac{2}{2}=\mathrm{Rs}\frac{82}{4} \\ \mathrm{We}\mathrm{know} \\ 82<103 \\ =>\frac{82}{4}<\frac{103}{4} \\ \mathrm{Thus},\mathrm{Mathematics}\mathrm{book}\mathrm{costs}\mathrm{more}. \\ \mathrm{Difference}\mathrm{in}\mathrm{the}\mathrm{cost}\mathrm{of}\mathrm{Mathematics}\mathrm{and}\mathrm{Science}\mathrm{book}=\mathrm{cost}\mathrm{of}\mathrm{Mathematics}\mathrm{book}-\mathrm{Cost}\mathrm{of}\mathrm{Science}\mathrm{book} \\ =\frac{103}{4}-\frac{82}{4} \\ =\frac{21}{4}=\mathrm{Rs}5\frac{1}{4} \\ \mathrm{So},\mathrm{Mathematics}\mathrm{book}\mathrm{costs}\mathrm{more}\mathrm{by}\mathrm{Rs}5\frac{1}{4} \end{gathered}$$