Question

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Q.1. Aarushi bought some ribbon. At first she used $\frac{1}{5}$ of it. Next she used $\frac{1}{8}$ of the remainder and finally she used 1.5 m. She is left with 2.7 m ribbon. What length of ribbon did she buy?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{ribbon}\mathrm{bought}=\mathrm{x}\mathrm{m} \\ \mathrm{Length}\mathrm{of}\mathrm{ribbon}\mathrm{used}\mathrm{at}\mathrm{first}=\frac{\mathrm{x}}{5}\mathrm{m} \\ \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{ribbon}\mathrm{left}=\mathrm{x}-\frac{\mathrm{x}}{5}=\frac{4\mathrm{x}}{5}\mathrm{m} \\ \mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{ribbon}\mathrm{used}=\frac{1}{8}\times \frac{4\mathrm{x}}{5}=\frac{\mathrm{x}}{10}\mathrm{m} \\ \mathrm{Now},\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{ribbon}\mathrm{left}=\frac{4\mathrm{x}}{5}-\frac{\mathrm{x}}{10}=\frac{8\mathrm{x}-\mathrm{x}}{10}=\frac{7\mathrm{x}}{10}\mathrm{m} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}: \\ \frac{7\mathrm{x}}{10}-\frac{15}{10}=\frac{27}{10} \\ \Rightarrow 7\mathrm{x}-15=27 \\ \Rightarrow 7\mathrm{x}=42 \\ \Rightarrow \mathrm{x}=6 \\ \mathrm{So},\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{ribbon}\mathrm{bought}=6\mathrm{m} \end{gathered}$$