Question

The denominator of a rational number is greater than its numerator by 6.if the numerator is decreased by 1 and denominator increased by 1 the number obtained is 1/3.find rational number

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{numerator}\mathrm{be}\mathrm{x} \\ \mathrm{therefore}\mathrm{denominator}\mathrm{is}\left(\mathrm{x}+6\right) \\ \mathrm{According}\mathrm{to}\mathrm{question}: \\ \frac{\mathrm{x}-1}{\mathrm{x}+6+1}=\frac{1}{3} \\ \Rightarrow 3\mathrm{x}-3=\mathrm{x}+7 \\ \Rightarrow 2\mathrm{x}=10 \\ \Rightarrow \mathrm{x}=5 \\ \mathrm{therefore}\mathrm{numerator}=5 \\ \mathrm{denominator}=5+6=11 \\ \mathrm{Required}\mathrm{number}=\frac{5}{11} \end{gathered}$$