Question

the denominator of a rational number is greater than its numerator by 8.if the numerator is increased by 17 and denominator is decreased by 1, the number obtain is 3/2.find the number?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{numerator}=\mathrm{x} \\ \mathrm{then}\mathrm{denominator}=\mathrm{x}+8 \\ \mathrm{Required}\mathrm{fraction}=\frac{\mathrm{x}}{\mathrm{x}+8} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}, \\ \frac{\mathrm{x}+17}{\mathrm{x}+8-1}=\frac{3}{2} \\ \Rightarrow \frac{\mathrm{x}+17}{\mathrm{x}+7}=\frac{3}{2} \\ \Rightarrow 3\mathrm{x}+21=2\mathrm{x}+34 \\ \Rightarrow \mathrm{x}=13 \\ \mathrm{So},\mathrm{fraction}=\frac{13}{13+8}=\frac{13}{21} \end{gathered}$$