Question

the denominator of a fraction is one more than twice its numerator if the numerator and the denominator are both decreased by one then the number obtained is 1 by 3 find the fraction.

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{numerator}\mathrm{be}\mathrm{x} \\ \mathrm{Then}\mathrm{denominator}\mathrm{will}\mathrm{be}1+2\mathrm{x} \\ \mathrm{Also},\mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{when}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{are}\mathrm{both}\mathrm{decreased} \\ \mathrm{by}\mathrm{one}\mathrm{then}\mathrm{the}\mathrm{number}\mathrm{obtained}\mathrm{is}\frac{1}{3} \\ \mathrm{i}.\mathrm{e}\frac{\mathrm{x}-1}{1+2\mathrm{x}-1}=\frac{1}{3} \\ \Rightarrow 3\mathrm{x}-3=2\mathrm{x} \\ \Rightarrow \mathrm{x}=3 \\ \mathrm{So},\mathrm{the}\mathrm{fraction}=\frac{\mathrm{x}}{1+2\mathrm{x}}=\frac{3}{1+6}=\frac{3}{7} \end{gathered}$$
Regards