Question

the denominator of a fraction is more than the numerator. if 5 is added to both the numerator and the denominator, the resulting fraction is 4/5. find the fraction

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{numerator}=\mathrm{x} \\ \mathrm{the}\mathrm{the}\mathrm{denominator}=\mathrm{x}+3 \\ \mathrm{Now},\mathrm{given}\mathrm{fraction}=\frac{\mathrm{x}}{\mathrm{x}+3} \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{given}\mathrm{condition}, \\ \frac{\mathrm{x}+5}{\left(\mathrm{x}+3\right)+5}=\frac{4}{5} \\ \Rightarrow \frac{\mathrm{x}+5}{\mathrm{x}+8}=\frac{4}{5} \\ \Rightarrow 5\mathrm{x}+25=4\mathrm{x}+32 \\ \Rightarrow 5\mathrm{x}-4\mathrm{x}=32-25 \\ \Rightarrow \mathrm{x}=7 \\ \mathrm{So},\mathrm{numerator}=7 \\ \mathrm{denominator}=7+3=10 \\ \mathrm{So},\mathrm{required}\mathrm{fraction}=\frac{7}{10} \end{gathered}$$