Question

1f 5m − n = m + 2n then find the value of (4m + n) : (4m − n).

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}: \\ 5m-n=m+2n \\ \Rightarrow 5m-m=2n+n \\ \Rightarrow 4m=3n \\ \therefore \frac{m}{n}=\frac{3}{4} \\ \mathrm{Now},\mathrm{we}\mathrm{have}\mathrm{to}\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\frac{4m+n}{4m-n}. \\ \mathrm{Dividing}\mathrm{both}\mathrm{the}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{by}n,\mathrm{we}\mathrm{get}: \\ \frac{4\times {\displaystyle \frac{m}{n}}+1}{4\times {\displaystyle \frac{m}{n}}-1} \\ =\frac{4\times {\displaystyle \frac{3}{4}}+1}{4\times {\displaystyle \frac{3}{4}}-1} \\ =\frac{4}{2} \\ =\frac{2}{1} \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ \left(4m+n\right):\left(4m-n\right)=2:1 \end{gathered}$$