Question

If $\frac{p}{q}=\frac{6}{5}$ find the values of the following ratios:

(i) $\frac{3p+4q}{3p-4q}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\frac{p}{q}=\frac{6}{5} \\ \frac{3p}{4q}=\frac{18}{20}\left(\mathrm{Multiplying}\mathrm{by}\frac{3}{4}\right) \\ \mathrm{Now}, \\ \frac{3p+4q}{3p-4q}=\frac{18+20}{18-20}(\mathrm{Componendo}\mathrm{and}\mathrm{dividendo}) \\ =\frac{38}{-2} \\ =\frac{19}{-1} \\ =\frac{-19}{1} \end{gathered}$$