Question

If $P:Q=\frac{1}{2}:\frac{1}{3}$ and $Q:R=1\frac{1}{2}:1\frac{1}{3}$, find $P:R$

Answer 1

$\frac{P}{Q}=\frac{\frac{1}{2}}{\frac{1}{3}}=\frac{3}{2}$

$\Rightarrow Q=\frac{2P}{3}$

$\frac{Q}{R}=\frac{1\frac{1}{2}}{1\frac{1}{3}}=\frac{\frac{3}{2}}{\frac{4}{3}}=\frac{3}{2}\times \frac{3}{4}=\frac{9}{8}$

$\Rightarrow \frac{2P}{3R}=\frac{9}{8}$

$\Rightarrow \frac{P}{R}=\frac{27}{16}$.