Question

if p:r =4/3 :3/2 and q:r =1/2:1/3 find p:r
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Answer 1

$\frac{p}{r} = \frac{ \frac{4}{3} }{ \frac{3}{2} } \\ \frac{p}{r} = ( \frac{4}{3} )( \frac{2}{3} ) \\ \frac{p}{r} = \frac{8}{9} \\ 9p = 8r \\ r = \frac{9}{8}p \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(i) \\ \\now \\ \frac{q}{r} = \frac{ \frac{1}{2} }{ \frac{1}{3} } \\ \frac{q}{r} = ( \frac{1}{2} )( \frac{3}{1} ) \\ \frac{q}{r} = \frac{3}{2} \\ q = \frac{3}{2} r = ( \frac{3}{2} )( \frac{9}{8} )p \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(from \: i) \\ q = \frac{27}{16} p \\ 16q = 27p \\ \frac{16}{27} = \frac{p}{q} \\ \frac{p}{q} = \frac{16}{27}$

Hence, p:q = 16:27