Question

If $1\frac{1}{4}:2\frac{1}{3}=p:q$ and $q:r=4\frac{1}{2}:5\frac{1}{4},$ find $p:r$

Answer 1

$1\frac{1}{4}:2\frac{1}{3}=p;q$ $\&$ $q:r=4\frac{1}{2}:5\frac{1}{4}$

$\frac{5}{4}:\frac{7}{3}=p:q$ $\&$ $q:r=\frac{9}{2}:\frac{21}{4}$

$\Rightarrow \frac{p}{q}=\frac{5}{4}\times \frac{3}{7}=\frac{15}{25}$

$\Rightarrow \frac{q}{r}=\frac{9}{2}\times \frac{9}{2}\times \frac{4}{21}=\frac{6}{7}$

$\Rightarrow p:r=\frac{p}{r}=\frac{p}{q}\times \frac{q}{r}$

$=\frac{15}{28}\times \frac{6}{7}$

$=\frac{15\times 3}{14\times 7}$

$=\frac{45}{98}$

Hence, the answer is $\frac{45}{98}.$