Question

If $l:m=1\frac{1}{2}:1\frac{3}{4}$ and $m:n=2\frac{1}{3}:4\frac{1}{5}$, find $l:n$.

Answer 1

Given $\frac{l}{m}=1\frac{1}{2}:1\frac{3}{4}=\frac{3}{2}:\frac{7}{4}$
$=\frac{\left(\frac{3}{2}\right)}{\left(\frac{7}{4}\right)}$ [since, $a:b=\frac{a}{b}$]
$\frac{l}{m}=\frac{3}{2}\times \frac{4}{7}$
$=\frac{6}{7}l=\frac{6}{7}m$ ........(i)
$\frac{m}{n}=2\frac{1}{3}:4\frac{1}{5}=\frac{7}{3}:\frac{21}{5}\frac{m}{n}=\frac{7}{3}\times \frac{5}{21}=\frac{5}{9}m=\frac{5}{9}nn=\frac{9}{5}m$......(ii)
From equation(i) $÷$ equation(ii), we get
$\frac{l}{n}=\frac{\frac{6}{7}m}{\frac{9}{5}m}=\frac{6}{7}\times \frac{5}{9}=\frac{10}{21}\therefore l:n=10:21$