Question

If l : m =1½:1¾ and m : n =2⅓:4 1/5 find (i)l:n; (ii) l:m:n

Answer 1

$l:m = 1 \frac{1}{2} : 1 \frac{3}{4} = \frac{3}{2} : \frac{7}{4} \\ \\ \Rightarrow \frac{l}{m} = \frac{3}{2} \div \frac{7}{4} = \frac{3}{2} \times \frac{4}{7} = \frac{6}{7}$

$m : n = 2 \frac{1}{3} : 4 \frac{1}{5} = \frac{7}{3} : \frac{21}{5} \\ \\ \Rightarrow \frac{m}{n} = \frac{7}{3} \div \frac{21}{5} = \frac{7}{3} \times \frac{5}{21} = \frac{5}{9}$

$i) \: \: l : n = \frac{l}{n} = \frac{l}{m} \times \frac{m}{n} \\ \\ \Rightarrow l : n = \frac{6}{7} \times \frac{5}{9} = \frac{30}{63} = \frac{10}{21}$

$ii) \: \: \frac{l}{m} = \frac{6}{7} = \frac{6 \times 5}{7 \times 5} = \frac{30}{35} \\ \\ \Rightarrow \frac{m}{n} = \frac{5}{9} = \frac{5 \times 7}{9 \times 7} = \frac{35}{63}$

So when l = 30, m = 35 and n = 63

$\Rightarrow l : m : n = 30 : 35 : 63$