Question

If l:m = 3/2 : 7/4 and m: n = 7/3 : 21/5 find l:n and l:n:m

Answer 1

Refer image you will get your answer.

Answer 2

Answer:

$l:n=\frac{10}{21}$

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

Step-by-step explanation:

Given : If $l : m=\frac{3}{2} :\frac{7}{4}$ and $m:n=\frac{7}{3} :\frac{21}{5}$

To find : The value of $l:n$ and $l:m:n$ ?

Solution :

$l : m=\frac{3}{2} :\frac{7}{4}$

$\frac{l}{m}=\frac{\frac{3}{2}}{\frac{7}{4}}$

$\frac{l}{m}=\frac{6}{7}$ ....(1)

$m:n=\frac{7}{3} :\frac{21}{5}$

$\frac{m}{n}=\frac{\frac{7}{3}}{\frac{21}{5}}$

$\frac{m}{n}=\frac{5}{9}$ ....(2)

To make m same multiply (1) by 5 and (2) by 7,

$\frac{l}{m}=\frac{30}{35}=k$

$\frac{l}{30}=\frac{m}{35}=k$

$l=30k$ and $m=35k$

$\frac{m}{n}=\frac{35}{63}=k$

$\frac{m}{35}=\frac{n}{63}=k$

$m=35k$ and $n=63k$

So, $l:n=\frac{l}{n}$

$l:n=\frac{30k}{63k}$

$l:n=\frac{30}{63}$

$l:n=\frac{10}{21}$

So, $l:m:n=30k:35k:63k$

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