Question

It is given that $l$ varies directly as $m$. Answer the following questions.
(i) Write an equation which relates $l$ and $m$.
(ii) Find the constant of proportion (k), when $l$ is $6$ then $m$ is $18$.
(iii) Find $l$, when $m$ is $33$.

Answer 1

Given: $l$ and $m$ vary directly.

(i) $l$ and $m$ are two quantities or variables which are linked with each other directly, then we can say $l\propto m$.

$\Rightarrow \frac{l}{m}=C,$ where $C$ is the constant of proportionality .....(i)
It can also be written as:
$\Rightarrow \frac{l_1}{m_1}=\frac{l_2}{m_2}$

(ii) Now, $l=6$ and $m=18$
On putting the values in equation (i), we get
$\Rightarrow \frac{l}{m}=\frac{6}{18}=\frac{6÷6}{18÷6}=\frac{1}{3}$
$\Rightarrow C=\frac{1}{3}$
Hence, the value of the constant will be $\frac{1}{3}$.

(iii) Now $m=33$ and $C=\frac{1}{3}$
We know that,
$\Rightarrow \frac{l}{m}=C$
$\Rightarrow \frac{l}{33}=\frac{1}{3}$
$\Rightarrow l=\frac{33}{3}=11$
Hence, the value of $l$ is $11$.