Question
It is given that I varies directly as $m$.
(i) Write an equation which relates I and $m$.
(ii) Find the constant of proportion (k) when $l$ is 6 and $m$ is 18 .
(iii) Find $l$ when $m$ is 33 .
(iv) Find $m$ when $l$ is 8 .

Answer

Given, $l \propto m$
$
\Rightarrow \quad l=k m
$
where, $k$ is any constant.
$
\Rightarrow \quad k=\frac{l}{m}
$
(i) $k=\frac{l}{m}$
(ii) Given, $l=6$ and $m=18$
$
\begin{array}{ll}
\because & k=\frac{l}{m} \Rightarrow k=\frac{6}{18} \\
\therefore & k=\frac{1}{3}
\end{array}
$
(iii) Given, $m=33$ and $l=$ ?
$\because k=\frac{1}{m} \Rightarrow \frac{1}{3}=\frac{1}{33}\qquad$ $[$$\because k=\frac{1}{3}$ from part (ii)$]$
$\therefore l=11$
(iv) Given, $I=8$ and $m=$ ?
$\because \quad k=\frac{1}{m} \Rightarrow \frac{1}{3}=\frac{8}{m}\qquad$ $[$$\because k=\frac{1}{3}$ from part (ii)$]$
$\Rightarrow \quad m=24$

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