Question

I varies directly as m and I is equal to 5, when m$ = \dfrac{2}{3}$. Find I when m $ = \dfrac{{16}}{3}$.

Answer 1

Hint: In the above question it is given that ‘$I$’ vary directly as ‘$m$’, it means if ‘$m$’ changes then ‘$I$’ will also change in the same ratio. If ‘$m$’ doubles in value, then ‘$I$’ will also double in value. If ‘$m$’ increases by 8, then ‘$I$’ will also increase by $8$. Now, we will keep this concept of direct proportion in our mind and change all statements into equations and solve for the unknown value.

Complete step by step solution:
According to the question,
$I$ varies directly as $m$ that is $I \propto m$.
Given, $I = 5$ when $m = \dfrac{2}{3}$
Now, if $m = \dfrac{{16}}{3}$, then we have to find the value of $I$
and we know that $I \propto m$
$ \Rightarrow I = km$---(1)
(Putting the value of ‘I’ and ‘m’)
$ \Rightarrow 5 = k \times \dfrac{2}{3}$
$ \Rightarrow k = \dfrac{{15}}{2}$
Now, putting the value of $k = \dfrac{{15}}{2}$ and $m = \dfrac{{16}}{3}$ in equation (1)
$ \Rightarrow I = \dfrac{{15}}{2} \times \dfrac{{16}}{3} = 40$
$ \Rightarrow I = 40$

$\therefore $ For m$ = \dfrac{{16}}{3}$, the value of $I$ is 40.

Note: These types of questions are related to the mathematics topic Direct Proportion. Direct proportion means the connection between two variables whose ratio is equal to a constant value. In other words, the direct proportion is a phenomenon where an increase in one quantity causes a corresponding increase in the other quantity or a decrease in one quantity causes a decrease in the other quantity. Direct proportion is denoted by the proportional symbol ($ \propto $ ). For example, if two variables a and b are directly proportional to each other, then this statement can be written as $a \propto b$. When we replace the proportionality sign ($ \propto $) with an equal sign (=). For example: $a \propto b \Rightarrow $a = $k \times b$.