Question

If $x$ and $y$ are in inverse proportion then find proportionality constant at $x = 3,y = 2$.
A). $4$
B). $5$
C). $6$
D). $7$

Answer 1

Hint: Inverse proportionality is the relation between two quantities in which if one quantity increases, then the other quantity decreases, and if one quantity decreases, then the other quantity increases. Here we will use this relation to find the proportionality constant between $x$ and $y$.

Complete step-by-step solution:
Given that: $x = 3,y = 2$
The given condition is: $x$ is inversely proportional to $y$.
According to inverse proportionality relation,
\[x\propto \dfrac{1}{y}\]
Here, $\propto $ is the proportionality sign.
Removing the proportionality sign and replacing it with a constant $k$,
$x = k \times \dfrac{1}{y}$
Here, $k$ is the proportionality constant.
Taking $y$ to the left side of the equation,
$xy = k$
Substituting the values of $x = 3,y = 2$ in the above equation,
$3 \times 2 = k$
Multiplying the values,
$k = 6$
The value of proportionality constant is $k = 6$.
Therefore, the correct option is option C. $6$.

Note: Two quantities can be compared using direct or indirect relation between them. In direct proportionality, if one quantity increases then the other one also increases, and if one quantity decreases, then the other one also decreases. Direct proportionality between $x$ and $y$ is given by $x\alpha y$ and after removing the proportionality sign and introducing a proportionality constant $k$, the relation becomes $xy = k$. In Inverse proportionality, if one quantity increases, then the other quantity decreases, and if one quantity decreases, then the other quantity increases.