Question

If $x\propto \frac{1}{y}$, complete the following table:

$x$	$36$	$12$	.....	.....
$y$	$2$	.....	$8$	$24$

Answer 1

$x$	$36$	$12$	$9$	$3$
$y$	$2$	$6$	$8$	$24$

Given proportionality is $x\propto \frac{1}{y}$
$\therefore x=k\frac{1}{y}$ (where $k$ is a constant of variation)
$\therefore k=xy$ ...(1)
Substituting $x=36$ and $y=2$ in equation (1),
$k=36\times 2=72$

(a) When $x=12$, $k=72$, $y=$?
$y=\frac{k}{x}$
$=\frac{72}{12}$
$=6$

(b) When $y=8$, $k=72$, $x=$?
$x=\frac{k}{y}=\frac{72}{8}=9$

(c) When $y=24$, $k=72$, $x=$?
$\Rightarrow x=\frac{k}{y}=\frac{72}{24}=3$