Question

If $a\propto \frac{1}{b}$, complete the following table:

$a$	$20$	$8$	$\_\_$	$\_\_$
$b$	$4$	$\_\_$	$5$	$40$

Answer 1

$a$	$20$	$8$	$16$	$2$
$b$	$4$	$10$	$5$	$40$

Given, $a\propto \frac{1}{b}$
$\therefore a=k\frac{1}{b}$ ....(where $k$ is a constant of variation)
$k=ab$ ...(1)
Substituting $a=20$ and $b=4$ in equation (1)
$k=20\times 4=80$
(a) When $a=8$, $k=80$, $b=$?
$b=\frac{k}{a}=\frac{80}{8}=10$
(b) When $b=5$, $k=80$, $a=$?
$a=\frac{k}{b}=\frac{80}{5}=16$
(c) When $b=40$, $k=80$, $a=$?
$a=\frac{k}{b}=\frac{80}{40}=2$