Question

If $x$ and $y$ are inversely proportional, find the values of $X_1,X_2$ and $Y_1,Y_2$ in the table given below:

$x$	$8$	$X_1$	$16$	$X_2$	$80$
$y$	$Y_1$	$4$	$5$	$2$	$Y_2$

Answer 1

Since $x$ and $y$ are inversely proportional, we know that $y=\frac{Constant}{x}\Rightarrow xy=Constant$

$\Rightarrow 8\times Y_1=16\times 5$
$\Rightarrow 8Y_1=80$

$\Rightarrow Y_1=\frac{80}{8}=10$

Now,

$\Rightarrow X_1\times 4=16\times 5$
$\Rightarrow 4X_1=80$

$\Rightarrow X_1=\frac{80}{4}=20$

Now,

$\Rightarrow X_2\times 2=16\times 5$
$\Rightarrow 2X_2=80$

$\Rightarrow X_2=\frac{80}{2}=40$

Now,

$\Rightarrow 80\times Y_2=16\times 5$
$\Rightarrow 80Y_2=80$
$\Rightarrow Y_2=\frac{80}{80}=1$

$\therefore X_1=20,X_2=40,Y_1=10,Y_2=1$