Question

If $x\text{and}y$ vary inversely, find the values of $l,m\text{and}n:$

$\begin{array}{ccccc}x& 4& 8& 2& 32\\ y& 4& l& m& n\end{array}$

Answer 1

Step: Find l, m and n

$\begin{array}{ccccc}x& 4& 8& 2& 32\\ y& 4& l& m& n\end{array}$

Let $x_1=4,x_2=8,x_3=2,x_4=32$

$y_1=4,y_2=l,y_3=m,y_4=n$

Find the product of $x\text{and}y$ in each case;

$x_1{y}_1=4\times 4=16$
$x_2{y}_2=8\times l=8l$
$x_3{y}_3=2\times m=2m$
$x_4{y}_4=32\times n=32n$

Since, x and y vary inversely.
So,
$x_1{y}_1=x_2{y}_2=x_3{y}_3=x_4{y}_4$

$16=8l=2m=32n$
$l=\frac{16}{8}=2$
$2m=16\to m=8$

$16=32n\to n=\frac{16}{32}=\frac{1}{2}=0.5$

Hence, $l=2,m=8,n=\mathrm{0.5.}$