Question

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

$\begin{array}{ccccc}x& 24& 32& m& 16\\ y& l& 12& 8& n\end{array}$

Answer 1

Step: Find $l,m\text{and}n$

$\begin{array}{ccccc}x& 24& 32& m& 16\\ y& l& 12& 8& n\end{array}$

Let $x_1=24,x_2=32,x_3=m,x_4=16$

$y_1=l,y_2=12,y_3=8,y_4=n$

Find the product of x and y in each case

$x_1{y}_1=24l$

$x_2{y}_2=32\times 12=384$

$x_3{y}_3=8\times m=8m$

$x_4{y}_4=16\times n=16n$

Since, x and y vary inversely.

So,

$x_1{y}_1=x_2{y}_2=x_3{y}_3=x_4{y}_4$

$24l=384=8m=16n$

$l=\frac{384}{24}=16$

$m=\frac{384}{8}=48$

$n=\frac{384}{16}=24$

Hence, $l=16,m=48,n=24.$