# If x and y vary inversely as each other and

Question:

If x and y vary inversely as each other and

(i) x = 3 when y = 8, find y when x = 4

(ii) x = 5 when y = 15, find x when y = 12

(iii) x = 30, find y when constant of variation = 900.

(iv) y = 35, find x when constant of variation = 7.

Solution:

(i) Since $x$ and $y$ vary inversely, we have:

$x y=k$

For $x=3$ and $y=8$, we have :

$3 \times 8=k$

$\Rightarrow k=24$

For $x=4$, we have $:$

$4 y=24$

$\Rightarrow y=\frac{24}{4}$

$=6$

$\therefore y=6$

(ii) Since $x$ and $y$ vary inversely, we have:

$x y=k$

For $x=5$ and $y=15$, we have :

$5 \times 15=k$

$\Rightarrow k=75$

For $y=12$, we have :

$12 x=75$

$\Rightarrow x=\frac{75}{12}$

$=\frac{25}{4}$

$\therefore x=\frac{25}{4}$

(iii) Given :

$x=30$ and $k=900$

$\therefore x y=k$

$\Rightarrow 30 y=900$

$\Rightarrow y=\frac{900}{30}$

$=30$

$\therefore y=30$

(iv) Given :

$y=35$ and $k=7$

Now, $x y=k$

$\Rightarrow 35 x=7$

$\Rightarrow x=\frac{7}{35}$

$=\frac{1}{5}$

$\therefore x=\frac{1}{5}$