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.

Answer 1

$\because$ x and y vary inersely
$\therefore$ x $\times$ y is constant of variation
(i) x=3, y =8
$\therefore$ Constant =$xy=3\times 8=24$
Now when x = 4, then $y=\frac{Constant}{x}$
$\Rightarrow y=\frac{24}{4}=6y=6$

(ii) $\because$ Constant =$xy=5\times 15=75$
If y = 12, then $x=\frac{Constant}{y}$
$\Rightarrow x=\frac{75}{12}=\frac{25}{4}$

(iii) $\because$ Constant = xy = 900
$y=\frac{Constant}{x}=\frac{900}{30}=30$

(iv) $\because$ Constant = xy =7
If y = 35, then
$x=\frac{Constant}{y}=\frac{7}{35}=\frac{1}{5}$