Question

If $x\text{and}y$ vary directly,
then find the value of $p,q\text{and}r$.

$x$	6	$p$	$q$	12
$y$	36	48	60	$r$

• A. $p=8q=10r=72$
• B. $p=10q=12r=72$
• C. $p=8q=70r=10$
• D. $p=16q=10r=72$

Answer 1

The correct option is A $p=8q=10r=72$

Given, $x\text{and}y$ vary directly.
$\therefore \frac{x_1}{y_1}=\frac{x_2}{y_2}$

$\left(i\right)$ Given,
$x_1=6$
$y_1=36$
$x_2=p$
$y_2=48$
$\Rightarrow \frac{6}{36}=\frac{p}{48}$
$\Rightarrow p=\frac{6\times 48}{36}=8$

$\left(ii\right)$ Given,
$x_1=6$
$y_1=36$
$x_2=q$
$y_2=60$
$\Rightarrow \frac{6}{36}=\frac{q}{60}$
$\Rightarrow q=\frac{6\times 60}{36}=10$

$\left(iii\right)$ Given,
$x_1=6$
$y_1=36$
$x_2=12$
$y_2=r$
$\Rightarrow \frac{6}{36}=\frac{12}{r}$
$\Rightarrow r=\frac{12\times 36}{6}=72$