Question

In which of the following tables do $x\text{and}y$ vary directly:

$x$	$27$	$45$	$54$	$75$
$y$	$81$	$180$	$216$	$225$

Answer 1

Finding the ratio of $x\text{and}y$ in each case

$x$	$27$	$45$	$54$	$75$
$y$	$81$	$180$	$216$	$225$

Let $x_1=27,x_2=45,x_3=54,x_4=75$

$y_1=81,y_2=180,y_3=216,y_4=225$

Finding the ratio of $x\text{and}y$ in each case:

$\frac{x_1}{y_1}=\frac{27}{81}=\frac{1}{3}$

$\frac{x_2}{y_2}=\frac{45}{180}=\frac{1}{4}$

$\frac{x_3}{y_3}=\frac{54}{216}=\frac{1}{4}$

$\frac{x_4}{y_4}=\frac{75}{225}=\frac{1}{3}$

Since, $\frac{x_1}{y_1}\ne \frac{x_2}{y_2}=\frac{x_3}{y_3}\ne \frac{x_4}{y_4}$

Therefore, $x\text{and}y$ does not vary directly.