Question

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

$x$	$16$	$30$	$40$	$56$
$y$	$32$	$60$	$80$	$84$

Answer 1

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

$x$	$16$	$30$	$40$	$56$
$y$	$32$	$60$	$80$	$84$

Let $x_1=16,x_2=30,x_3=40,x_4=56$

$y_1=32,y_2=60,y_3=80,y_4=84$

Finding the ratio of x and y in each case:

$\frac{x_1}{y_1}=\frac{16}{32}=\frac{1}{2}$

$\frac{x_2}{y_2}=\frac{30}{60}=\frac{1}{2}$

$\frac{x_3}{y_3}=\frac{40}{80}=\frac{1}{2}$

$\frac{x_4}{y_4}=\frac{56}{84}=\frac{2}{3}$

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

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