Question

Complete the following table if $x\text{and}y$ vary directly.

x	5	$x_2$	10
y	15	27	$y_3$

• A. $x_2=12y_3=30$
• B. $x_2=9y_3=40$
• C. $x_2=9y_3=30$
• D. $x_2=18y_3=60$

Answer 1

The correct option is C $x_2=9y_3=30$

$\text{Given,}x\text{and}y\text{vary directly.}$
$\therefore \frac{x_1}{y_1}=\frac{x_2}{y_2}=\frac{x_3}{y_3}$

$\left(i\right)$
Given,
$x_1=5$
$y_1=15$
$y_2=27$
$\text{then,}{x}_2=\frac{x_1\times y_2}{y_1}$
$\Rightarrow x_2=\frac{5\times 27}{15}$
$\Rightarrow x_2=9$

$\left(ii\right)$
Given,
$x_1=5$
$y_1=15$
$x_3=10$
$\text{then,}{y}_3=\frac{x_3\times y_1}{x_1}$
$\Rightarrow y_3=\frac{10\times 15}{5}$
$\Rightarrow y_3=30$