Question

If $x$ and $y$ vary inversely, find $x_2$ and $y_3.$
$\begin{array}{cccc}x& 25& x_2& \frac{55}{2}\\ Y& 60& 55& y_3\end{array}$

• A. $x_2=\frac{250}{11},y_3=\frac{600}{11}$
• B. $x_2=\frac{30}{11},y_3=\frac{60}{11}$
• C. $x_2=\frac{300}{11},y_3=\frac{600}{11}$
• D. $x_2=\frac{300}{11},y_3=\frac{610}{11}$

Answer 1

The correct option is C $x_2=\frac{300}{11},y_3=\frac{600}{11}$

Given, $x$ and $y$ vary inversely.
$x_1\times y_1=x_2\times y_2=x_3\times y_3$
$x_1=25,y_1=60,y_2=55,x_3=\frac{55}{2}$
So, $x_2=\frac{x_1\times y_1}{y_2}$
$\Rightarrow x_2=\frac{25\times 60}{55}=\frac{300}{11}$
$y_3=\frac{x_1\times y_1}{x_3}$
$\Rightarrow y_3=\frac{25\times 60}{\left(\frac{55}{2}\right)}=\frac{600}{11}$