Question

Suppose $y$ is equal to the sum of two quantities of which one varies directly as $x$ and the other inversely as $x$. If $y=6$ when $x=4$ and $y=\frac{10}{3}$ when $x=3$. then what is the relation between $x$ and $y$?

• A. $y=x+\frac{4}{x}$
• B. $y=-2x+\frac{4}{x}$
• C. $y=2x+\frac{8}{x}$
• D. $y=2x-\frac{8}{x}$

Answer 1

The correct option is D $y=2x-\frac{8}{x}$

$y\alpha ax$ & $y\alpha \frac{a}{x}$

$\Rightarrow y=ax+\frac{b}{x}$

$y=6$ when $x=4$

$\Rightarrow 6=4a+\frac{b}{4}\Rightarrow 16a+b=24...\left(1\right)$

$y=10/3$ when $x=3$

$\Rightarrow \frac{10}{3}=3a+\frac{6}{3}\Rightarrow 9a+b=10...\left(2\right)$

Solution (1) & (2) we get $\left(\right(1)-(2\left)\right)$

$7a=14\Rightarrow a=2$

$\therefore b=-8$

Hence $y=2x-\frac{8}{x}$