Question

If y is inversely proportional to cube of x, and $x=5$ when $y=1$, find the value of $y$, when $x=3$

• A. $\frac{125}{27}$
• B. $\frac{125}{3}$
• C. $\frac{5}{27}$
• D. $\frac{5}{3}$

Answer 1

The correct option is A $\frac{125}{27}$

Given that $y\propto \frac{1}{x^3}\Rightarrow y=\frac{k}{x^3}$

Given,
At $x=5,$ the value of $y=1$
Substituting value in above equation
$\Rightarrow 1=\frac{k}{5^3}\Rightarrow k=125$

At $x=3$ , let's find $y$
$y=\frac{k}{x^3}$
$\Rightarrow y=\frac{125}{3^3}$ $(\because k=125\text{and}x=3)$
$\Rightarrow y=\frac{125}{27}$