Question

If p varies directly as the square of q and inversely as the square root of r, and p = 60 when q = 6 and r = 81, find p when q = 8 and r = 144.

• A. $80$
• B. $70$
• C. $60$
• D. None of these

Answer 1

The correct option is A $80$

$y=\frac{kx}{z}\Rightarrow p=\frac{k{q}^2}{\sqrt{r}}$
$60=\frac{k\left(6^2\right)}{\sqrt{81}}$
$60=\frac{36k}{9}$
$540=36k$
$k=15$
$p=\frac{15q^2}{\sqrt{r}}$
$p=\frac{15\left(8^2\right)}{\sqrt{(}144)}$
$p=\frac{5\left(64\right)}{4}$
$p=80$