Answer
$y=216$
Work Step by Step
To find out the solution we need to follow the four-step procedure:
Step (1)
In the question it is provided that $y$ varies directly as $m$ , ${{n}^{2}}$ and varies inversely as $p$.
Thus, we have $y=k\frac{m{{n}^{2}}}{p}$.
Here $k$ is a constant.
Step (2)
Find out the value of $k$.
Substitute the values $m=2,\ n=1$ and $p=6$ then $y=15$ in $y=k\frac{m\cdot {{n}^{2}}}{p}$.
$\begin{align}
& 15=k\frac{2\times 1}{6} \\
& k=\frac{15\times 6}{2} \\
& k=45 \\
\end{align}$
Step (3)
Substitute the value of $k$ in $y=k\frac{m\cdot {{n}^{2}}}{p}$.
$y=\left( 45 \right)\frac{m\cdot {{n}^{2}}}{p}$
Step (4)
In this step, substitute the values $m=3,n=4,p=10$.
$\begin{align}
& y=45\times \frac{3\times 16}{10} \\
& y=\frac{9\times 3\times 16}{2} \\
& y=216 \\
\end{align}$
