$\begin{align} & P\text{ varies jointly as }m\text{ and }u,\text{ varies inversely as }q.\text{ Given that }p=4,\text{ }m=3\text{ } \\ & \text{and }u=2\text{ when }q=1,\text{find the value of }p\text{ when }m=6,u=4\text{ and }q=\tfrac{8}{5} \\ & (A)\text{ }\tfrac{128}{5}\text{ (B) }15\text{ (C) 10 (D) }\tfrac{288}{5} \\\end{align}$
$\begin{align} & p\propto \frac{mu}{q} \\ & \text{Given }p=4,m=3,u=2\text{ and }q=1 \\ & p=\frac{kmu}{q}\text{ }\!\!\{\!\!\text{ }k\text{ is the proportionality constant }\!\!\}\!\!\text{ } \\ & k=\frac{pq}{mu} \\ & k=\frac{4\times 1}{3\times 2}=\frac{2}{3} \\ & \text{so when }m=6,u=4\text{ and }q=\tfrac{8}{5}\text{ }p\text{ will be } \\ & p=\frac{kmu}{q}=\frac{2\times 6\times 4}{3}\times \frac{5}{8} \\ & p=10 \\\end{align}$