According to the formula, If pipe A  and B fills a tank in x and y hours respectively, but a third pipe C empties the full tank in z hours then the net portion filled in 1 hour when all of them are opened together is $\frac{\mathrm{xyz}}{\mathrm{xy}+\mathrm{yz}+\mathrm{zx}}$hours.

So,

 $$\begin{gathered} \frac{4\times 5\times 10}{(4\times 5)+(5\times 10)+(4\times 10)} \\ =\frac{200}{110}=\frac{20}{11} \mathrm{or} 1\frac{9}{11}\mathrm{hours} \end{gathered}$$

The tank will be filled in $1\frac{9}{11}$ hours when all the pipes are opened simultaneously.

Hence option C is correct