Time taken by all tohethet to fill the tank is 15 minutes

Let the capacity of the tank be x gallons

Quantity of water filled in the tank in 1 min when all the pipes A, B and C are opened simultaneously,

$$\begin{gathered} =\frac{\mathrm{x}}{20}+\frac{\mathrm{x}}{24}-3=\frac{\mathrm{x}}{15} \\ \Rightarrow \frac{{\displaystyle \mathrm{x}}}{{\displaystyle 20}}+\frac{{\displaystyle \mathrm{x}}}{{\displaystyle 24}}-\frac{{\displaystyle \mathrm{x}}}{{\displaystyle 15}}=3 \\ \Rightarrow \frac{{\displaystyle 6\mathrm{x}+5\mathrm{x}-8\mathrm{x}}}{{\displaystyle 120}}=3 \\ \Rightarrow 3\mathrm{x}=3\times 120 \\ \Rightarrow \mathrm{x}=\frac{3\times 120}{3}=120 \mathrm{gallons} \end{gathered}$$

Hence option C is correct.