The initial amount of water in the tank was 1600 liters.
Let's denote the initial amount of water in the tank as W.
First, two-fifths of the water are used, leaving
of the water remaining.
![\[\text{Remaining amount} = (3)/(5) * W\]](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ov5xhaomq44f6bfr2vef4osazb29d47ni5.png)
Then, three-quarters of the remaining water are used, leaving \(\frac{1}{4}\) of the remaining water.
![\[\text{Final amount} = (1)/(4) * \left((3)/(5) * W\right)\]](https://img.qammunity.org/2020/formulas/mathematics/middle-school/5dvabjc8i0t5woguqsmxmlluuogfw4ndik.png)
According to the problem, the final amount is 240 liters:
![\[(1)/(4) * \left((3)/(5) * W\right) = 240\]](https://img.qammunity.org/2020/formulas/mathematics/middle-school/7k9lhtz304w0a19jg3exky3m5zfuslir5z.png)
Now, solve for W:
![\[(3)/(5) * W = 240 * 4\]](https://img.qammunity.org/2020/formulas/mathematics/middle-school/da82saxhcxv76mu6wyhesz0388htr51crw.png)
![\[(3)/(5) * W = 960\]](https://img.qammunity.org/2020/formulas/mathematics/middle-school/5o6slzr0n72zr311ghu416cmg8ctz7mcc3.png)
![\[W = (960 * 5)/(3)\]](https://img.qammunity.org/2020/formulas/mathematics/middle-school/5v0jc31xyg2js6343rq5mrczpzxvc0f6sc.png)
![\[W = 1600\]](https://img.qammunity.org/2020/formulas/mathematics/middle-school/8fxddf0y67c5fn4059fgtfomkoe1iewf30.png)
So, the initial amount of water in the tank was 1600 liters.