Two pumps, A and B, are capable of filling a liquid reservoir in 25 minutes and 30 minutes respectively. A third pump, C, can fill the reservoir at a rate of 15 litres per minute. If all three pumps function simultaneously to fill the reservoir in 10 minutes, determine the total capacity of the reservoir (in litres).

The correct answer is 562.5 litres.

Let the total capacity of the reservoir be $V$ litres.

We are given the following information about the three pumps:

1. Pump A can fill the reservoir in 25 minutes.
Work done per minute by Pump A = $\frac{V}{25}$ litres per minute.

2. Pump B can fill the reservoir in 30 minutes.
Work done per minute by Pump B = $\frac{V}{30}$ litres per minute.

3. Pump C can fill the reservoir at a rate of 15 litres per minute.
Work done per minute by Pump C = $15$ litres per minute.

When all three pumps function simultaneously, they fill the reservoir in 10 minutes.
Therefore, the combined rate of all three pumps is:

$\frac{V}{10}$

Setting up the rate equation for the combined work of pumps A, B, and C:

$\frac{V}{25}+\frac{V}{30}+15=\frac{V}{10}$

To solve for $V$, let's move all terms involving $V$ to one side of the equation:

$15=\frac{V}{10}-\frac{V}{25}-\frac{V}{30}$

Find a common denominator for the fractions on the right side. The least common multiple of 10, 25, and 30 is 150.

Rewrite each fraction with a denominator of 150:

$\frac{V}{10}=\frac{15V}{150}$

$\frac{V}{25}=\frac{6V}{150}$

$\frac{V}{30}=\frac{5V}{150}$

Substitute these fractions back into the equation:

$15=\frac{15V-6V-5V}{150}$

$15=\frac{4V}{150}$

Now, solve for $V$:

$4V=15\times 150$

$4V=2250$

$V=\frac{2250}{4}=562.5$

Thus, the total capacity of the reservoir is 562.5 litres.