Two pipes P and Q can fill a tank in 25 minutes and 30 minutes respectively. Pipe R fills the tank at a rate of 15 litres per minute. If all three pipes working together can fill the tank in 10 minutes, what is the capacity of the tank (in litres)?

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**Solution:**

1. Calculate the filling rates of pipes P and Q:
   - Pipe P fills the tank in 25 minutes, so its rate is $ $\frac{1}{25}$ $ tank per minute.
   - Pipe Q fills the tank in 30 minutes, so its rate is $ $\frac{1}{30}$ $ tank per minute.

2. Let the capacity of the tank be $ C $ litres.

3. Pipe R fills at 15 litres per minute, so in 10 minutes it fills $ $15 \times 10 = 150 $$ litres.

4. All three pipes together fill the tank in 10 minutes, so their combined rate is $ $\frac{1}{10}$ $ tank per minute.

5. The combined rate in terms of tank per minute is:
   $$
  $ \frac{1}{25} + \frac{1}{30} + \frac{150}{10C} = \frac{1}{10}$
   $$
   Here, $ $\frac{150}{10C} = \frac{15}{C}$ $ is the rate of pipe R in tank per minute.

6. Simplify the equation:
   $$
   $\frac{1}{25} + \frac{1}{30} + \frac{15}{C} = \frac{1}{10}$
   $$

7. Find common denominator for the fractions on the left:
   $$
   $\frac{6}{150} + \frac{5}{150} + \frac{15}{C} = \frac{1}{10}$
   $$
   $$
   $\frac{11}{150} + \frac{15}{C} = \frac{1}{10}$
   $$

8. Rearranging to isolate $ \frac{15}{C} $:
   $$
   $\frac{15}{C} = \frac{1}{10} - \frac{11}{150} = \frac{15}{150} - \frac{11}{150} = \frac{4}{150} = \frac{2}{75}$
   $$

9. Solve for $ C $:
   $$
   $\frac{15}{C} = \frac{2}{75} \implies C = \frac{15 \times 75}{2} = \frac{1125}{2} = 562.5$
   $$

**Answer:** The capacity of the tank is $ 562.5 $ litres.

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