Three heavy-duty water pumps, designated P1, P2, and P3, can fill an industrial reservoir independently in 12 hours, 18 hours, and 36 hours, respectively. To manage energy consumption, the pumps are operated sequentially for one hour at a time: Pump P1 runs during the first hour, Pump P2 during the second hour, Pump P3 during the third hour, and this rotation repeats continuously in the same order. How many hours will be required to completely fill the reservoir?

The correct option is 18 hours.

Step 1: Determine the individual work rate of each pump

Let the total capacity of the industrial reservoir be 1 unit.

Work done by Pump P1 in 1 hour = $\frac{1}{12}$

Work done by Pump P2 in 1 hour = $\frac{1}{18}$

Work done by Pump P3 in 1 hour = $\frac{1}{36}$

Step 2: Calculate the work completed in one 3-hour rotation cycle

Since the pumps operate sequentially for 1 hour each (P1 in the 1st hour, P2 in the 2nd hour, and P3 in the 3rd hour), one complete rotation cycle takes 3 hours.

Total work done in 3 hours = $\frac{1}{12}+\frac{1}{18}+\frac{1}{36}$

Taking the least common multiple (LCM) of 12, 18, and 36, which is 36:

Work done in 3 hours = $\frac{3+2+1}{36}=\frac{6}{36}=\frac{1}{6}$

Thus, $\frac{1}{6}$ of the reservoir is filled during each 3-hour cycle.

Step 3: Calculate the total time required to completely fill the reservoir

Number of 3-hour cycles required = $\frac{1}{1/6}=6$ cycles

Total time required = $6\times 3\text{hours}=18\text{hours}$

Therefore, it will take 18 hours to completely fill the reservoir.