Two pipes A and B can independently fill a tank completely in 20 and 30 minutes respectively. If both the pipes are opened simultaneously, how much time will they take to fill the tank completely?

The correct option is 12 minutes.

To find the time taken by both pipes A and B together to fill the tank, we can determine the work done by each pipe in one minute.

The time taken by Pipe A to fill the tank completely = 20 minutes.
Therefore, the fraction of the tank filled by Pipe A in 1 minute is:
$$\frac{1}{20}$$

Similarly, the time taken by Pipe B to fill the tank completely = 30 minutes.
Therefore, the fraction of the tank filled by Pipe B in 1 minute is:
$$\frac{1}{30}$$

If both pipes are opened simultaneously, the fraction of the tank filled by both pipes together in 1 minute is the sum of their individual 1-minute rates:
$$\text{Combined Rate in 1 minute}=\frac{1}{20}+\frac{1}{30}$$

To add these fractions, we find the Least Common Multiple (LCM) of 20 and 30, which is 60:
$$\frac{1}{20}+\frac{1}{30}=\frac{3+2}{60}=\frac{5}{60}=\frac{1}{12}$$

Since the two pipes together can fill $\frac{1}{12}$ of the tank in 1 minute, the total time required to fill the tank completely is the reciprocal of this rate:
$$\text{Total Time}=\frac{1}{\left(\frac{1}{12}\right)}=12\text{minutes}$$
Thus, both pipes working together will take 12 minutes to fill the tank completely.