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?

Explanation: 1. Calculate the rate of each pipe: Pipe A fills the tank in 20 minutes, so its rate is 1/20 of the tank per minute. Pipe B fills the tank in 30 minutes, so its rate is 1/30 of the tank per minute. 2. Calculate their combined rate when opened simultaneously: Combined rate = Rate of A + Rate of B Combined rate = 1/20 + 1/30 To add these fractions, find a common denominator, which is 60. Combined rate = (3/60) + (2/60) = 5/60 = 1/12 of the tank per minute. 3. Determine the time taken to fill the tank completely: If they fill 1/12 of the tank per minute, they will fill the entire tank (1 unit) in 12 minutes. Therefore, the correct time is 12 minutes. Analysis of Options: A) 10 mins: Incorrect. This would imply an even faster combined rate than calculated. B) 12 mins: Correct, as calculated from the combined work rate. C) 15 mins: Incorrect. D) 25 mins: Incorrect. This is the average of the two times (20+30)/2. When working together, the time taken must always be less than the time taken by the faster individual worker (in this case, less than 20 minutes). So, 25 minutes is logically impossible.