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

To determine the time taken by both pipes working simultaneously, their individual filling rates are combined.

Pipe A fills $\frac{1}{20}$ of the tank in 1 minute.
Pipe B fills $\frac{1}{30}$ of the tank in 1 minute.
When both pipes are opened, their combined filling rate per minute is the sum of their individual rates:

Combined rate = $\frac{1}{20} + \frac{1}{30}$

To sum these fractions, a common denominator (LCM of 20 and 30, which is 60) is used:

Combined rate = $\frac{3}{60} + \frac{2}{60} = \frac{5}{60} = \frac{1}{12}$ of the tank per minute.

Therefore, if both pipes fill $\frac{1}{12}$ of the tank in 1 minute, they will fill the entire tank in 12 minutes.

Option 1 (10 minutes): This would imply a combined filling rate of $\frac{1}{10}$ of the tank per minute. However, the calculated combined rate is $\frac{1}{12}$ . A time of 10 minutes is faster than the actual combined rate and does not result from the correct summation of individual rates.
Option 3 (15 minutes): This value is incorrect because it does not correspond to the sum of the individual filling rates. If the combined time were 15 minutes, the rate would be $\frac{1}{15}$ , which is not equal to $\frac{1}{20} + \frac{1}{30}$ .
Option 4 (25 minutes): This represents the simple average of the individual times (20 + 30) / 2 = 25 minutes. In 'work and time' problems, the combined time taken by multiple entities working together is always less than the time taken by the fastest individual entity. Since Pipe A takes 20 minutes, the combined time must be less than 20 minutes. Therefore, 25 minutes is logically incorrect.