QUESTION

CSAT

Easy

Maths

Prelims 2015

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?

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Explanation

Step 1: Calculate the rate of each pipe.

Pipe A can fill the tank in 20 minutes, so its rate is $\frac{1}{20}$ of the tank per minute.
Pipe B can fill the tank in 30 minutes, so its rate is $\frac{1}{30}$ of the tank per minute.

Step 2: Find the combined rate. Combined rate = $\frac{1}{20} + \frac{1}{30}$ The least common denominator of 20 and 30 is 60, so: Combined rate = $\frac{3}{60} + \frac{2}{60} = \frac{5}{60} = \frac{1}{12}$

Step 3: Calculate the total time. If the combined rate is $\frac{1}{12}$ of the tank per minute, it will take: Total time = $1 / (\frac{1}{12}) = 12$ minutes.