Two pipes A and B can fill a cistern in 24 minutes and 30...

Two pipes $A$ and $B$ can fill a cistern in 24 minutes and 30 minutes, respectively. There is also an outlet C. If all the three pipes are opened together, the cistern is full in 20 minutes. How much time will be taken by $C$ to empty the full cistern? (a) 30 minutes (b) 40 mintues (c) 45 mintues (d) None of these

Two pipes $A$ and $B$ can fill a cistern in 24 minutes and 30 minutes, respectively. There is also an outlet C. If all the three pipes are opened together, the cistern is full in 20 minutes. How much time will be taken by $C$ to empty the full cistern?
(a) 30 minutes
(b) 40 mintues
(c) 45 mintues
(d) None of these

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Key Concepts

Work Rate

Work rate refers to the amount of work completed per unit of time. In problems involving pipes and cisterns, it is often expressed as a fraction of the cistern filled or emptied per minute, providing a standard measure to combine individual contributions.

Combined Work Rates

When multiple pipes operate simultaneously, their individual work rates are added together to form an overall or net work rate. For pipes that fill the cistern, their rates add, whereas any outlet that empties the cistern contributes a negative rate, decreasing the overall rate.

Inverse Relationship of Time and Rate

There is an inverse relationship between time and work rate: the time taken to complete a task is the reciprocal of the net work rate. This means that if the net rate is known, the total time required can be computed by taking the inverse of that rate.

Negative Work Rate for Outlets

Outlets or taps that empty a cistern have a negative work rate because they remove water rather than add it. When calculating the net effect on the cistern's volume, this negative rate is subtracted from the combined positive work rates of the filling pipes.

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