If two pipes can together fill a cistern in minutes. If one pipe takes 3 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.

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Detailed Solution

Concept- We will consider the duration of one of the pipes to be variable, then calculate the percentage of the cistern that each pipe fills in a minute, using that information to calculate the total duration of the two pipes when they are both being used to fill the cistern. In order to determine the answer, we will compare this to the relevant facts.
We are informed that filling the cistern with one pipe takes 3 minutes longer than with the other. Let

minutes be the amount of time needed for just one of the pipelines to fill the cistern. Then, 3 minutes will be added to this, or

minutes, for the time needed by others to fill the cistern
alone.fraction of the cistern filled by first pipe in 1 minute is given by

the time taken by the other pipe to fill the cistern in 1 minute is given by

Therefore, if both pipes are together to fill the same cistern, then fraction of cistern filled by them in 1 minute will be

Taking LCM,
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Therefore, the time taken by both the pipes together to completely fill the cistern will be

time taken by both pipes together to fill the cistern

Therefore,

Cross multiplying, we get,

By using distributive law, we get,

Subtracting

from both sides, we get,
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