Question

Two pipes A and B can separately fill a cistern in 20 minutes and 30 minutes respectively, while a third pipe C can empty the full cistern in 15 minutes. If all the pipes are opened together, in what time the empty cistern is filled?​

Answer 1

If all the pipes are opened together, the empty cistern will be filled in 60 minutes.

Step-by-step explanation:

Pipe A can fill the cistern = 20 minutes

So, In 1 minute the fraction of cistern filled by pipe A  = $\frac{1}{20}$

Pipe B can fill the cistern = 30 minutes

So, In 1 minute the fraction of cistern filled by pipe B  = $\frac{1}{30}$

 Pipe C can empty the full cistern = 15 minutes

So, In 1 minute the fraction of cistern emptied by pipe C  = $\frac{1}{15}$

Therefore,

In 1 minute, the fraction of cistern filled, if all the 3 pipes are opened together is,

$= \frac{1}{20} + \frac{1}{30} - \frac{1}{15} \\= \frac{3 + 2 - 4}{60} \\= \frac{1}{60}$

Thus, if all the 3 pipes are opened together, then the empty cistern is filled in 60 minutes.

 

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Also View:

Two pipes a and b can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 3 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill ?

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Two pipes a and b can fill a cistern in 15 and 20 minutes respectively while third pipe c can empty the tank in 30 minutes. if the three taps are opened successively for one minute each, how long will it take to fill the cistern?

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Answer 2

Answer: 1 hour

Step-by-step explanation:

Pipe A can fill the cistern = 20 minutes

So, In 1 minute = 1/20

Pipe B can fill the cistern = 30 minutes

So, In 1 minute=1/30

Pipe C can empty the full cistern = 15 minutes

So,In 1 minute =1/15

Therefore, In 1 minute, the fraction of cistern filled if all the 3 pipes are opened together is

= 1/20+1/30=1/15

=3+2-4/60

=1/60

Thus, if all the 3 pipes are opened together, then the empty cistern is filled in 60 minutes =1 hour.

Hope it's helps you......