Question

A cistern has two inlet pipes A and B which can fill it in 8 hours and 6 hours, respectively.
An outlet pipe C can empty the full cistern in 4 hours. If the pipes A, B and C are opened
simultaneously in the empty cistern, how much time will they take to fill the cistern
completely?
​

Answer 1

Answer:

• All the pipes together will take 24 hours to fill the cistern.

Step-by-step explanation:

Given that:

• A can fill the cistern in 8 hours.
• B can fill the cistern in 6 hours.
• C can empty a full cistern in 4 hours.

To Find:

• How much time will all pipes together take to fill the cistern completely?

Process:

We have been given time taken by different pipes to fill/empty the cistern. We will calculate every pipe's one hour work. Then, we will add every pipe's one hour work to get the one hour work of all the pipes together. After that we can find time taken by all pipes together to fill the cistern completely.

Solution:

A can fill the cistern in 8 hours.

B can fill the cistern in 6 hours.

C can empty a full cistern in 4 hours.

$\sf{A's \:one \:hour \:work = \dfrac{1}{8}}$

$\sf{B's \:one \:hour \:work = \dfrac{1}{6}}$

$\sf{C's \:one \:hour \:work = \dfrac{-1}{4}}$

$\sf{[because \:C \:is \:emptying\: the \:cistern.]}$

$\sf{(A+B+C)'s \:one \:hour \:work = \dfrac{1}{8}+\dfrac{1}{6}-\dfrac{1}{4}}$

$\because \texttt{LCM of 8, 6 and 4 is 24.}$

$\therefore\sf{\dfrac{3+4-6}{24}}$

$=\sf{\dfrac{7-6}{24}}$

$=\sf{\dfrac{1}{24}}$

Hence, if we open all the pipes it will take 24 hours to fill the cistern completely.

Answer 2

Step-by-step explanation:

ANSWER : 24 HOURS OR 1 DAY

PLEASE REFER TO THE ATTACHMENT FOR THE METHOD!!

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