## Pipes and Cisterns

Note – Problems on Pipes and Cisterns are same as that of Time and Work.

1. If a pipe fills a tank in x hours, then the part filled in 1 hour = 1/x.
2. If a pipe empty a tank in x hours, then the part of tank emptied in 1 hour = 1/x hours
3. If a Pipe A alone fills a tank in x hours and another Pipe B alone fills in y hours. Then the time taken to fill the tank when both pipes are open = (x × y/x + y) hours.
4. If two pipes A and B together fills a tank in x hours and A alone fills in y hours, then the time taken by B to fill the tank = (x × y/y – x) hours
5. If a Pipe A alone empties a tank in x hours and another Pipe B alone empty it in y hours. Then the time taken to empty the tank when both pipes are open = (x × y/x + y) hours
6. If A, B, and C alone fills a tank in x, y, and z hours, then the time taken to fill the tank when all are open =
• (xyz/xy + yz + zx) hours
7. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (x>y), then the net part emptied in 1 hour will be –
• [(1/y) – (1/x)]

Example-

Two pipes can fill a tank in 24 hours and 36 hours respectively. If both the pipes are opened at the same time, then how much time will be taken to fill the tank ?

Solution-

Pipe A in 1 hour = 1/24

Pipe B in 1 hour = 1/36

Pipe A and B together in 1 hour = (1/24) + (1/ 36) = 1/9

So, Both Pipes will take 9 hours to fill the tank. (Reason- Check Statement 1)

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