In this section, you will learn the shortcuts which can be useful to solve problems on pipes and cisterns.
1. If a pipe can fill a tank in ‘m’ hours, it can fill (1/m) part of the tank in 1 hour.
2. If (1/m) part of the tank is filled by a pipe in 1 hour, time taken by the pipe to fill the entire tank is "m" hours.
3. If a pipe can emty a tank in ‘x’ hours, it can empty (1/x) part of the tank in 1 hour.
4. If (1/m) part of the tank is emptied by a pipe in 1 hour, time taken by the pipe to empty the entire tank is "x" hours
5. If a pipe can fill a tank in "x" hours and another pipe can empty the full tank in "y" hours (x > y), then on opening both the pipes, the net part emptied in 1 hour is
= 1/y - 1/x
Problem 1 :
A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely ?
Problem 2 :
Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, how long will it take for the tank to be filled ?
Problem 3 :
Bucket A has twice the capacity as bucket B. It takes 54 turns for bucket A to fill the empty cistern. How many turns will it take for both the buckets A and B, having each turn together to fill the empty cistern ?
Problem 4 :
80 buckets of water fill a tank when the capacity of each bucket is 12. 5 liters. How many buckets will be needed to fill the same tank if the capacity of each bucket is 10 liters ?
Problem 5 :
Taps A and B can fill a cistern in 12 minutes and 15 minutes respectively. If both are opened and A is closed after 4 minutes, how much further time would it take for B to fill the cistern ?
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