Pipes and Cistern
1. Pipes X, Y and Z take respectively 20
minutes, 15 minutes and 12 minutes to fill a cistern. How much time they would
take, if all the three pipes are opened together to fill the cistern?
Answer: 5 minutes. Apply the formula XYZ / (XZ + YZ + XY)
2. Pipes X and Y can fill a tank in 10
hours and 12 hours respectively while pipe Z takes 20 hours to empty the tank.
If all the three pipes are opened together, then in how much time the tank will
be filled?
Answer: 7 hours 30
minutes. Apply the
formula XYZ / (XZ + YZ – XY)
3. Pipes A and B can fill a bucket in 12
minutes and 15 minutes respectively. If both the pipes are opened initially for
three minutes, after which pipe A is closed, then in how many more minutes pipe
B will fill the bucket?
Answer: 8 minutes and 15
seconds
Pipe
A in one minute 1/12. In three minutes 3/12 ie ¼ bucket.
Pipe
B in one minute 1/15. In three minutes 3/15 ie 1/5 bucket.
Thu
both the pipes in three minutes would fill 1/4 + 1/5 = 9/20 bucket.
Remaining
11/20 bucket to be filled by Pipe B alone.
The
time taken by Pipe B to do this is (11/20) / (1/15) = 8 ¼ minutes.
4. A leak at the bottom of a tank can
empty the full tank in 6 hours. There is an inlet pipe that fills water at the
rate of 4 litres a minute. When the tank is full the inlet pipe is opened and
the tank is emptied in 8 hours. What is the capacity of the tank in litres?
Answer: 5760 litres. (
In questions like the above, where a leak is mentioned, please treat the leak
as a pipe that drains the tank)
Normally
the leak takes 6 hours to drain a full tank. Keep this as ‘x’ Now when the
inlet is opened and pours water, the leak takes 8 hours to drain the full tank.
Keep this as ‘y’. If the inlet is opened on an empty tank it would have taken
xy / y – x hours to fill the tank. Apply this formula and you get 24 hours to
fill the tank.
We
are given that the inlet in one minute fills 4 litres. Hence in 24 hours it
would fill
4 x 60 x 24 = 5760
litres.
5. A cistern has two pipes that fill a
tank in 12 minutes and 16 minutes respectively. There is also a drain pipe in
the tank. When all the three pipes are opened, the tank gets filled in20
minutes. How long the drain pipe would take to empty a full tank?
Answer: 10 minutes
Let
us assume the drain pipe takes ‘x’ minutes to drain a full tank. Then in one
minute the following equation arise:
1/12 + 1/16 – 1/x = 1/20 solving this we get in one minute the drain
pipe can drain 1/10 of the tank. Hence to drain the full tank it would take 10
minutes.
6. Pipes A and B can fill a tank in 6
hours and 4 hours respectively. If the pipes are kept open alternately for one
hour each, with pipe A starting the schedule, then in how much hour the tank
will be full?
Answer: 5 hours
Pipe
A is opened first. In the first hour the tank is full up to 1/6 level.
Pipe
B is opened next. In the 2nd hour the tank is full upto 1/4 + 1/6
level = 5/12 level.
Thus
in 2 hours the tank is full upto 5/12 level.
In
four hours the tank will be full upto 10/12 or 5/6 level. The remaining
capacity of the tank is 1 – 5/6 = 1/6 level.
This
pipe A in the third cycle will fill completely. Thus the total time taken is 5 hours.
7. A tap can fill a tank in 16 minutes
and another tap can empty the tank in 8 minutes. If the tank is already full
and then both the taps are opened the tank will be
a) Filled in 12 minutes b) emptied in
12 minutes
(c) Filled in 8 minutes d)
empties in 8 minutes
Answer: emptied in 8
minutes.
When
both the taps are opened the net effect of filling in one minute is
1/16–1/8
= -1/16. The drain pipe takes 16 minutes to drain a full tank. The tank is half
full and hence it would take 8 minutes to drain.
X ---x--- X
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