Pipes and Cistern
Question
Q1.
12 Pumps working 6 hours a days can empty a completely filled reservoir in 15 days.How many such pumps working a hours a day will empty
the same reservoir in 12 days?.
(a)15 (b)9 (c)10 (d)12
Solution.
Hours/day = 6,9
Days = 15,12
Pumps = 12,x
Let x be number of pumps.
9:6::12:x = 12:15::12:x
9 x 12 x (x) =
6 x 12 x 15
x = (6 x 12 x 15)/(9 x 12) = 10
Solution
Q2.
Two pipes A and B are fill a tank in 20 minutes and 30 minutes respectively. If both pipes are opened together the time taken to fill
the tank is.
(a)50 minutes (b)12 minutes (c)25 minutes (d)15 minutes
Solution.
Part of the tank filled by both pipes in one minute.
= 1/20 + 1/30
Required time = 1/(1/20 + 1/30)
20 x 30/50 = 12 minutes
Solution
Q3.
Two pipes A and B can fill a tank in 36 hrs and 45 hrs respectively . If both the pipe are opened simultaneously, how much time
will be taken to fill the tank .
Solution.
Part filled by A alone in 1 hour =
1/36
Part filled by B alone in 1 hour =
1/45
∴ Part Filled by
(A + B) in 1 hour = (
1/36
+
1/45
) =
9/180
=
1/20
Hence, both the pipes together will fill the tank in 20 hrs.
Solution
Q4.
Two pipes A and B can fill a tank in 24 hrs and 32 hrs respectively. If both the pipes are opened simultaneously, after how much time
should B be closed so that the tank is full in 18 minutes ?
(a) 20 minutes (b) 8 minutes (c) 6 minutes
(d) 19 minutes
Solution.
Let pipe B be closed after minutes.
x(1/24 + 1/32) + (18 - x)/24 = 1
x = 8
Solution
Q5.
Pipe A can fill a tank in 20 hrs, pipe B alone can fill it in 10 hrs and pipe C can empty the full tank in 30 hrs. If all the pipes
are opened together, how much time will be needed to make the tank fill.
(a) 30 hrs (b) 60/7hrs (c) 20 hrs
(d) 20/7 hrs
Solution.
= 1/10 + 1/20 - 1/30 = 60/7
Solution
Q6.
Two pipes x and y can fill a tank in 5 hrs and 10 hrs respectively. If both the pipes are opened simultaneously after how much time should y
be closed so that the tank is full in 8 hrs.
(a) 1 hrs (b) 2 hrs (c) 3 hrs (d) 4 hrs
Solution.
let y be closed after t hrs.
t(1/5 + 1/10) + (8 - t)/10 = 1
t(3/10) + (8 - t)/10 = 1
(3t + 8 - t)/10 = 1
2t + 8 = 10
2t = 2
t = 1
Solution
Q7.
A tank has a leak which would empty it in 8 hrs. A tap is turned on which admits 10 litres a minute into the tank, and it is
now emptied in 12 hrs. How many litres does the tank hold ?
Solution.
The tab can fill the tank in
12 x 8/12 - 8
= 24 hrs
So, capacity of tank = 24 x 60 x 10 = 14,400 litres
Solution
Q8.
A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in bottom. If the cistern is full,
the leak will empty it in ____________ hrs.
Solution.
Let the leak can empty the tank in x hrs.
8 x (x)/x - 8
= 10
8x = 10x -80
x = 40 hrs.
Solution
Q9.
Two pipes A and B can fill the tank in 6 hrs and 4 hrs, if they open alternatly for one-one hour. In how many hours the tank
will be filled if A opens first.
Solution.
First pipe A will work for 1 hr = 1/6
then pipe B will work for 1 hr = 1/4
both pipe will work in 2 hrs = 5/12
both pipe can fill in 4 hrs = 5/6
now remaining part 1/6 will be filled by
pipe A in 1 hr.
so, total time taken by the pipes to fill the tank = 5 hrs.
Solution
Q10.
Two taps A and B can fill the tank in 12 hrs and 16 hrs respectively, initially both tab open after how many hours
tab B should be closed so that whole tank will fill in 9 hours.
Solution.
Let tab B will work for x hrs.
9/ 12
+
x/16
= 1
3/ 4
+
x/16
= 1
48 + 4x/ 64
= 1
48 + 4x = 64
4x = 16
x = 4
So the tab B will close after 4 hrs.
Solution
