Gateway to SBI Mains: Concept and Quiz on Pipe and Cisterns

Nature of Pipe :                                              
Inlet: A pipe connected with a tank or reservoir for filling is called as inlet
Outlet: A pipe connected with a tank and used for empties it is called outlet.
Concept:
If a pipe can fill a tank in x hours, then the part filled in 1 hour = 1 / x

If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours, then the net part filled in 1 hour, when both the pipes are opened:
                                                         (1/x-1/y)
Time taken to fill the tank, when both the pipes are opened:
                                                   (x×y / y-x)

 If a pipe can fill a tank in x hours and another fill the same tank in y hours, then the net part filled in 1 hr, when both pipes are opened:
                                                   (1/x+1/y)
So time to fill the tank will be:
                                                  [x×y/(x+y)]

If a pipe fills a tank in x hrs and another fills the same tank in y hrs, but a third empties the full tank in z hrs and all of them are opened together, the net part filled in 1 hr:
                                               (1/x+1/y-1/z)
So time taken to fill the tank:
                                               xyz/(yz+xz-xy)

Practice questions:-
1). Two pipes A & B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are open simultaneously. How much times will be taken to fill the tank?
A) 15 hour
B) 25 hour
C) 20 hour
D) 30 hour
E) None of these

2) If A & B two pipes can fill a tank in 10 hour, when A pipe can fill a tank in 6 hour alone ,then in how much time will be taken to fill/empty the tank when pipe B open alone ?
A) Filled in 20 hr
B) Empty in 15 hr
C) Empty in 20 hr
D) Filled in 15 hr
E) None of these

3) Pipe A and B can fill a tank in 10 hour and 12 hour respectively but pipe C can empty the same tank in 15 hour, In how much time it will take fill the tank when the three pipes are opened together? 
A) 8.5 hour
B) 10 hour
C) 12 hour
D) 15 hour
E) None of these

4) Two pipes A & B fill an empty tank in 40 minutes and 60 minutes respectively, If both pipes are open simultaneously after how much time should A be closed so that tank is filled in 36 minutes? 
A) 36 min
B) 20 min
C) 25 min
D) 16 min
E) None of these.

5) Three taps A,B and C together can fill an empty tank in 4 hours, After 1hour , C is closed and the tank is filled in 6 more hours. Find the time in which C alone can fill the empty tank?
A) 18 hour
B) 10 hour
C) 12 hour
D) 15 hour
E) None of these.

6) Two pipe p1 and p2 can fill a tank in 40 minutes and 60 minutes respectively, both the taps are opened and after 10 minutes P1 was shut. In how much more time would the tank would be fill ?
A) 35 minutes
B) 45 minutes
C) 40 minutes
D) 50 minutes
E) None of these.

7) Three taps A,B and C can fill a tank in 20,30 and 40 minutes respectively. All the taps are opened  simultaneously and after 5 minutes tap A  was closed and then after 6 minutes tab B was closed .At the moment a leak developed which can empty the full tank in 60 minutes. What is the total time taken for the completely full?
A) 44 minutes
B) 25 minutes
C) 35 minutes
D) 24 minutes
E) None of these

8) Pipe A can fill the tank in half the time in which Pipe B can fill the same tank. If both the pipes are open simultaneously .it takes 8 hour to fill the tank .In how many hours can A alone fill the tank?
A) 12 hour
B) 10 hour
C) 8 hour
D) 15 hour
E) None of these

9) Three taps P,Q and R can individually fill a cistern in 7, 14 and 21 hours respectively .Tap P is opened  first for 1 hour and then Tap P is closed and Tap Q is opened for 1hour, tap Q is then closed and Tap R is then opened for 1 hour  after which Tap R is closed and Tap P opened again. This Process is continued till the tank is full. In how much time will the tank be completely full ?
A) 11 hour 
B) 12 hour
C) 13 hour
D) 14 hour
E) None of these.

10) There are three taps A,B, and C. A takes thrice as much time as B and C together to fill the tank . B takes twice as much time as A and C to fill the tank. In how much time can the Tap C fill the tank individually, if they would require 10 hours to fill the tank, When opened simultaneously ?
A) 14 hour
B) 25 hour
C) 15 hour
D) 20 hour
E) None of these.

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Answers
1) C
2) B
3) A
4) D
5) E
6) A
7) D
8) A
9) A
10)E

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