Pipes and Cisterns Solved Problems

1. Two pipes can fill a tank in 10 hours and 12 hours respectively while a third, pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time will the tank be filled?
A. 4 hrs 30 min                    
B. 7 hrs 30 min
C. 8 hrs 10 min                    
D. None of these
Answer: B

Explanation:

Net part filled in 1 hour = (1/10) + (1/12)-(1/20) = (8/60) = (2/15).
The tank will be full in 15/2 hrs = 7 hrs 30 min.

2. An electric pump can fill a tank in 3 hours. Because of a leak in, the tank it took 3(1/2) hours to fill the tank. If the tank is full, how much time will the leak take to empty it?
A. 14 hours                         
B. 16 hours
C. 18 hours                         
D. 21 hours
Answer: D

Explanation:

Work done by the leak in 1 hour= (1/3)-(1/ (7/2))
= (1/3)-(2/7) = (1/21).
The leak will empty .the tank in 21 hours.

3. Two pipes A and B can fill a tank in 36 min. and 45 min. respectively. A water pipe C can empty the tank in 30 min. First A and B are opened. After 7 min, C is also opened. In how much time, the tank is full?
A. 17 min                            
B. 24 min
C. 28 min                            
D. 39 min
Answer: D

Explanation:

Part filled in 7 min. = 7*((1/36) + (1/45)) = (7/20).
Remaining part= (1-(7/20)) = (13/20).
Net part filled in 1 min. when A, B and C are
opened= (1/36) + (1/45)-(1/30) = (1/60).
Now, (1/60) part is filled in one minute.
(13/20) part is filled in (60*(13/20)) =39 minutes.

4. Two pipes A, B can fill a tank in 24 min. and 32 min. respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 min.?
A. 5 min                             
B. 14 min
C. 8 min                             
D. 19 min
Answer: C

Explanation:

Let B be closed after x min. then,
Part filled by (A+B) in x min. +part filled by A in (18-x) min = 1
Therefore x*((1/24) + (1/32)) + (18-x)*(1/24) =1
=>  (7x/96) + ((18-x)/24) =1.
=> 7x +4*(18-x) =96.

Hence, be must be closed after 8 min.

5. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
A. 12 min                          
B. 15 min
C. 25 min                          
D. 50 min
Answer: A

Explanation:

Part filled by A in 1 min =     1/20
Part filled by B in 1 min =     1/30
Part filled by (A + B) in 1 min = (1/20  + 1/30) = 1/12
Both pipes can fill the tank in 12 minutes.