Pipe And CisternPage 1
1.  Two pipes A and B can fill a tank in 12 and 18 minutes respectively. If both the pipes are opened simultaneously, how long will it take to fill the tank?  (a)7.2 minutes  (b)7.4 minutes  (c)7.6 minutes  (d)7.8 minutes 

Answer is: APart of the tank filled by A in 1 minute = 1/12
Part of the tank filled by B in 1 minute = 1/18
Part of the tank filled by both the pipes in one minute = 1/12 + 1/18 = 5/36
∴ The tank can be filled in 36/5 minutes = 7.2 minutes
2.  Pipe A can fill a tank in 12 minutes and Pipe B in 18 minutes and pipe C can empty a full tank in 36 minutes. If all of them work together, find the time taken to fill the empty tank?  (a)7 min  (b)8 min  (c)9 min  (d)10 min 

Answer is: CWork done by the 3 pipes together in 1 minute = 1/12 + 1/18 – 1/36 = 1/9
So, the empty tank will be filled in 9 minutes.
3.  Two pipes A and B can fill a tank in 20 and 30 minutes respectively. There is an outlet C. if all the 3 pipes are opened, the tank will be filled in 24 minutes. How much time will it take for C alone to empty the full tank?  (a)26 min  (b)24 min  (c)23 min  (d)25 min 

Answer is: BWork done by C in one minute.
Work done by C in one minute = (1/20 + 1/30) – 1/24 = 1/12 – 1/24 = 1/24
∴ C can empty the tank in 24 minutes.
4.  Two pipes A and B fill a tank in 20 and 30 minutes respectively. If both pipes are opened at once, after how much time should A be closed so that the tank is filled in 15 minutes?  (a)12 min  (b)10 min  (c)14 min  (d)16 min 

Answer is: BPipe B works for 15 min.
In 1 min B fills (1/30)th of the tank
in 15 min it fills 15 x (1/30) = 1/2
The remaining 1/2 is filled by A. since A fills the tank fully in 20 min, it takes 10 min to fill 1/2 of the tank.
Hence, A worked for 10 min. So, A should be closed after 10 minutes.
5.  Three taps A, B and C together can fill a tank in 3 hours. After 1 hour C is closed and the tank is filled in 4 more hours. Find the time in which C alone can fill the tank?  (a)8 hours  (b)4 hours  (c)5 hours  (d)6 hours 

Answer is: DWork of A + B + C in 1 hour = 1/3
Remaining part of the tank = 1 – 1/3 = 2/3
Time taken by (A + B) to fill this (2/3)rd of the tank = 4 hours.
⇒ A and B together fill the tank in 6 hours.
Now, we know A + B + C = 3 hours
⇒ A + B = 6 hours
∴ C = 1/3 – 1/6 = 1/6
So, C alone can till the tank in 6 hours.
6.  A tank has a leak, which would empty it in 8 hours. A tap is turned on which fills at the rate of 4 liters per minute and the tank is now emptied in 12 hours. Find the capacity of the tank?  (a)5870 liters  (b)5720 liters  (c)5760 liters  (d)5860 liters 

Answer is: CWork done by leak and the filling tap in 1 hour = 1/12
Work done by filling tap = 1/8 – 1/12 = 1/24
⇒ Tank can be filled in 24 hours.
∴ Capacity of tank = 24 x 60 x 4 = 5760 liters
7.  A filling tap can fill a tank in 6 hours and an emptying tap can empty the tank in 12 hours. If both the taps are opened simultaneously, in how many hours will the tank be filled?  (a)6 hours  (b)12 hours  (c)18 hours  (d)24 hours 

Answer is: BFilling tap can fill (1/6)th of the tank in 1 hour.
Emptying tap can empty (1/12)th of the tank in 1 hour.
in 1 hour, the quantity of water filled by both the taps working together is
= 1/6 – 1/12 = (1/12)th of the tank.
∴ It takes 12 hours to completely fill the tank.
8.  Tap A can fill a tank in 2 hours and tap B can fill the tank in 3 hours. If both the taps are opened, simultaneously, then in how many minutes can they fill an empty tank?  (a)90 min  (b)36 min  (c)72 min  (d)120 min 

Answer is: CTap A can fill (1/2) of the tank in 1 hour.
Tap B can fill (1/3) of the tank in 1 hour.
Tap A and tap B together fill (1/2 + 1/3) of the tank i. e. (5/6)th of the tank in 1 hour.
time taken by them to fill the tank = 1/(5/6) = 6/5 hours = 6/5 x 60 min = 72 min.