Aptitude 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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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.
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