Pipes and Cistern
- A tank can be filled with water by two pipes A and B together in 36 minutes. If the pipe B was stopped after 30 minutes, the tank is filled in 40 minutes. The pipe B can alone fill the tank in
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Let the pipe B fill the tank in t minutes.
Part of the tank filled by pipes A and B in 1 minute = 1 36 ∴ Part of the tank filled by pipe A in 1 minute = 1 - 1 36 t
According to the question,30 × 1 + 40 
1 - 1 
= 1 t 36 t ⇒ 30 + 10 - 40 = 1 t 9 t
Correct Option: D
Let the pipe B fill the tank in t minutes.
Part of the tank filled by pipes A and B in 1 minute = 1 36 ∴ Part of the tank filled by pipe A in 1 minute = 1 - 1 36 t
According to the question,30 × 1 + 40 1 - 1 = 1 t 36 t ⇒ 30 + 10 - 40 = 1 t 9 t ⇒ 40 - 30 = 10 - 1 t t 9 ⇒ 10 = 1 ⇒ t = 90 minutes t 9
- Pipe A can fill a Tank in 30 min, while pipe B can fill the same tank in 10 min and pipe C can empty the full tank in 40 min. If all the pipes are opened together, how much time will be needed to make the tank full?
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Part filled by A in 1 min = 1/30
Part filled by B in 1 min = 1/10
Part emptied by C in 1 min = - 1/40
Net part filled in 1 h by ( A + B + C ) = ( 1/30 + 1/10 - 1/40 )Correct Option: A
Part filled by A in 1 min = 1/30
Part filled by B in 1 min = 1/10
Part emptied by C in 1 min = - 1/40
Net part filled in 1 h by ( A + B + C ) = ( 1/30 + 1/10 - 1/40 )
= (4 + 12 - 3)/120 = 13/120
∴ Required time to fill the tank = 120/13 = 93/13 h
- There are three taps of diameter 1 cm, 4/3 cm and 2 cm, respectively. The ratio of the water flowing through them is equal to the ratio of the square of their diameters. The biggest tap can fill the tank alone in 61 min. If all the taps are opened simultaneously, how long will the tank take to be filled?
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Time taken to fill the tank by the tap having 2 cm diameter = 61 min
∴ Time taken to fill the tank by the tap having 1 cm diameter
= 61 x (2/1)2 = 244 min
Similarly, time taken to fill the tank by the tap having 4/3 cm diameter
= 61 x [(2 x 3)/4]2 = 61 x 9/4 = 549/4 min.Correct Option: D
Time taken to fill the tank by the tap having 2 cm diameter = 61 min
∴ Time taken to fill the tank by the tap having 1 cm diameter
= 61 x (2/1)2 = 244 min
Similarly, time taken to fill the tank by the tap having 4/3 cm diameter
= 61 x [(2 x 3)/4]2 = 61 x 9/4 = 549/4 min.
∴ Part of the tank filled by all the three pipes in 1 min
= 1/61 + 1/244 + 1/(549/4)
= (36 + 9 + 16)/2196 = 61/2196 = 1/36
Hence, required time taken = 36 min
- A cistern has three pipes A, B and C. Pipes A and B can fill it in 3 and 4 h, respectively, while pipe C can empty the completely filled cistern in 1 h. If the pipes are opened in order at 3:00 pm, 4:00 pm and 5:00 pm, respectively , at what time will the cistern be empty?
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Let the cistern gets emptied in m h after 3:pm
Work done by A in m h, by B in (m - 1) h and by c in (m - 2) h= 0Correct Option: B
Let the cistern gets emptied in m h after 3:pm
Work done by A in m h, by B in (m - 1) h and by c in (m - 2) h= 0
⇒ m/3 + (m - 1)/4 - (m - 2) = 0
⇒ 4m + 3(m - 1) - 12(m - 2) = 0
⇒ 5m = 21
⇒ m = 21/5 = 4.2
∴ m = 4 h 12 min
∵ Required time = 7 : 12 pm.
- A tank can be filled by a tap in 20 min and by another tap in 60 min. Both the taps are kept open for 5 min and then the 1st tap is shut off. After this, how much time the tank will be completely filled?
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Part of the tank filled by both taps in 5 min = 5 x (1/20 + 1/60)
= 5 x (6 +2 )/120 = 8/24 = 1/3
∴ Remaining part = (1 - 1/3) = 2/3
∵ 1/60 Part is now filled in 1 min.Correct Option: D
Part of the tank filled by both taps in 5 min = 5 x (1/20 + 1/60)
= 5 x (6 +2 )/120 = 8/24 = 1/3
∴ Remaining part = (1 - 1/3) = 2/3
∵ 1/60 Part is now filled in 1 min.
∴ 2/3 Part is now filled in 60 x 2/3 = 40 min.
