Pipes and Cistern
- 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
- Through an inlet, a tank takes 8 h to get filled up. Due to a leak in the bottom, it takes 2 h more to get it filled completely. If the tank is full, how much time will the leak take to empty it?
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Let the leak takes x h to empty the tank.
Now, part filled by inlet in 1 h = 1/8
part filled in 1 h when both tap and leak works together = 1/(8+2) = 1/10
According to the question.
1/x = 1/8 - 1/10 = (5 - 4) / 40 = 1/40Correct Option: D
Let the leak takes x h to empty the tank.
Now, part filled by inlet in 1 h = 1/8
part filled in 1 h when both tap and leak works together = 1/(8+2) = 1/10
According to the question.
1/x = 1/8 - 1/10 = (5 - 4) / 40 = 1/40
∴ x = 40 h
- Two pipes A and B can fill a tank in 1 h and 75 min, respectively. There is also an outlet C . If all the three pipes are opened together. The tank is full 50 min. How much time will be taken by C to empty the full tank?
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Work done by C in 1 min = (1/60 + 1/75 - 1/50 )
= (5 + 4 - 6)/300 = 3/300 = 1/100Correct Option: A
Work done by C in 1 min = (1/60 + 1/75 - 1/50 )
= (5 + 4 - 6)/300 = 3/300 = 1/100
Hence, C can empty the full tank in 100 min.
- A, B and C are three pipes connected to a tank. A and B together fill the tank in 6 h, B and C together fill the tank in 10 h and A and C together fill the tank in 12 h. in how much time A, B and C fill up the tank together?
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Part filled by ( A + B ) in 1 h = 1/6
Part filled by ( B + C ) in 1 h = 1/10
Part filled by ( A + C ) in 1 h = 1/12
∴ Part filled by 2 ( A + B + C ) in 1 h = 1/6 +1/10 + 1/12 = (10 + 6 + 5)/60 = 21/60 = 7/20
∴ Part filled by ( A + B + C ) in 1 h = 7/(2 x 20) = 7/40Correct Option: D
Part filled by ( A + B ) in 1 h = 1/6
Part filled by ( B + C ) in 1 h = 1/10
Part filled by ( A + C ) in 1 h = 1/12
∴ Part filled by 2 ( A + B + C ) in 1 h = 1/6 +1/10 + 1/12 = (10 + 6 + 5)/60 = 21/60 = 7/20
∴ Part filled by ( A + B + C ) in 1 h = 7/(2 x 20) = 7/40
∴ Required time 40/7 = 55/7 h
- Two pipes P and Q can fill a cistern in 12 and 15 min, respectively. If both are opened together and at the end of 3 min, the first is closed. How much longer will the cistern take to fill?
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Part filled by pipe P in 1 min = 1/12
Part filled by pipe Q in 1 min = 1/15
Part filled by both pipes in 1 min = 1/12 + 1/15 + = (5 + 4)/60 = 9/60
Now, Part filled by both pipes in 3 min = (3 x 9)/60 = 27/60 = 9/20
∴ Remaining part = 1 - 9/20 = 11/20Correct Option: A
Part filled by pipe P in 1 min = 1/12
Part filled by pipe Q in 1 min = 1/15
Part filled by both pipes in 1 min = 1/12 + 1/15 + = (5 + 4)/60 = 9/60
Now, Part filled by both pipes in 3 min = (3 x 9)/60 = 27/60 = 9/20
∴ Remaining part = 1 - 9/20 = 11/20
Let the remaining part is filled by pipe Q in T min.
Then, T/15 = 11/20
T = (15 x 11)/20 = (3 x 11)/4
= 33/4 = 84/4 min