Pipes and Cistern
- Two pipes A and B are opened together to fill a tank. Both pipes fill the tank in a certain time. If A separately takes 16 min more than the time taken by ( A + B ) and B takes 9 min more than the time taken by ( A + B ). Find the time taken by A and B to fill the tank when both the pipes are opened together.
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Here, a = 16 and = 9
Required time = √abCorrect Option: B
Here, a = 16 and = 9
Required time = √ab
√16 x 9 = 4 x 3 = 12 min
- There are three pipes connected with a tank. The first pipe can fill 1/2 part of the tank in 1 h, second pipe can fill 1/3 part of the tank in 1 h. Third pipe is connected to empty the tank. After opening all the three pipes, 7/12 part of the tank can be filled in 1 h, then how long will third pipe take to empty the full tank.
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1st pipe takes 1 h to fill 1/2 part of the tank.
So, time taken to fill the whole tank (m) = 2 h
2nd pipe takes 1 h to 1/3 part of the tank
So, time taken to fill the whole tank (n) = 3 h
Let 3rd pipe takes P h to empty the tank = x
∴ 1/m + 1/n - 1/x = 7/12 ⇒ 1/2 + 1/3 - 1/x = 7/12
⇒ 1/x = (6 + 4 - 7)/12 = 3/12 = 1/4Correct Option: B
1st pipe takes 1 h to fill 1/2 part of the tank.
So, time taken to fill the whole tank (m) = 2 h
2nd pipe takes 1 h to 1/3 part of the tank
So, time taken to fill the whole tank (n) = 3 h
Let 3rd pipe takes P h to empty the tank = x
∴ 1/m + 1/n - 1/x = 7/12 ⇒ 1/2 + 1/3 - 1/x = 7/12
⇒ 1/x = (6 + 4 - 7)/12 = 3/12 = 1/4
∴ x = 4 h
- Two pipes can fill a tank in 20 and 24 min, respectively and a waste pipe can empty 6 gallon per min. All the three pipes working together can fill the tank in 15 min. Find the capacity of the tank.
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Part filled by 1st pipe in 1 min = 1/20
Part filled by 2nd pipe in 1 min = 1/24
Part filled by all the pipes in 1 min = 1/15
Work done by the waste pipe 1 min
= 1/15 - (1/20 + 1/24 )
= 1/15 - 11/120
= (8 - 11)/120 = ( - 3/120 ) = ( -1/40 )Correct Option: D
Part filled by 1st pipe in 1 min = 1/20
Part filled by 2nd pipe in 1 min = 1/24
Part filled by all the pipes in 1 min = 1/15
Work done by the waste pipe 1 min
= 1/15 - (1/20 + 1/24 )
= 1/15 - 11/120
= (8 - 11)/120 = ( - 3/120 ) = ( -1/40 )
[-ve sign indicates emptying]
Now, volume of 1/40 part = 6 gallon
∴ Volume of whole tank = 40 x 6 = 240 gallon
- 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.
- 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.