Pipes and Cistern

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Pipes and Cistern:


What is Inlet?

A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as inlet.

What is Outlet?

A pipe connected with a tank or a cistern or a reservoir, emptying it, is known as an outlet.

  • If a pipe can fill a tank in x hours, then:

part filled in 1 hour = 1/x

  • If a pipe can empty a full tank in y hours, then:

part emptied in 1 hour = 1/y

  • If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y>x), then on opening both the pipes, the net part filled in 1 hour = (1/x – 1/y)
  • If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where x>y), then on opening both the pipes, the net part emptied in 1 hour = (1/y – 1/x)

Aptitude Questions (Pipes and Cistern):

1. A tap can fill a tank in 6 hours. Once the half the tank is filled, three more similar taps are opened. In how much time the tank will fill completely?

A)    3 hrs 30 min

B)    3 hrs 45 min

C)    4 hrs

D)    4 hrs 15 min

E)    None of these

View Answer

Answer: option (B)

Explanation:

Time taken by one tap to fill half tank = 3 hrs

Some part filled by the four taps in 1 hour = (4 * (1/6)) = 2/3

Remaining Part = (1 -(1/2)) = 1/2

∴ 2/3 : 1/2 : : 1 : x or x = (1/2)*1*(3/2) = 3/4 hrs i.e. 45 mins.

So, total time taken = 3hrs 45 mins.

 

2. Two pipes X and Y can fill a tank in 20 and 30 minutes respectively. If we use both the pipes together, then how long will it take to fill the tank?

A)    12 min

B)    20 min

C)    25 min

D)    18 min

E)    None of these

View Answer

Answer: option (A)

Explanation:

Part filled by X in 1 min = 1/20; Part filled by Y in 1 min = 1/30


Part filled by (X + Y) in 1 min. = (1/20 + 1/30) = 1/12

∴ both pipes fill the tank in 12 minutes.

 

3. A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If we open both the taps simultaneously then after how much time will the cistern get filled?

A)    4.5 hrs

B)    5 hrs

C)    6.5 hrs

D)    7.2 hrs

E)    None of these

View Answer

Answer: option (D)

Explanation:

Net part filled in 1 hour = (1/4 – 1/9) = 5/36

∴ cistern will be filled in 36/5 hrs i.e. 7.2 hrs

 

4. A water tank is two-fifth full. Pipe X can fill a tank in 10 minutes and pipe Y can empty it in 6 minutes. If we open both the pipes, then how long will it take to empty or fill the tank completely?

A)    6 min to empty

B)    7 min to fill

C)    7 min to empty

D)    6 min to fill

E)    None of these

View Answer

Answer: option (A)

Explanation:

Pipe Y is faster than pipe X and so, the tank will be emptied

Part to be emptied = 2/5

Part emptied by (X + Y) in 1 minute = (1/6 – 1/10) = 1/15

∴ 1/15 : 2/5 : : 1 : x or x = ((2/15)*1*15) = 6 min

So, the tank will get emptied in 6 min.

 

5. Pipe X can fill a tank in 5 hours, pipe Y in 10 hours and pipe Z in 30 hours. In how many hours will the tank be filled if all the pipes are open?

A)    2

B)    2.5

C)    3

D)    3.5

E)    None of these

View Answer

Answer: option (C)

Explanation:

Part filled by (X + Y + Z) in 1 hour = ((1/5)+(1/10)+(1/30)) = 1/3

∴ the three pipes will fill the tank in 3 hours.

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