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Pipes and Cisterns Test 1
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Pipes and Cisterns Test 1

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  • Question 1/10
    1 / -0

    A cistern has two taps (which fill it in 12 min and 15 min, respectively) and an exhaust tap. When all three taps are opened together, it takes 20 min to fill the empty cistern. How long will the exhaust tap take to empty it?

    Solutions

    Let the exhaust tap empties the tank in x minutes.

    Then,

    ⇒ 

    ⇒ 

    ⇒ x = 10 min

  • Question 2/10
    1 / -0

    If two pipes function simultaneously, the reservoir is filled in 12 hrs. One pipe fills the reservoir 10 hrs faster than the other .How many hours does the faster pipe take to fill the reservoir?

    Solutions

    Let the faster pipe fills the tank in x hrs.

    Then the slower pipe fills the tank in x + 10 hrs.

    When both of then are opened, the reservoir will be filled in

     = 12

    ⇒ x² – 14x – 120 = 0

    ∴ x = 20, – 6

    But x can’t be – ve, hence the faster pipe will fill the reservoir in 20 hrs.

  • Question 3/10
    1 / -0

    Two pipes P and Q would filled a cistern in 24 hours and 32 hours respectively . If both pipes are opened together, find when the first pipe must be turned off so that the cistern may be just filled in 16 hours?

    Solutions

    Suppose the first pipe was closed after x hrs.

    Then, first’s x hrs supply + second’s 16 hrs supply = 1

    or, =1

    ∴  = 1 – ½= ½

    ∴ x = 12 hrs.

    Quicker method :

    The first pipe should work for

    × 24 hrs.

    = 12hrs

  • Question 4/10
    1 / -0

    A hot pipe takes 3 minutes longer to fill a tank than the cold pipe. Together they take 6 minutes 40 seconds. Time taken by the cold pipe alone to fill the tank is :

    Solutions

    Let cold pipe take X minutes, then hot pipe will take (X + 3) minutes.

    Together 

    = 

    40X + 60 = 3X (X + 3)

    ⇒ 40X + 60 = 3X² + 9X

    ⇒ 3X² – 31X – 60 = 0

    ⇒ X = 12 minutes

  • Question 5/10
    1 / -0

    Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, then the tank will be full in:

    Solutions

    (A + B)’s 1 hour’s work

    = 

    (A + C)’s 1 hour’s work

    = 

    Part filled in 2 hrs

    = 

    Part filled in 6 hrs

    = 

    Remaining part

    = 

    Now, it is the turn of A and B and 3/20 part is filled by A and B in 1 hour.

    ∴ Total time taken to fill the tank

    = (6 + 1) hrs = 7 hrs.

  • Question 6/10
    1 / -0

    Three fill pipes A, B and C can fill separately a cistern in 3, 4 and 6 minutes respectively. A was opened first. After 1 minute, B was opened and after 2 minutes from the start of A, C was also opened. Find the time when the cistern will be full?

    Solutions

    Let cistern will be full in x min. Then,

    part filled by A in x min + part filled by B in

    (x – 1) min + part filled by c in (x – 2)min = 1

  • Question 7/10
    1 / -0

    Two fill taps A and B can separately fill a cistern in 45 and 40 minutes respectively. They started to fill a cistern together but tap A is turned off after few minutes and tap B fills the rest part of cistern in 23 minutes. After how many minutes, was tap A turned-off?

    Solutions

    Let A was turned off after x min. Then,

    cistern filled by A in x min + cistern filled by B in

    (x + 23) min = 1

  • Question 8/10
    1 / -0

    Two fill pipes A and B can fill a cistern in 12 and 16 minutes respectively. Both fill pipes are opened together, but 4 minutes before the cistern is full, one pipe A is closed. How much time will the cistern take to fill?

    Solutions

    Let cistern will be full in x min. Then,

    part filled by B in x min + part filled by A in

    (x – 4) min = 1

  • Question 9/10
    1 / -0

    Two pipes A and B can fill a cistern in 10 and 15 minutes respectively. Both fill pipes are opened together, but at the end of 3 minutes, ‘B’ is turned off. How much time will the cistern take to fill?

    Solutions

    In one min, (A + B) fill the cistern

    In 3 min, (A + B) fill the cistern

    = 

    Remaining part

    since part filled by A in one min.

    ∴ ½nd part filled by A in 10 × ½ = 5 minutes

    ∴ Total time = 3 + 5 = 8 min.

  • Question 10/10
    1 / -0

    Two taps can fill a tank in 12 and 18 minutes respectively. Both are kept open for 2 minutes and the first is turned off. In how many minutes more will the tank be filled?

    Solutions

    Part filled by first tap in 1 min

    Part filled by second tap in 1 min

    Now, 

    since  part of tank is filled by second tap in 1min.

    ∴  part of tank is filled by second tap in 1 min.

    = 13 min.

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