Pipes and Cistern

Pipes and Cistern

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Aptitude miscellaneous
  1. Two pipes X and Y can fill a cistern in 24 min. and 32 min. respectively. If both the pipes are opened together, then after how much time Y should be closed so that the tank is full in 18 minutes ?








  1. View Hint View Answer Discuss in Forum

    Let Y be closed after T min
    Then, T x (1/ 24 + 1/32) + (18 - T) x 1/24 = 1

    Correct Option: B

    Let Y be closed after T min
    Then, T x (1/ 24 + 1/32) + (18 - T) x 1/24 = 1
    ⇒ (7 x T)/96 + (18 - T)/24 = 1
    or 7T + 72 - 4T = 96.
    ∴ 3T = 24
    or T = 8 min.

  1. A leak in the bottom of a tank can empty the full tank in 6 hours. An Inlet pipe fills water at the rate of 4 litres per minute. When the tank is full, the Inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank is ?








  1. View Hint View Answer Discuss in Forum

    Part filled by intel in 1 hour = (1/6 - 1/8) = 1/24
    So, the inlet can fill the tank in 24 hours

    Correct Option: B

    Part filled by inlet in 1 hour = (1/6 - 1/8) = 1/24
    So, the inlet can fill the tank in 24 hours
    ∴ Capacity of the tank = Water that flows in 24 hours = (4 x 24 x 60) liters = 5760 liters

  1. A pipe can fill a tank in 4 hours, but due to a leak in the tank, it is filled in 5 hours. If the tank is full, how much time will the leak take to empty the tank completely?








  1. View Hint View Answer Discuss in Forum

    As per the given in question ,

    In 1 hour, water filled =
    1
    		 th of the tank.
    4

    1
    		 th is emptied by leakage in 5 hours. Full tank would be emptied in 20 hours (i.e. 5 × 4).
    4

    Using the given formula ,
    Here , a = 5 , b = 4
    Required time ( t ) =
    a × b
    a - 4

    Correct Option: C

    As per the given in question ,

    In 1 hour, water filled =
    1
    		 th of the tank.
    4

    1
    		 th is emptied by leakage in 5 hours. Full tank would be emptied in 20 hours (i.e. 5 × 4).
    4

    Using the given formula ,
    Here , a = 5 , b = 4
    Required time ( t ) =
    a × b
    a - 4

    Required time =
    5 × 4
    		 = 20 hours
    5 - 4

  1. Which of these pipes will empty a pool the fastest?
    (i) One pipe of diameter 60 cm
    (ii) Two pipes of diameter 30 cm each
    (iii) Three pipes of diameter 20 cm each








  1. View Hint View Answer Discuss in Forum

    If the flow of water per unit time be y km, then
    ∵ Pipe is in cylinderical shape .
    ∴ Volume of cylinder ( V ) = πr²h
    Greater the radius, larger the capacity of pipe.
    Radius is greatest in (i) i.e. 30cm. Hence, pipe with 60 cm diameter will empty the pool fastest.

    Correct Option: A

    If the flow of water per unit time be y km, then
    ∵ Pipe is in cylinderical shape .
    ∴ Volume of cylinder ( V ) = πr²h
    Greater the radius, larger the capacity of pipe.
    Radius is greatest in (i) i.e. 30cm. Hence, pipe with 60 cm diameter will empty the pool fastest. Therefore, V ∝ r²
    So , correct answer is option A .

  1. A tap drips at a rate of one drop/ sec. 600 drops make 100ml. The number of litres wasted in 300 days is








  1. View Hint View Answer Discuss in Forum

    We know that , 1 day = 24 hours = 24 × 60 × 60 seconds
    ⇒ 300 days = (300 × 24) hours = (300 × 24 × 60 × 60) seconds
    ∴ Number of drops = 300 × 24 × 60 × 60
    ∵ 600 drops = 100 ml.

    ∴ 300 × 24 × 60 × 60 drops =
    300 × 24 × 60 × 60
    		 ml.
    6

    300 × 24 × 60 × 60 drops = (1200 × 60 × 60) ml.

    Correct Option: D

    We know that , 1 day = 24 hours = 24 × 60 × 60 seconds
    ⇒ 300 days = (300 × 24) hours = (300 × 24 × 60 × 60) seconds
    ∴ Number of drops = 300 × 24 × 60 × 60
    ∵ 600 drops = 100 ml.

    ∴ 300 × 24 × 60 × 60 drops =
    300 × 24 × 60 × 60
    		 ml.
    6

    300 × 24 × 60 × 60 drops = (1200 × 60 × 60) ml.
    Required answer =
    1200 × 60 × 60
    		 litre.
    1000

    Required answer = 4320 litre.