Quantitative Aptitude: Pipes and Cisterns Set 13

  1. A Tullu pump can be used for filling as well as for emptying a Cistern. The capacity of the Cistern is 2400m³. The emptying capacity of the Cistern is 10m³ per minute higher than its filling capacity and the pump needs 8 minutes lesser to Cistern the tank than it needs to fill it. What is the filling capacity of the pump?
    40m³/min
    60m³/min
    50m³/min
    90m³/min
    80m³/min
    Option C
    Filling Capacity of the Pump = x m/min.
    Emptying Capacity of the pump = (x+10) m/min.
    2400/x – 2400/x+10 = 8
    (x – 50) + (x + 60) = 0
    x = 50m³/min

     

  2. There is a tank in which a leak is present in the bottom, which can empty the full tank in 4 hours. An inlet pipe fills water at the rate of 2 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 20 hours. How many liters does the tank hold?
    630 litres
    580 litres
    660 litres
    520 litres
    600 litres
    Option E
    Water filled by the inlet pipe in 20 hours = water emptied by the leak in 20-2=18 hours.
    Therefore, water emptied by the leak in 4 hours = water filled by the inlet pipe in 5 hours
    i.e., capacity of the tank = water filled by the inlet pipe in 88 hours
    = 5×60×2 = 600 litres

     

  3. A leakage is developed in one of the side of the rectangular tank which has the capacity to empty the whole tank in 7 hours. An inlet pipe fills water at the rate of 2 litres a minute. When the tank is full the inlet is opened and due to the leak the tank is empty in 8 hours. What is the capacity of the tank (in litres).
    6220 litres
    6666 litres
    6550 litres
    672 litres
    6720 litres
    Option E
    In 1 hr = 1/7 – 1/8 = 8-7/56 = 1/56
    In 1 min = 1/(56*60) = 1/3360
    Inlet pipe fill water at the rate of 2 liters a minute = 2*3360 = 6720 litres

     

  4. A X company of pump can be used for filling as well as for emptying a tank. 10 m3 per minute takes for emptying the tank which is higher than its filling capacity and the pump takes 8 minutes less time to empty the tank .Find out the filling capacity of the pump? [If the capacity of the tank is 2400 m3.]
    40
    50
    70
    60
    30
    Option B
    Let the filling capacity of the pump be x m3/min.
    Then, emptying capacity of the pump=(x+10)m3/min.
    2400/x − 2400/(x+10) = 8
    =>x^2 + 10x − 3000 = 0
    =>(x−50)+(x+60) = 0
    =>x = 50

     

  5. In a hall there are 16 buckets of water fill a tank when the capacity of each tank is 11 liters. Find out how many buckets will be needed to fill the same tank,if the capacity of each bucket is 4 liters?
    52
    40
    63
    44
    55
    Option D
    Capacity of the tank =(16 x 11) liters
    = 176 liters.
    Number of buckets needed = 176/4 = 44

     

  6. Two pipes A and B can separately fill a cistern in 15 and 30 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 5 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill ?
    12 seconds
    29 seconds
    24 seconds
    20 seconds
    15 seconds
    Option C
    1/15 + 1/30 = 1/10 x 5 = 1/2
    1 – 1/2 = 1/2
    1/15 + 1/30 – 1/x = 1/2
    x = 24 sec.

     

  7. A swimming pool can be filled by a cold pipe in 15 minutes and by a hot pipe in 10 minutes. Aman opened both the tap and leaves to fill and returns at the time when the pool completely filled with water. After some time he observed that a waste pipe is opened at the bottom, he now closes it. Now the pool will take more 5 minutes to fill the tank, how much time that leakage can empty the pool.
    39/8
    33/7
    36/5
    31/4
    35/6
    Option C
    (1/15 + 1/10 – 1/x)*6 + (1/15 + 1/10)*5 = 1
    x = 36/5

     

  8. Four filling pipes and 3 emptying pipes capable of filling and emptying in 12 minutes and 15 minutes respectively. At some time all the pipes are opened together then tank fill 10 litres of water per minute. What is the capacity of the tank.
    70 litre
    66 litre
    77 litre
    62 litre
    75 litre
    Option E
    (4/12 – 3/15)*t = 1
    t = 15/2 minute
    So, the capacity = (15/2)*10 = 75 litre

     

  9. How much time a tank would take to be filled by 3 pipes which diameters are 2 cm, 3 cm and 4 cm running together, when the largest pipe alone takes 58 minutes time to fill the tank. [Note:The amount of water flowing in each pipe is proportional to the square of its diameter.]
    25 minutes.
    30 minutes.
    27 minutes.
    32 minutes.
    28 minutes.
    Option D
    Amount of water from three pipes is 4 units, 9 units and 16 units.
    Let the capacity of cistern be ‘p’ units.
    p/58 = 16
    => p = 928 units.
    In 1 minute, quantity to be filled by 3 pipes = 29 units
    Total time required = 928/29 = 32 minutes.

     

  10. Two pipes A and B, one pipe can fill a tank 6 times as fast as another pipe. If together the two pipes can fill the tank in 22 minutes. How much time taken by the slower pipe alone will be able to fill the tank.
    140 minute.
    140 minute.
    132 minute.
    150 minute.
    148 minute.
    154 minute.
    Option E
    Let faster pipe alone can fill the tank in x minutes.
    Then, slower pipe alone can fill the tank in 6x minutes
    1/x+1/6x = 22 6x/7 = 22
    x = (22×7)/6 = 154/6
    Required time = 6x = 154 minutes

     


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