• Three taps are fitted in a cistern. The empty cistern is filled by the first and the second taps in 3 and 4 h, respectively. The full cistern is emptied by the third tap in 5 h. If all three taps are opened simultaneously, the empty cistern will be filled up in

    A) \( \Large 1\frac{14}{23} \)

      B) \( \Large 2\frac{14}{23} \)

    C) 2 h 40 min

      D) 1 h 56 min

    Correct Answer:
      B) \( \Large 2\frac{14}{23} \)

    Description for Correct answer

    Part of tank filled by first tap in 1 h = \( \Large \frac{1}{3} \)

    Part of tank filled by second tap in 1 h = \( \Large \frac{1}{4} \)

    Part of tank emptied by third tap in 1 h = \( \Large \frac{1}{5} \)

    Part of the tank filled by all pipes opened simultaneously in 1 h

    = \( \Large \frac{1}{3} \) + \( \Large \frac{1}{4} \) - \( \Large \frac{1}{5} \)

    = \( \Large \frac{20+15-12}{60} \) = \( \Large \frac{23}{60}\)

    Time taken by all the taps to fill the tank when it is empty

    = \( \Large \frac{60}{23} \)h = \( \Large 2\frac{14}{23} \) h

Similar Questions
1). Pipe A can fill a tank in 30 min, while pipe B can fill the same tank in 10 min and pipe C can empty the full tank in 40 min. If all the pipes are opened together, how much time will be needed to make the tank full?
A). \( \Large 9\frac{3}{13} \) h B). \( \Large 9\frac{4}{13} \) h
C). \( \Large 9\frac{7}{13} \) h D). \( \Large 9\frac{9}{13} \) h
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2). Pipes A and B can fill a tank in 5 and 6 h, respectively. Pipe C can fill it in 30 h. If all the three pipes are opened together, then in how much time the tank will be filled up?
A). \( \Large 3\frac{3}{14} \) h B). \( \Large 2\frac{1}{2} \) h
C). \( \Large 3\frac{9}{14} \) h D). \( \Large 2\frac{1}{14} \) h
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3). Through an inlet, a tank takes 8 h to get filled up. Due to a leak in the bottom, it takes 2 h more to get it filled completely. If the tank is full, how much time will the leak take to empty it?
A). 16 h B). 20 h
C). 32 h D). 40 h
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4). A tap can fill an empty tank in 12 h and a leakage can empty the tank in 20 h. If tap and leakage both work together, then how long will it take to fill the tank?
A). 25 h B). 40 h
C). 30 h D). 35 h
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5). Three taps A, B and C together can fill an empty cistern in 10 min. The tap A alone can fill it in 30 min and the tap B alone can fill it in 40 min. How long will the tap C alone take to fill it?
A). 16 min B). 24 min
C). 32 min D). 40 min
-- View Answer
6). Two pipes P and Q can fill a cistern in 12 and 15 min, respectively. If both are opened together and at the end of 3 min, the first is closed. How much longer will the cistern take to fill?
A). \( \Large 8\frac{1}{4} \) B). \( \Large 8\frac{3}{4} \)
C). 5 min D). \( \Large 8\frac{1}{2} \)
-- View Answer
7). There are three pipes connected with a tank. The first pipe can fill \( \Large \frac{1}{2} \) part of the tank in 1 h, second pipe can fill \( \Large \frac{1}{3} \) part of the tank in 1 h. Third pipe is connected to empty the tank. After opening all the three pipes, \( \Large 7\frac{1}{2} \) part of the tank can be filled in 1 h, then how long will third pipe take to empty the full tank?
A). 3 h B). 4 h
C). 5 h D). 6 h
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8). A pipe can fill a cistern in 12 min and another pipe can fill it in 15 min, but a third pipe can empty it in 6 min. The first two pipes are kept open for 5 min in the beginning and then the third pipe is also opened. Time taken to empty the cistern is
A). 38 min B). 22 min
C). 42 min D). 45 min
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9). 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?
A). 6:15 pm B). 7:12 pm
C). 8:12 pm D). 8:35 pm
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10). Three pipes A, B and C can fill a tank in 30 min, 20 min and 10 min, respectively. When the tank is empty, all the three pipes are opened. If A, B and C discharge chemical solutions P, Q and R respectively, then the part of solution R in the liquid in the tank after 3 min is
A). \( \Large \frac{8}{11} \) B). \( \Large \frac{5}{11} \)
C). \( \Large \frac{6}{11} \) D). \( \Large \frac{7}{11} \)
-- View Answer