CAT Quantitative Aptitude Questions | CAT Time and Work questions

CAT Questions | Time and work | Pipes and Cisterns

The question is from Pipes and Cisterns. The filling rates of three pipes are given and we need to find out the time to fill the tank in three given conditions. Sometimes 100 + 25 - 50 is different from 75. Think about this before going to the solutions. Mathematicians are creatures of habit. This topic has been called Pipes and Cisterns because someone named it like it long ago. Pipes and Tanks would be much better - at least makes it sound like wartime.

Question 3: Pipe A fills a tank at the rate of 100lit/min, Pipe B fills at the rate of 25 lit/min, pipe C drains at the rate of 50 lit/min. The three pipes are kept open for one minute each, one after the other. If the capacity of the tank is 7000 liters, how long will it take to fill the tank if

  1. A is kept open first, followed by B and then C.
  2. B first, followed by A, and then C.
  3. B first, followed by C, and then A.
  1. 279.25 mins, 280 mins and 280 mins
  2. 280 mins, 280 mins and 279.25 mins
  3. 279 mins, 280 mins and 279.25 mins
  4. 279.25 mins, 280 mins and 279 mins

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Explanatory Answer

Method of solving this CAT Question from Pipes Cisterns and Work Time: Sometimes 100 + 25 - 50 is different from 75. Think about this before going to the solutions.

  1. A is kept open first, followed by B and then C

    Each cycle of 3 minutes, 75 liters get filled. 100 + 25 - 50. So, after 3 minutes the tank would have 75 liters
    6 mins - 150 liters
    9 mins - 225 liters
    30 mins - 750 liters
    270 mins - 6750 liters
    273 mins - 6825 liters
    279 mins - 6975 liters

    In the 280th minute, pipe A would be open and it would fill the remaining 25 liters in 15 seconds. So, it would take 279 mins and 15 seconds to fill the tank.

    The most important thing in these type of questions is to think in terms of cycles till we reach close to the required target and then think in simple steps.

  2. B first, followed by A, and then C

    Each cycle of 3 minutes, 75 liters get filled. 25 + 100 - 50. So, after 3 minutes the tank would have 75 liters.
    6 mins - 150 liters
    9 mins - 225 liters
    30 mins - 750 liters
    270 mins - 6750 liters
    273 mins - 6825 liters
    279 mins - 6975 liters

    In the 280th minute, pipe B would be open and it would fill the remaining 25 liters in one minutes. So, it would take 280 mins.

  3. B first, followed by C, and then A

    In this case also, Each cycle of 3 minutes, 75 liters get filled. 25 -50 + 100. But there is a small catch here. In the first set of 3 minutes, we would fill up to about 100 liters. After 1 minute, we would be at 25 liters, after 2 minutes, we would be at 0 liters and in the third minute, the tank would be 100 liters full.
    6 mins - 175 liters
    9 mins - 250 liters
    30 mins - 775 liters
    270 mins - 6775 liters
    273 mins - 6850 liters
    276 mins - 6925 liters
    279 minutes - 7000 liters

    So, it would take 279 mins to fill the tank.

    The most important thing in these type of questions is to think in terms of cycles till we reach close to the required target and then think in simple steps.

The question is "how long will it take to fill the tank if"

Hence, the answer is "279.25 mins, 280 mins and 279 mins".

Choice D is the correct answer.

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