CAT Practice : Pipes cisterns, Work time

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Sometimes 100 + 25 - 50 is different from 75. Think about this before going to the solutions.

Three Pipes

    Q.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
    i.   A is kept open first, followed by B and then C.
    ii.  B first, followed by A, and then C.
    iii. 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. 277 mins, 277 mins and 45 secs and 279 mins

 

  • Correct Answer
    Choice D. 277 mins, 277.45 mins and 279 mins

Detailed Solution

i.   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
276 mins - 6900 litres
During the 277th min, Pipe A is Opened and it fills at the rate of 100 litres/min. Therefore, at the end of 277 mins, the tank is filled.

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.

ii.   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
276 mins - 6900 litres
During the 277th min, Pipe B is Opened and it fills at the rate of 25 litres/min. At the end of 277 mins, 6925 litres. Then, Pipe A is opened and it fills at the rate of 100 litres/min. Therefore, it takes 3/4 th of a minute to fill the remaining 75 litres. Time taken = 277 + 3/4 th minute = 277 mins and 45 secs .

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

In this case also, Each cycle of 3 minutes, 75 litres 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 litres. 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 litres 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.
Answer Choice (D).

Correct Answer: 277 mins, 277 mins and 45 secs and 279 mins



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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.