CAT Quantitative Aptitude Questions | CAT Time and Work questions

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CAT Quantitative Aptitude
Pipes,Cisterns; Work,Time ▽

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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
   276 mins - 6900 liters
   
   Now, A will be open, A can fill 100 liters in a minute.
   
   277 mins - 7000 liters
   
   So, it would take 277 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.


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
   276 mins - 6900 liters
   
   Now, B will be open, B can fill 25 liters in a minute.
   
   277 mins - 6925 liters
   
   Now, A will be open, A can fill 100 liters in a minute. Therefore, A can fill 75 liters in 45 seconds.
   
   277 mins 45 sec - 7000 liters
   
   So, it would take 277 mins 45 sec .


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
   Now, B will be open, B can fill 25 liters in a minute.
   
   277 mins - 6950 liters
   
   Now, C will be open, C will drain 50 liters in a minute.
   
   278 mins - 6900 liters
   
   Now, A will be open, A can fill 100 liters in a minute.
   
   279 mins - 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 "277 mins, 277 mins 45 sec and 279 mins".

Choice D is the correct answer.