CAT Practice : Pipes cisterns, Work time

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Classic Work - Time Question!!

Pipes Cisterns - Work Time

    Q.14: A can complete a task 4 hours lesser time than B takes to complete the same. If A and B together can complete the task in 288 minutes, how long does B alone take to complete the task?
    1. 1 hr
    2. 2 hrs
    3. 3 hrs
    4. 12 hrs

 

  • Correct Answer
    Choice D. 12 hrs

Detailed Solution

Let time taken by A be 'a' hours and time taken by B be 'a+4' hours
Then A does of the work in an hour.

B does of the work in an hour.

Together they take 288 minutes to finish the job , 288 minutes = hours.

Therefore, both A and B together complete every hour.





We get, 48a + 96 = 5(a2 + 4a)
=> 5a2 - 28a - 96 = 0
=> 5a2 - 40a + 12a - 96 = 0
5a (a - 8) + 12(a - 8) = 0
(5a + 12)(a - 8) = 0 . Therefore, Since a cannot be negative, a = 8 hours.
Hence, a + 4 = 12 hours. Therefore, Time taken by B to complete the work on his own is 12 hours.


Correct Answer: 12 hrs



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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.