# 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

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 $\frac{1}{a}$ of the work in an hour.

B does $\frac{1}{a+4}$ of the work in an hour.

Together they take 288 minutes to finish the job , 288 minutes = $\frac{288}{60} = \frac{24}{5}$ hours.

Therefore, both A and B together complete $\frac{5}{24}$ every hour.

$\frac{1}{a} + \frac{1}{a+4} = \frac{5}{24}$

$\frac{2a+4}{a(a+4)} = \frac{5}{24}$

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.

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## More questions from Pipes Cisterns, Work Time

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.