CAT Practice : Pipes cisterns, Work time

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Another one from Work and time for more practice.

Pipes Cisterns - Work Time

    Q.10: B takes 12 more hours than A to complete a task. If they work together, they take 16 fewer hours than B would take to complete the task. How long will it take A and B together to complete a task twice as difficult as the first one?
    1. 16 hrs
    2. 12 hrs
    3. 14 hrs
    4. 18 hrs

 

  • Correct Answer
    Choice A. 16 hrs

Detailed Solution

Let us assume that A takes ‘x’ hours to finish a task. Then, B takes ‘x+12’ hours to finish the same task. Given, if they work together, they take 16 fewer hours than B would take to complete the task = ‘x-4’ hours.

A completes the task in ‘x’ hours => A finishes th of the task in 1 hour. B finishes the th of the task in 1 hour. A and B finish th of the task in one hour .

Therefore, + = . Solving for x, we get = .

(2x+12)(x-4) = x2 + 12x.

x2 – 8x -48 =0.

x2 – 12x+4x -48 =0 => x(x-12)+4(x-12)

(x-12)(x+4) =0. X=12 or x=-4. Only x =12 is possible, since x cannot be negative.

Therefore, when A and B work together they finish a task in x-4 = 12-4 = 8 hours.

If the task is twice as difficult as the first one, they finish it in 2*8 = 16 hours.

Correct Answer: 16 hrs



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  6. Pipes Cisterns - Algebra
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.