# 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

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 ${\frac{1}{x}}$th of the task in 1 hour. B finishes the ${\frac{1}{(x+12)}}$th of the task in 1 hour. A and B finish ${\frac{1}{(x-4)}}$th of the task in one hour .

Therefore, ${\frac{1}{x}}$ + ${\frac{1}{(x+12)}}$ = ${\frac{1}{(x-4)}}$ . Solving for x, we get ${\frac{(x+12+x)}{(x^2+12x)}}$ = ${\frac{1}{(x-4)}}$ .

(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.

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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.