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: Another one from Work and time for more practice.

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.

The question is "How long will it take A and B together to complete a task twice as difficult as the first one?"

Hence, the answer is "16 hrs".

Choice A is the correct answer.