The question is from Time and work. Efficiency of two people is given and we need to find out how long it would take to complete the task together. Practice Questions from CAT Time and Work.

Question 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?

- 16 hrs
- 12 hrs
- 14 hrs
- 18 hrs

16 hrs

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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) = x^{2} + 12x.

x^{2} – 8x -48 =0.

x^{2} – 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?"**

Choice A is the correct answer.

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