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) = 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.
Correct Answer: 16 hrs