(Solution):

Adam takes 12 hours to paint a certain wall. In 1 hour, Adam will paint\(\frac{1}{12}\) of the wall.

Ben takes 8 hours to paint a certain wall. In 1 hour, Adam will paint \(\frac{1}{8}\) of the wall.

Adam started work and painted alone for 3 hours. Therefore, the amount of work done by Adam is:

=> \(\frac{1}{12}\) * 3 = \(\frac{1}{4}\) .


Adam and Ben together can finish (\(\frac{1}{12}\) + \(\frac{1}{8}\) = \(\frac{5}{24}\) ) work in 1 hour.

Ben painted for 1 hour alone at the end. Therefore, the amount of work done by Ben is:

=> 1 * \(\frac{1}{8}\) = \(\frac{1}{8}\).

Total work done:

=> \(\frac{1}{4}\) + \(\frac{1}{8}\) = \(\frac{3}{8}\).

Remaining work:

=> 1 - \(\frac{3}{8}\) = \(\frac{5}{8}\) of the work.

This work was done by Adam and Ben together:

=> \(\frac{5}{24}\) work in 1 hour = \(\frac{5}{8}\) the part of work to be completed in 3 hours since ( \(\frac{5}{24}\)) * 3 = \(\frac{5}{8}\).

Hence, Adam and Ben worked together for 3 hours.

Therefore, B is the correct answer

Answer B