Relative Velocity

Let the length of the escalator be , the speed of the girl be , and the speed of the escalator be .
When the girl walks up the stationary escalator, she takes 20 sec. So, the speed of the girl is:
When the girl remains stationary on the escalator, the escalator takes her up in 30 sec. So, the speed of the escalator is: Now, when the girl walks on the moving escalator, the relative speed is . The time taken for her to reach the top is:
Thus, the time taken by her to walk up on the moving escalator is 12 sec.

The correct answer is (C) : 12 sec.