Question

One day in my college, when I had descended seven steps on the staircase, I saw my colleague on the ground floor just about to climb up the same staircase. I continued descending and greeted him when we crossed each other. To my surprise, when I had still 4 more steps to go, my colleague had already reached the first floor. I later learnt that he took two steps at a time while I took only one at a time.

Answer 1

Not quite sure what the question here is. Are you supposed to determine how many steps there are on the staircase? If so, I assume you and your colleague were taking steps in unison so that you each took the same number of steps total.

Answer 2

Yes, total no. of steps is?

Answer 3

Let's consider how many steps you both took in tandem. When he started, you had already taken 7 steps. When he finished, you still had 4 steps to go. That means that he had to "travel" 11 steps more than you during the time you were both on the staircase. Since his travel speed is twice that of yours, 2x = x + 11 where x is the number of steps you took in tandem. Therefore, you both took 11 steps together on the staircase.

Since he travelled the entire staircase in those 11 steps (2 at a time), there must be 22 steps total on the staircase.