Multiple choice general knowledge math & puzzles

Mr. Bean decided to walk down the escalator of a tube station. He found that if he walks down 26 steps, he requires 30 seconds to reach the bottom. However, if he steps down 34 stairs he would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the height of the stair way in steps?

  1. Insufficient Data

  2. 45

  3. 46

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let S be total steps and e be escalator speed (steps/second). When Bean walks 26 steps in 30 seconds, the escalator contributes the remaining steps: S = 26 + 30e. When he walks 34 steps in 18 seconds: S = 34 + 18e. Solving these equations: 26 + 30e = 34 + 18e gives e = 2/3, so S = 26 + 30(2/3) = 46 steps.

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