Multiple choice general knowledge math & puzzles

You walk upwards on an escalator, with a speed of 1 step per second.After 50 steps you are at the end.You turn around and run downwards with a speed of 5 steps per second.After 125 steps you are back at the beginning of the escalator.How many steps do you need if the escalator stands still?

  1. 100

  2. 99

  3. 98

  4. 101
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let N = total visible steps and e = escalator speed (steps/sec). Going up: N = 50(1+e). Going down: N = 125(5-e). Equating: 50(1+e) = 125(5-e). 50+50e = 625-25e. 75e = 575, so e = 23/3. Then N = 50(1+23/3) = 50(26/3) = 1300/3... wait, let me verify. Actually: time up = N/(1+e) = 50, time down = N/(5-e) = 125. From these: N = 50(1+e) and N = 125(5-e). Setting equal: 50+50e = 625-25e, so 75e = 575, e = 23/3. This gives N = 50(26/3) = 1300/3, which isn't 100. Let me reconsider: The steps counted are the steps the person takes. Total visible steps when escalator is still is constant. Let that be S. When going up at 1 step/sec for 50 seconds, escalator has moved up e*50 steps. So person covered 50 steps and escalator contributed e*50 steps, total S = 50 + 50e. When going down at 5 steps/sec for 25 seconds (125 steps at 5/sec = 25 sec), escalator moves down e*25 steps. Person covers 125 steps down but escalator takes away e*25, so total S = 125 - 25e. Equating: 50 + 50e = 125 - 25e, so 75e = 75, e = 1. Then S = 50 + 50 = 100 steps.

AI explanation

Let e be the escalator's own speed in steps/second. Walking up at 1 step/sec, the rider takes 50 steps, so the trip takes 50 seconds, and the escalator itself contributes 50e steps over that time, giving total visible steps N = 50 + 50e. Running down at 5 steps/sec against the escalator, 125 steps take 25 seconds, and the escalator removes 25e steps from the count, giving N = 125 - 25e. Setting 50+50e = 125-25e gives e = 1, so N = 100 steps — the count you'd see on a stationary escalator.

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