An escalator is descending at constant speed.A walks down and takes 50 steps to reach the bottom.B runs down and takes 90 steps in the same time as A takes 10 steps.How many steps are visible when the escalator is not operating?

• Lets suppose that A walks down 1 step / min and
  escalator moves n steps/ min
  It is given that A takes 50 steps to reach the bottom
  In the same time escalator would have covered 50n steps
  So total steps on escalator is 50 + 50n.
  Again it is given that B takes 90 steps to reach the bottom and time
  taken by him for this is equal to time taken by A to cover 10 steps i.e
  10 minutes. So in this 10 min escalator would have covered 10n steps.
  So total steps on escalatro is 90 + 10n
  Again equating 50 + 50n = 90 + 10n we get n = 1
  Hence total number of steps on escalator is 100.
• 7 years agoHelpfull: Yes(4) No(0)
• visible steps when not operating = n
  escalator speed = s
  steps taken by A to reach the bottom = 50
  steps taken by B to reach the bottom = 90 + (50 - 10) = 130
  
  When walking down, time taken = (n - 50) / s
  When running down, time taken = (n - 130) / s
  
  [(n - 50) / s] : [(n - 130) / s] = 5 : 1
  (n - 50) : (n - 130) = 5 : 1
  (n - 50) * 1 = (n - 130) * 5
  n - 50 = 5n - 650
  n - 50 - n + 650 = 5n - 650 - n + 650
  4n = 600
  n = 150
• 9 years agoHelpfull: Yes(1) No(1)