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DIRECTIONS for the question: Solve the following question and mark the best possible option.
2 kids, John and Jim, are running on an escalator (a moving stairway). John is running three times as fast as Jim, and by the time they are off the escalator, John has stepped on 150 stairs while Jim has stepped on 100 stairs. What is the ratio of the elevator’s speed to Jim’s speed?
  • a)
    1 : 1
  • b)
    3 : 1
  • c)
    2 : 1
  • d)
    2 : 3
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
DIRECTIONSfor the question:Solve the following question and mark the b...
Correct Answer :- a
Explanation : Assume A takes 1 step per unit time. Then B will take 3 steps per same unit time. Also, assume the the escalator is moving at E steps per unit time.
Let T be the total number of steps.
Let ta be time taken by A on the escalator, tb = time taken by B on the escalator.
Since A takes 50 steps - therefore we have:
50 = T/(1+E) units of time.
similarly,
75 /3= T/(3+E) units of time.
Solving for T, E we get E = 1 step per unit time; T = 100 steps
Jim has stepped on 100 stairs.
Elevator Speed : Jim
100 : 100
1 : 1
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Most Upvoted Answer
DIRECTIONSfor the question:Solve the following question and mark the b...
Speed to John's speed?

Let's assume that the speed of the escalator is "e" and the speed of Jim is "x". Then, the speed of John would be "3x" (as he is running three times as fast as Jim).

We can use the formula:

(distance) = (speed) x (time)

Let's assume that the length of the escalator is "d" and the time taken by both John and Jim to get off the escalator is "t".

For John:

distance = 150 stairs + d
speed = 3x + e
time = t

Therefore,

150 + d = (3x + e) x t

For Jim:

distance = 100 stairs + d
speed = x + e
time = t

Therefore,

100 + d = (x + e) x t

We can solve these two equations to get the value of "e/x":

150 + d = 3xt + et
100 + d = xt + et

Subtracting the second equation from the first, we get:

50 = 2xt

Therefore, e/x = 50/2x = 25/x

Hence, the ratio of the elevator speed to John's speed is 25/x.
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DIRECTIONSfor the question:Solve the following question and mark the best possible option.2 kids, John and Jim, are running on an escalator (a moving stairway). John is running three times as fast as Jim, and by the time they are off the escalator, John has stepped on 150 stairs while Jim has stepped on 100 stairs. What is the ratio of the elevator’s speed to Jim’s speed?a)1 : 1b)3 : 1c)2 : 1d)2 : 3Correct answer is option 'A'. Can you explain this answer?
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