total no of steps 50*3+75*1 150+75 225

total time taken 1 step 3 step 2 steps diff

225/2 112.5 while moving

when stopped 112.5/50 2.25

112.5/75 1.25

time taken by first person > time taken by second person (proof)

sorry to say no one give the correct approach to this problem

You have to use relative velocity concept to solve this problem and this types of problems

solution:

Let L be the steps of the stationary escalator and v be the velocity of the

the escalator steps/second (and that is constant for both the person).

Now

If A takes 1 step in one second then B takes 3 steps in one second. If A takes t1 seconds to

take 50 steps then B takes 150 steps in t1 seconds.

For B to take 150 steps he requires t1 seconds

then to take 75 steps he requires t1/2 seconds.

now use relative velocity

L - v*t1 50 (for first person)

L-v*t1/2 75(for second person)

S(escalator w.r.t ground)-s(person w.r.t escalator) s1(person w.r.t ground)

S s s1 are the steps

now put the v*t1 from 1 into the second equation and u get

L- (L-50)/2 75

L+50 150

L 100;