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Question

Preeti reached a metro station and found that the escalator was not working. She walked up the stationary escalator in time t1. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t2. The time taken by her to walk up on a moving escalator will be

A
t1t2t2t1
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B
t1t2t2+t1
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C
t1t2
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D
t1+t22
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Solution

The correct option is B t1t2t2+t1
Let v1 be the velocity of Preeti and v2 be the velocity of of the escalator and l be the distance moved.

When she remains stationary on the moving escalator, the escalator takes her up in time t2,

t2=lv2 .....(i)

When she moves along with the escalator, her velocity w.r.t the ground will be v1+v2

t=lv1+v2 .....(ii)

where t time taken to travel the distance l when both the escalator and Preeti are moving.

When the escalator is stationary, she walks up the stationary escalator in time t1

t1=lv1 .....(iii)

From equations (i), (ii) & (iii),

t=lv1+v2

t=llt1+lt2

t=t1t2t2+t1

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