Question

A person walks up a stalled escalator in 90 second. when standing on the same escalator, now moving, he is carried in 60 second. The time he would take to walk up the moving escalator will be
A. 27s
B. 72s
C. 18s
D. 36s

Answer 1

Hint: Proceed the solution of question using distance formula so that we can write their speed in terms of distance hence at last using relative speed concept distance term will cancel and we will have our answer.

Formula used- Distance = speed × Time

Complete Step-by-Step solution:
In the question it is given the time taken by person i.e. 90s and time taken by escalator i.e. 90s to travel a distance d
Hence using the formula
Distance = speed × Time
Time taken by person ${t_1} = 90s$ to travel a distance d
⇒${V_m} \times {t_1} = d$
$ \Rightarrow {V_m} \times 90 = d$
This can be written as
$ \Rightarrow 90 = \dfrac{d}{{{V_m}}}$………. (1)
Time taken by escalator ${t_2} = 60s$ to travel a distance d
${t_2} = 60s$
⇒${V_a} \times {t_2} = d$
$ \Rightarrow {V_a} \times 60 = d$
This can be written as
$ \Rightarrow 60 = \dfrac{d}{{{V_a}}}$………. (2)
We know that when both escalator and person are moving then their speed will add.
$ \Rightarrow t = \dfrac{d}{{{V_m} + {V_a}}}$
On putting values from equation (1) & (2)
$ \Rightarrow t = \dfrac{d}{{\dfrac{d}{{90}} + \dfrac{d}{{60}}}}$
Cancel d from numerator and denominator
$ \Rightarrow t = \dfrac{1}{{\dfrac{1}{{90}} + \dfrac{1}{{60}}}}$
$ \Rightarrow t = \dfrac{{60 \times 90}}{{150}} \Rightarrow 36{\text{sec}}$
So the time he would take to walk up the moving escalator will be 36 sec.
Hence option D is correct.

Note- In this particular question we should know that here we have assumed that person and escalator both are moving in same direction so that we simply add their speed if person and escalator will move in opposite direction then we will have taken the difference of speed of person and escalator