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**Hint:**In this question we have to find the value of time taken by the man to move on a moving escalator. The time taken by the man to walk on a stalled escalator is given and the time for which the escalator was moving is given. We will use the formula of time to solve this question.

**Complete step by step solution:**

Given,

Let the time taken by the man to walk on stalled escalator is ${t_1}$, ${t_1} = 90s$

Let the time for which the escalator was moving is ${t_2}$, ${t_2} = 60s$

Let the total distance travelled is d and the speed of man is ${v_m}$ and the speed of escalator is ${v_e}$

As we know that the formula of time given by,

$time = \dfrac{{distance}}{{velocity}}$

The time taken by man ${t_1} = \dfrac{d}{{{v_m}}}$

$\Rightarrow 90 = \dfrac{d}{{{v_m}}}$

Speed of man is ${v_m} = \dfrac{d}{{90}}$

The time taken by escalator ${t_2} = \dfrac{d}{{{v_e}}}$

$\Rightarrow 60 = \dfrac{d}{{{v_e}}}$

$\Rightarrow {v_e} = \dfrac{d}{{60}}$

If total time taken is t then

Total time taken \[t = \dfrac{d}{{{v_m}}} + \dfrac{d}{{{v_e}}}\]

Putting the values of ${v_m}$and ${v_e}$in above equation

\[\Rightarrow t = \dfrac{d}{{\dfrac{d}{{90}}}} + \dfrac{d}{{\dfrac{d}{{60}}}}\]

\[\Rightarrow t = \dfrac{1}{{\dfrac{1}{{90}}}} + \dfrac{1}{{\dfrac{1}{{60}}}}\]

\[\Rightarrow t = \dfrac{{60 \times 90}}{{60 + 90}}\]

\[\Rightarrow t = \dfrac{{5400}}{{150}}\]

\[\Rightarrow t = 36s\]

Result- Hence, the total time taken by the man to walk up the moving escalator is \[t = 36s\].

**Hence, option (D) is correct.**

**Note;**In this question we had to find the value of time that the man will take to walk up the escalator. So, it is important to understand that the total time is the one that we have to calculate and we can find it in a very simple way by using the formula of time. The calculation in this question is quite easy but we have to remember that in such types of questions first we will find individual time taken by both man and escalator and then we will find total time taken.

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