Mr. Shah decided to walk down the escalator of a tube station. He found that if he walks down 26 steps, he requires 30 seconds to reach the bottom. However, if he steps down 34 stairs he would only require 18 seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom, find out the eight of the stair way in steps?

To find the height of the stairway in steps, we need to determine the difference in time it takes for Mr. Shah to walk down different numbers of steps.

Let's assume that the time it takes for Mr. Shah to walk down one step is "t" seconds, and the height of one step is "h" units.

According to the information given, when Mr. Shah walks down 26 steps, he takes 30 seconds. Therefore, the time it takes for him to walk down one step is:

$\frac{30 \text{ seconds}}{26 \text{ steps}} = \frac{t \text{ seconds}}{1 \text{ step}}$

Simplifying this equation, we can find the value of "t":

$t = \frac{30 \text{ seconds}}{26 \text{ steps}}$

Similarly, when Mr. Shah walks down 34 steps, he takes 18 seconds. Therefore, the time it takes for him to walk down one step is:

$\frac{18 \text{ seconds}}{34 \text{ steps}} = \frac{t \text{ seconds}}{1 \text{ step}}$

Simplifying this equation, we can find the value of "t":

$t = \frac{18 \text{ seconds}}{34 \text{ steps}}$

Now, we can equate the two values of "t" to find the height of one step:

$\frac{30 \text{ seconds}}{26 \text{ steps}} = \frac{18 \text{ seconds}}{34 \text{ steps}} = \frac{h \text{ units}}{1 \text{ step}}$

Simplifying this equation, we can find the value of "h":

$h = \frac{30 \text{ seconds} \times 34 \text{ steps}}{26 \text{ steps} \times 18 \text{ seconds}}$

$h = \frac{1020 \text{ steps-seconds}}{468 \text{ steps-seconds}}$

$h = 2.18 \text{ steps}$

Therefore, the height of the stairway in steps is approximately 2.18 steps.

Since we are looking for the number of steps, the closest option is:

D) 46 steps.

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