Question

Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyom's steps. Shyama gets to the top after taking 25 steps, while Vyom takes 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?

• A. 40
• B. 50
• C. 60
• D. 80

Hint:

Relative speed of person plus escalator determines total steps covered; set equal for both travellers.

Answer 1

The Correct Option is B

Let escalator speed = $e$ steps/sec, Shyama speed = $s$, Vyom speed = $\frac23 s$.
Time for Shyama: $25/s$, distance covered = $(s+e)(25/s) = N$ steps (total length). Vyom: time $= 20/(\frac23 s) = 30/s$, distance = $(\frac23 s + e)(30/s) = N$. Equating: $(s+e)(25/s) = (\frac23 s + e)(30/s) \Rightarrow 25 + \frac{25e}{s} = 20 + \frac{30e}{s} \Rightarrow 5 = \frac{5e}{s} \Rightarrow e = s$. Then $N = 25 + 25 = 50$.