X gets on a lift at the ground floor which goes up at speed of 30 floors per minute whereas Y gets on another lift at the same time on the 50th floor which goes down at the speed of 45 floors per minute. At which floor will their paths cross? (lifts are moving without stopping at any floor)

Correct option is D

Given:
X starts from ground floor (0) and moves upward at 30 floors/min.
Y starts from 50th floor and moves downward at 45 floors/min.
Formula Used:
Distance covered by X + Distance covered by Y = Total distance (50 floors).
Time = Distance ÷ Speed.
Solution:
Let the time when they meet be t minutes.
Distance covered by X in t minutes = 30t
Distance covered by Y in t minutes = 45t
Since they start together and move towards each other:
30t + 45t = 50
75t = 50
t = $$\frac{50}{75}$$​ = $$\frac 23$$​minutes
Floor at which they meet = Distance covered by X = 30 ×$$\frac 23$$​= 20