Two persons are climbing up on two moving escalators which have 120 steps. The ratio of 1st person’s speed to that of 1st escalator is 2:3 (steps). The ratio of 2nd person’s speed to that of $$2^{nd}$$ escalator is 3:5 (steps). Find the total number of steps they both have taken
together.

First person: For every 2 steps he takes, the escalator moves by 3 steps at the same time.
Hence, 5 steps are covered at a time.
This is repeated 24 times(120/5).
Hence, first person takes = 24 *2 = 48 steps
Second person: For every 3 steps he takes, the escalator moves by 5 steps at the same time.
Hence, 8 steps are covered at a time.
This is repeated for 15 times(120/8)
Hence, second person takes = 3 * 15 = 45 steps
Total number of steps = 48 + 45 = 93