Question

Two persons are climbing up on two moving escalators which have 120 steps. The ratio of 1st person’s speed to that of1st escalator is 2 : 3 (steps). The ratio of 2nd person’s speed to that of 2nd escalator is 3 : 5 (steps). The total number of steps taken by both the persons are ?

Answer 1

Okay, this problem is a little trickier than it seems, it helps to look a how many steps the escalator takes vs how many steps you take (E-steps vs. U-Steps). Note that your speed is in relation to the escalator, that is important. If your speed is zero in relation to the escalator, then you will still get to the top but the escalator will be doing all the steps; so E-steps = 120, U-Steps =0. If you are moving 1:1 ratio in relation to the Escalator, then you split the work with the escalator 50:50 ie. E-Steps = 60, U-Steps =60. So for each part of the question above, we know that the number of steps YOU take is between zero and 60, since 1:1 ratio is faster than part one and part two of the question.

Lets do the first part of the question, 2:3 ratio. ie. your speed in relation of the escalator is 2:3. Think of it like splitting the number of steps with the escalator; 2+3=5 so cut the escalator into 5 pieces, you walk 2/5 of the way and the escalator does 3/5 of the work. Note that 2/5 over 3/5 is a 2:3 ratio. So the answer to the first part of the question is (2/5)*120 = 48. That's the number of steps you take.(U-steps)

Check to make sure part one is correct. E-Steps + U-Steps =120. E-steps = (3/5)*120=72. 72+48 =120.

I'll leave the second part of the question to you. Let me know if you need more help.