UOLIUI
Due to a technical glitch, the escalator in a shopping mall moves two steps upward
and one step downward. Rahul, who is in a hurry to meet his friend, doesn't wait for
the escalator to take him upstairs but instead walks on it. If he covers 60 steps in
total and he takes 15 seconds for it, find the number of steps he would have covered
had the escalator been functioning properly.
A)
45
B)
30
40
C)
D)
Cannot be determined
Answers
Answer:
answer
options B
sorry ok enuku therithu ok
Answer:
The answer is option A) 45.
Explanation:
Let the number of steps in the escalator be x.
When Rahul walks on the escalator, he covers (2+x) steps in one cycle of the escalator.
In one cycle of the escalator, the escalator covers (1+x) steps.
Given that Rahul covers a total of 60 steps in 15 seconds.
Therefore, his speed = total distance covered / time taken = 60 / 15 = 4 steps per second.
Now, in one cycle of the escalator, the net number of steps covered by Rahul is (2+x)-(1+x) = 1 step.
The time taken by the escalator to cover one cycle is (1+x)/2 seconds (since it covers (1+x) steps in (1+x)/2 seconds).
Thus, in one cycle of the escalator, Rahul's speed relative to the ground (i.e., the speed at which he covers the steps if the escalator were functioning properly) is:
Speed relative to ground = distance covered relative to ground / time taken relative to ground
= 1 step / [(1+x)/2 seconds]
= 2 / (1+x) steps per second
So, we have:
4 (Rahul's speed) = Speed relative to ground + Speed of escalator
4 = (2 / (1+x)) + [(1 / (1+x)) x 2]
4 = 4 / (1+x)
1+x = 4
x = 3
Therefore, the number of steps Rahul would have covered had the escalator been functioning properly is:
60 - (3 x 15 / 2) = 45 steps
Hence, the answer is option A) 45.
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