Q38 (CISF/2018) Science & Technology › Basic Science (Physics, Chemistry, Biology)

While coming down on an escalator of a station, when a man walks down twenty-six steps of the staircase, he requires thirty seconds to reach the bottom. However, if he steps down thirty-four steps, it takes eighteen seconds to reach the bottom. How many steps are there in the escalator ?

Explanation

Let N be the total number of steps on the escalator and v_e be the speed of the escalator in steps per second. The total number of steps is the sum of the steps the man walks and the steps the escalator moves during that time.

From the first condition: N = 26 + 30v_e ... (i)
From the second condition: N = 34 + 18v_e ... (ii)

Equating (i) and (ii):
26 + 30v_e = 34 + 18v_e
30v_e - 18v_e = 34 - 26
12v_e = 8
v_e = 8/12 = 2/3 steps/second

Substituting v_e = 2/3 in equation (i):
N = 26 + 30 × (2/3)
N = 26 + 20 = 46

Therefore, the total number of steps in the escalator is 46.

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While coming down on an escalator of a station, when a man walks down twenty-six steps of the staircase, he requires thirty seconds to reach the bottom. However, if he steps down thirty-four steps, it takes eighteen seconds to reach the bottom. How many steps are there in the escalator ?

Explanation

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