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 ?<\/p>\n
[amp_mcq option1=”42″ option2=”44″ option3=”46″ option4=”48″ correct=”option3″]<\/p>\n
Alternatively, consider the total steps E. In time T, the man takes N steps relative to the escalator (so V_m = N\/T). The escalator moves V_e * T steps.
\nE = N + V_e * T.<\/p>\n
Case 1: Man takes N1 = 26 steps, T1 = 30 seconds.
\nE = 26 + V_e * 30 (Equation 1)<\/p>\n
Case 2: Man takes N2 = 34 steps, T2 = 18 seconds.
\nE = 34 + V_e * 18 (Equation 2)<\/p>\n
We have a system of two linear equations with two variables (E and V_e).
\nEquating the expressions for E:
\n26 + 30 * V_e = 34 + 18 * V_e
\n30 * V_e – 18 * V_e = 34 – 26
\n12 * V_e = 8
\nV_e = 8 \/ 12 = 2\/3 steps\/second.<\/p>\n
Substitute the value of V_e into either equation. Using Equation 1:
\nE = 26 + (2\/3) * 30
\nE = 26 + 2 * 10
\nE = 26 + 20
\nE = 46.<\/p>\n