Number of Steps in the Escalator | CE Board Problem in Mathematics, Surveying and Transportation Engineering

Date of Exam

November 2017

Subject

Mathematics, Surveying and Transportation Engineering

Problem
A certain businessman, who is always in a hurry, walks up an ongoing escalator at the rate of one step per second. Twenty steps bring him to the top. Next day he goes up at two steps per second, reaching the top in 32 steps. How many steps are there in the escalator?

A. 80	C. 50
B. 60	D. 70

Answer Key

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[ A ]

Solution

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Let
s = number of steps in the escalator
v = velocity of the escalator in steps/second

The first day, the businessman made 20 steps. To bring him to the top, the escalator will do (s - 20) steps for him. It all happened in 20 seconds
$s - 20 = 20v$

$s - 20v = 20$ ← Equation (1)

The next day, the businessman made 32 steps, the escalator did (s - 32) steps for him bringing him to the top. 32 steps at 2 steps/second, it all happened in 16 seconds.
$s - 32 = 16v$

$s - 16v = 32$ ← Equation (2)

From Equations (1) and (2)
s = 80 and v = 3 ← Answer: [ A ]