Question

Two persons move down on an escalator. A takes 50 steps and B takes 75 steps while the escalator is moving down. The time taken by A to take 1 step is equal to time taken by B to take 3 steps.
What is the number of steps on the escalator when it is stationary?

• A. 125 steps
• B. 150 steps
• C. 100 steps
• D. 25 steps
• E. None of these

Answer 1

The correct option is C 100 steps

Let A take 1 step in $t$ minutes.
$\Rightarrow$ B takes 3 steps in $t$ minutes.
Let the escalator take $s$ steps per minute.
$50+50t\times s=75+\frac{(75t\times 3)}{3}$
$50+50st=75+25st$
$st=1$
$\Rightarrow$ Number of steps on the escalator = $50+50\times 1$ = 100 steps