NIMCET 2009 — Reasoning PYQ

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Question

NIMCET 2009 — Reasoning PYQ

NIMCET | Reasoning | 2009

Recentily, while in Benguluru, I decided to walk down the escalator of a tube station. I did some quick calculation in my mind. I found that if I walk down twenty six steps, I require thirty seconds to reach the bottom. However, if I am able to step down thirty four stairs I would only require eighteen seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time I step off the last step at the bottom, what is the height of the stairway in steps ?

Choose the correct answer:

Explanation

To solve this problem, we need to understand that the total number of steps in the escalator remains constant. The total distance covered is the sum of the steps walked by the person and the steps moved by the escalator itself.

1. Define the Variables:

Let $N$ be the total number of steps in the stairway (height of the escalator).
Let $v$ be the speed of the escalator in steps per second.

2. Formulate Equations for both cases:

The total steps $N$ is given by:

\text{Total Steps} = \text{Steps walked by person} + (\text{Speed of escalator} \times \text{Time taken})

Case 1: The person walks $26$ steps in $30$ seconds.

$N = 26 + 30v \quad \text{--- (Equation 1)}$
Case 2: The person walks $34$ steps in $18$ seconds.

$N = 34 + 18v \quad \text{--- (Equation 2)}$

3. Solve for $v$ :

Since both equations equal $N$ , we can set them equal to each other:

26 + 30v = 34 + 18v

Subtract $18v$ and $26$ from both sides:

30v - 18v = 34 - 26

12v = 8

v = \frac{8}{12} = \frac{2}{3} \text{ steps/second}

4. Calculate the total height ( $N$ ):

Substitute the value of $v$ back into Equation 1:

N = 26 + 30 \left( \frac{2}{3} \right)

N = 26 + (10 \times 2)

N = 26 + 20

N = 46

Final Answer

The total height of the stairway is 46 steps.

Correct Option: (b)