Question

A person climbs up a stalled escalator in $60\, s$ . If standing on the same but escalator running with constant velocity he takes $40\, s$. How much time is taken by the person to walk up the moving escalator ?

• A. 37 s
• B. 27 s
• C. 24 s
• D. 45 s

Answer 1

The Correct Option is C

To solve the problem, let's break down the given information and the requirements:

1. The person climbs up the escalator, which is stalled (not moving), in 60\,s.
2. When the escalator is running, and the person stays still, it takes 40\,s to travel the same distance.
3. We need to find the time taken by the person to walk up the moving escalator.

Let's define some variables:

• Let D be the total distance that needs to be covered.
• Let v_p be the speed of the person climbing.
• Let v_e be the speed of the escalator.

From the first scenario (stalled escalator):

v_p = \frac{D}{60}

From the second scenario (escalator moving, person standing):

v_e = \frac{D}{40}

In the third scenario, where the person is moving up the running escalator, the effective speed v_{\text{eff}} would be:

v_{\text{eff}} = v_p + v_e = \frac{D}{60} + \frac{D}{40}

To find a common denominator and sum the fractions:

v_{\text{eff}} = \frac{2D}{120} + \frac{3D}{120} = \frac{5D}{120} = \frac{D}{24}

The time taken T_{\text{eff}} for the person to walk up the moving escalator is given by:

T_{\text{eff}} = \frac{D}{v_{\text{eff}}} = \frac{D}{D/24} = 24\,s

The time taken by the person to walk up the moving escalator is 24 seconds.

This matches the provided correct answer: 24 s.