A person climbs up a stalled escalator in 60s. 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?

Options

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

Explanation

To solve the problem, we need to determine how long it takes for a person to walk up a moving escalator. We will use the information given about the time taken to climb the escalator when it is stalled and when it is moving.

### Step-by-Step Solution:

1. **Define Variables:**
- Let the length of the escalator be \( x \) meters.
- Let the speed of the person (when climbing the escalator) be \( v_m \).
- Let the speed of the escalator be \( v_e \).

2. **Calculate the Speed of the Person:**
- When the person climbs the stalled escalator, it takes him 60 seconds.
- Therefore, the speed of the person is:
\[ v_m = \frac{x}{60} \text{ m/s} \]

3. **Calculate the Speed of the Escalator:**
- When the person stands on the moving escalator, it takes him 40 seconds to reach the top.
- Therefore, the speed of the escalator is:
\[ v_e = \frac{x}{40} \text{ m/s} \]

4. **Calculate the Combined Speed When Both are Moving:**
- When the person walks up the moving escalator, their effective speed is the sum of their speed and the escalator's speed:
\[ v_{combined} = v_m + v_e = \frac{x}{60} + \frac{x}{40} \]

5. **Finding a Common Denominator:**
- The least common multiple of 60 and 40 is 120. Thus, we can rewrite the speeds:
\[ v_m = \frac{x}{60} = \frac{2x}{120} \]
\[ v_e = \frac{x}{40} = \frac{3x}{120} \]
- Therefore,
\[ v_{combined} = \frac{2x}{120} + \frac{3x}{120} = \frac{5x}{120} \]

6. **Calculate the Time Taken to Walk Up the Moving Escalator:**
- The time taken to walk up the moving escalator can be calculated using the formula:
\[ t = \frac{\text{Distance}}{\text{Speed}} = \frac{x}{v_{combined}} = \frac{x}{\frac{5x}{120}} = \frac{120}{5} = 24 \text{ seconds} \]

### Final Answer:
The time taken by the person to walk up the moving escalator is **24 seconds**.