A person walks up a stalled escalator in 90 s. When standingon the same escalator, now moving, he is carried in 60 s.The time it would take him to walk up the moving escalator will be:

Options

A. 27 s
B. 72 s
C. 18 s
D. 36 s

Answer

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

### Step-by-Step Solution:

1. **Define Variables:**
- Let the speed of the person be \( V_p \) (in escalator lengths per second).
- Let the speed of the escalator be \( V_e \) (in escalator lengths per second).
- Let the length of the escalator be \( L \) (in escalator lengths).

2. **Time Taken on Stalled Escalator:**
- When the person walks up the stalled escalator, it takes him 90 seconds.
- Therefore, the equation for this scenario is:
\[ L = V_p \times 90 \quad \text{(1)} \]

3. **Time Taken on Moving Escalator:**
- When the person stands on the moving escalator, it takes him 60 seconds.
- Therefore, the equation for this scenario is:
\[ L = V_e \times 60 \quad \text{(2)} \]

4. **Relate Speeds to Length:**
- From equation (1), we can express \( V_p \):
\[ V_p = \frac{L}{90} \]
- From equation (2), we can express \( V_e \):
\[ V_e = \frac{L}{60} \]

5. **Walking Up the Moving Escalator:**
- When the person walks up the moving escalator, his effective speed is \( V_p + V_e \).
- The time taken \( t \) to walk up the moving escalator can be expressed as:
\[ L = (V_p + V_e) \times t \]

6. **Substituting the Speeds:**
- Substitute \( V_p \) and \( V_e \) into the equation:
\[ L = \left(\frac{L}{90} + \frac{L}{60}\right) \times t \]

7. **Simplifying the Equation:**
- Factor out \( L \):
\[ 1 = \left(\frac{1}{90} + \frac{1}{60}\right) \times t \]
- Find a common denominator (which is 180):
\[ \frac{1}{90} = \frac{2}{180}, \quad \frac{1}{60} = \frac{3}{180} \]
- Therefore:
\[ 1 = \left(\frac{2}{180} + \frac{3}{180}\right) \times t \]
\[ 1 = \frac{5}{180} \times t \]

8. **Solving for Time \( t \):**
- Rearranging gives:
\[ t = \frac{180}{5} = 36 \text{ seconds} \]

### Final Answer:
The time it would take him to walk up the moving escalator is **36 seconds**.