A man walks up a stationary escalator in 90sec. When this man stands on a moving escalator he goes up in 60 sec. The time taken by the man to walk up the moving escalator is

Options

A. 30 s
B. 45 s
C. 36 s
D. 48 s

Answer

To solve the problem step by step, we will analyze the situation using the information provided about the man walking on the stationary escalator and the moving escalator.

### Step 1: Define Variables
Let:
- \( L \) = Length of the escalator
- \( v_m \) = Velocity of the man
- \( v_e \) = Velocity of the escalator

### Step 2: Calculate the Velocity of the Escalator
When the man stands on the moving escalator, he goes up in 60 seconds. Therefore, the velocity of the escalator can be calculated as:
\[ v_e = \frac{L}{60} \quad \text{(1)} \]

### Step 3: Calculate the Velocity of the Man
When the man walks up a stationary escalator, it takes him 90 seconds. Thus, the velocity of the man can be calculated as:
\[ v_m = \frac{L}{90} \quad \text{(2)} \]

### Step 4: Determine the Velocity of the Man on the Moving Escalator
When the man walks up the moving escalator, his effective velocity with respect to the ground is the sum of his walking velocity and the escalator's velocity:
\[ v_{mg} = v_m + v_e \]

Substituting equations (1) and (2) into this equation:
\[ v_{mg} = \frac{L}{90} + \frac{L}{60} \]

### Step 5: Find a Common Denominator
To add the two fractions, we need a common denominator. The least common multiple of 90 and 60 is 180. Therefore, we rewrite the velocities:
\[ v_{mg} = \frac{2L}{180} + \frac{3L}{180} = \frac{5L}{180} = \frac{L}{36} \]

### Step 6: Calculate the Time Taken to Walk Up the Moving Escalator
The time taken \( t \) to walk up the moving escalator can be calculated using the formula:
\[ t = \frac{\text{Distance}}{\text{Velocity}} = \frac{L}{v_{mg}} = \frac{L}{\frac{L}{36}} = 36 \text{ seconds} \]

### Conclusion
Thus, the time taken by the man to walk up the moving escalator is **36 seconds**.