When a man stands on a moving escalator he goes up in 50 sec. and when he walks up the moving escalator he goes up in 30 sec. Then the man walks up the stationary escalator in a time of ........ sec

Options

A. 60
B. 75
C. 90
D. 18.75

Answer

To solve the problem, we need to find the time taken by a man to walk up a stationary escalator given the times taken when he is on a moving escalator. Let's break it down step by step.

### Step 1: Define Variables
Let:
- \( l \) = length of the escalator
- \( v_m \) = speed of the man
- \( v_e \) = speed of the escalator

### Step 2: Analyze the First Case
When the man stands on the moving escalator, he takes 50 seconds to reach the top. The only speed contributing to his ascent is the speed of the escalator.

Using the formula for speed:
\[ v_e = \frac{l}{50} \quad \text{(1)} \]

### Step 3: Analyze the Second Case
When the man walks up the moving escalator, he takes 30 seconds. In this case, both the man's speed and the escalator's speed contribute to his ascent.

The combined speed is:
\[ v_m + v_e = \frac{l}{30} \quad \text{(2)} \]

### Step 4: Set Up the Equations
From equation (1), we have \( v_e = \frac{l}{50} \). We can substitute this into equation (2):
\[ v_m + \frac{l}{50} = \frac{l}{30} \]

### Step 5: Solve for \( v_m \)
Rearranging the equation gives:
\[ v_m = \frac{l}{30} - \frac{l}{50} \]

To combine these fractions, we find a common denominator (which is 150):
\[ v_m = \frac{5l}{150} - \frac{3l}{150} = \frac{2l}{150} = \frac{l}{75} \quad \text{(3)} \]

### Step 6: Find Time for the Stationary Escalator
Now, we need to find the time \( t \) it takes for the man to walk up the stationary escalator. When the escalator is stationary, the speed of the escalator \( v_e = 0 \), so:
\[ v_m = \frac{l}{t} \]

Using equation (3):
\[ \frac{l}{75} = \frac{l}{t} \]

### Step 7: Solve for \( t \)
Cancelling \( l \) from both sides (assuming \( l \neq 0 \)):
\[ \frac{1}{75} = \frac{1}{t} \]
Thus, we have:
\[ t = 75 \text{ seconds} \]

### Final Answer
The time taken by the man to walk up the stationary escalator is **75 seconds**.

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