A train passes the platform in 18 seconds and a man standing on the platform in 8 seconds .if the length ofthetrain is 100 metres , the length of the platform is :

Options

A. a) 125 m
B. b) 140 m
C. c) 150 m
D. d) 130 m

Answer

To solve the problem step by step, we will use the information given about the train, the platform, and the time taken to pass both the platform and a man standing on the platform.

### Step 1: Understand the problem
We know:
- The length of the train (L_train) = 100 meters
- Time taken to pass the platform (T_platform) = 18 seconds
- Time taken to pass a man (T_man) = 8 seconds

We need to find the length of the platform (L_platform).

### Step 2: Calculate the speed of the train
When the train passes the man, it covers its own length in the time taken. The speed of the train can be calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

For the man:
\[ \text{Speed} = \frac{L_{train}}{T_{man}} = \frac{100 \text{ meters}}{8 \text{ seconds}} = 12.5 \text{ m/s} \]

### Step 3: Set up the equation for the platform
When the train passes the platform, it covers both its length and the length of the platform. Therefore, the total distance covered when passing the platform is:
\[ \text{Distance} = L_{train} + L_{platform} = 100 + x \text{ meters} \]
where \( x \) is the length of the platform.

Using the speed we calculated, we can set up the equation:
\[ \text{Speed} = \frac{100 + x}{T_{platform}} \]
Substituting the known values:
\[ 12.5 = \frac{100 + x}{18} \]

### Step 4: Solve for the length of the platform
Now we can solve for \( x \):
1. Multiply both sides by 18:
\[ 12.5 \times 18 = 100 + x \]
\[ 225 = 100 + x \]

2. Rearranging gives:
\[ x = 225 - 100 \]
\[ x = 125 \text{ meters} \]

### Conclusion
The length of the platform is 125 meters.