A train 100m long is running at the speed of 30 km/hr. The time (in second) in which it will pass a man standing near the railway lines is:

Options

A. 10
B. 11
C. 12
D. 15

Answer

To solve the problem step by step, we need to determine the time it takes for a train that is 100 meters long and traveling at a speed of 30 km/hr to pass a man standing near the railway lines.

### Step 1: Understand the given information
- Length of the train = 100 meters
- Speed of the train = 30 km/hr

### Step 2: Convert the speed from km/hr to m/s
To convert the speed from kilometers per hour (km/hr) to meters per second (m/s), we use the conversion factor:
1 km = 1000 meters
1 hour = 3600 seconds

Thus, the conversion formula is:
\[ \text{Speed in m/s} = \text{Speed in km/hr} \times \frac{1000 \text{ m}}{3600 \text{ s}} \]

Substituting the given speed:
\[ \text{Speed in m/s} = 30 \times \frac{1000}{3600} \]

### Step 3: Simplify the conversion
Calculating the above:
\[ \text{Speed in m/s} = 30 \times \frac{1000}{3600} = 30 \times \frac{5}{18} = \frac{150}{18} = \frac{25}{3} \text{ m/s} \]

### Step 4: Use the formula for time
The formula for time when distance and speed are known is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

### Step 5: Substitute the values
Now, substituting the values we have:
- Distance = 100 meters
- Speed = \(\frac{25}{3}\) m/s

So,
\[ \text{Time} = \frac{100}{\frac{25}{3}} = 100 \times \frac{3}{25} \]

### Step 6: Calculate the time
Calculating the above:
\[ \text{Time} = \frac{300}{25} = 12 \text{ seconds} \]

### Final Answer
The time in which the train will pass the man is **12 seconds**.

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