A train running at the speed of 84 km/hr passes a man walking in opposite direction at the speed of 6 km/hr in 4 seconds. What is the length of train (in metre) ?
84 km/hr की गति से चल रही एक गाड़ी विपरित दिशा में 6km/ hr की गति से चल रहे एक आदमी को 4 सेकंड में पार करती है। गाड़ी की लम्बाई (मीटर में) क्या है?

Options

A. A)100
B. B)90
C. C)150
D. D)120

Explanation

To find the length of the train, we can follow these steps:

### Step 1: Determine the speeds of the train and the man
- Speed of the train = 84 km/hr
- Speed of the man = 6 km/hr

### Step 2: Calculate the relative speed
Since the train and the man are moving in opposite directions, we add their speeds to find the relative speed:
- Relative speed = Speed of the train + Speed of the man
- Relative speed = 84 km/hr + 6 km/hr = 90 km/hr

### Step 3: Convert the relative speed from km/hr to m/s
To convert km/hr to m/s, we use the conversion factor (1 km/hr = 5/18 m/s):
- Relative speed in m/s = 90 km/hr × (5/18)
- Relative speed = 90 × 5 / 18 = 25 m/s

### Step 4: Use the time taken to pass the man
The time taken for the train to pass the man is given as 4 seconds.

### Step 5: Calculate the length of the train
The length of the train can be calculated using the formula:
- Length of the train = Relative speed × Time
- Length of the train = 25 m/s × 4 s = 100 meters

### Final Answer
The length of the train is **100 meters**.

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