A 600-m-long train is running at the speed of 30 kmh. The time (in seconds) in which it would pass a man standing near the railway line is:

Options

A. 85
B. 90
C. 72
D. 78

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Convert the speed from kilometers per hour to meters per second.
The speed of the train is given as 30 km/h. We can convert this speed to meters per second using the conversion factor:

\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]

Thus, to convert 30 km/h to m/s:

\[ \text{Speed in m/s} = 30 \times \frac{5}{18} \]

Calculating this gives:

\[ \text{Speed in m/s} = 30 \times \frac{5}{18} = \frac{150}{18} = \frac{25}{3} \text{ m/s} \]

### Step 2: Identify the distance to be covered.
The length of the train is given as 600 meters. This is the distance that the train needs to cover to completely pass the man standing near the railway line.

### Step 3: Use the formula to calculate time.
We know that time can be calculated using the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values we have:

\[ \text{Time} = \frac{600 \text{ meters}}{\frac{25}{3} \text{ m/s}} \]

### Step 4: Simplify the calculation.
To divide by a fraction, we multiply by its reciprocal:

\[ \text{Time} = 600 \times \frac{3}{25} \]

Calculating this gives:

\[ \text{Time} = \frac{600 \times 3}{25} = \frac{1800}{25} = 72 \text{ seconds} \]

### Final Answer:
The time in which the train would pass the man is **72 seconds**.

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