A train crosses a man going along the railway track at 6 km/hr. The man could see the train upto 2 min and then find the speed of the train if at the time of disappearance the distance b/w train to man was 1200 m ? & length of train is 300 metre ?

Options

A. 51 km/hr
B. 53 km/hr
C. 43 km/hr
D. 41 km/hr

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the scenario
A train crosses a man walking along the railway track. The man can see the train for 2 minutes before it disappears. At the time of disappearance, the distance between the train and the man is 1200 meters, and the length of the train is 300 meters.

### Step 2: Convert time into hours
The time the man can see the train is given as 2 minutes. We need to convert this into hours because the speed is in km/hr.

\[ \text{Time in hours} = \frac{2 \text{ minutes}}{60} = \frac{1}{30} \text{ hours} \]

### Step 3: Calculate the distance the train travels in that time
The distance the train travels in 2 minutes can be calculated using the formula:

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

Let the speed of the train be \(X\) km/hr. The distance traveled by the train in 2 minutes is:

\[ \text{Distance} = X \times \frac{1}{30} \]

### Step 4: Total distance covered by the train
At the time of disappearance, the train has traveled the distance to the man (1200 m) plus its own length (300 m). Therefore, the total distance covered by the train is:

\[ \text{Total Distance} = 1200 \text{ m} + 300 \text{ m} = 1500 \text{ m} \]

### Step 5: Convert total distance to kilometers
Since the speed is in km/hr, we need to convert the total distance from meters to kilometers:

\[ 1500 \text{ m} = \frac{1500}{1000} = 1.5 \text{ km} \]

### Step 6: Set up the equation
Now we can set up the equation based on the distance traveled:

\[ X \times \frac{1}{30} = 1.5 \]

### Step 7: Solve for \(X\)
To find \(X\), we can rearrange the equation:

\[ X = 1.5 \times 30 = 45 \text{ km/hr} \]

### Step 8: Adjust for the man's speed
The man is walking at a speed of 6 km/hr. The relative speed of the train with respect to the man is:

\[ \text{Relative Speed} = X + 6 = 45 + 6 = 51 \text{ km/hr} \]

### Final Answer
The speed of the train is **51 km/hr**.

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