A superfast Duronto express running at 90 kmph overtakes a bike running at 36 kmph in 25 seconds . What is the length of the train in meters ?

Options

A. 375 m
B. 225 m
C. 275 m
D. 325 m

Answer

To solve the problem of finding the length of the train that overtakes a bike, we can follow these steps:

### Step 1: Determine the speeds of the train and the bike
- Speed of the train = 90 km/h
- Speed of the bike = 36 km/h

### Step 2: Calculate the relative speed
- Since the train is overtaking the bike, we calculate the relative speed by subtracting the speed of the bike from the speed of the train:
\[ \text{Relative Speed} = \text{Speed of Train} - \text{Speed of Bike} = 90 \text{ km/h} - 36 \text{ km/h} = 54 \text{ km/h} \]

### Step 3: Convert the relative speed from km/h to m/s
- To convert km/h to m/s, we use the conversion factor \( \frac{1000 \text{ m}}{3600 \text{ s}} \):
\[ \text{Relative Speed in m/s} = 54 \text{ km/h} \times \frac{1000}{3600} = \frac{54000}{3600} = 15 \text{ m/s} \]

### Step 4: Use the time taken to overtake to find the distance
- The time taken to overtake the bike is given as 25 seconds. We can use the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Substituting the values we have:
\[ \text{Distance} = 15 \text{ m/s} \times 25 \text{ s} = 375 \text{ m} \]

### Step 5: Conclusion
- The length of the train is equal to the distance it covers while overtaking the bike, which is 375 meters.

### Final Answer
The length of the train is **375 meters**.

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