Two trains travel in the same direction at 60 km/hr and 96 km/hr. If the faster train passes a man in the slower train in 20 seconds, then the length of the faster train is

Options

A. 100 m
B. 125 m
C. 150 m
D. 200 m

Answer

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

### Step 1: Determine the speeds of the trains
The speeds of the two trains are given as:
- Speed of the slower train = 60 km/hr
- Speed of the faster train = 96 km/hr

### Step 2: Calculate the relative speed
Since both trains are moving in the same direction, the relative speed is calculated by subtracting the speed of the slower train from the speed of the faster train.

\[ \text{Relative Speed} = \text{Speed of Faster Train} - \text{Speed of Slower Train} \]
\[ \text{Relative Speed} = 96 \, \text{km/hr} - 60 \, \text{km/hr} = 36 \, \text{km/hr} \]

### Step 3: Convert the relative speed to meters per second
To convert km/hr to m/s, we multiply by \(\frac{5}{18}\).

\[ \text{Relative Speed in m/s} = 36 \, \text{km/hr} \times \frac{5}{18} = 10 \, \text{m/s} \]

### Step 4: Use the time to find the distance (length of the faster train)
The faster train passes a man in the slower train in 20 seconds. We can use the formula for distance, which is:

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

Here, the distance is the length of the faster train, the speed is the relative speed we calculated, and the time is given as 20 seconds.

\[ \text{Length of Faster Train} = \text{Relative Speed} \times \text{Time} \]
\[ \text{Length of Faster Train} = 10 \, \text{m/s} \times 20 \, \text{s} = 200 \, \text{meters} \]

### Final Answer
The length of the faster train is **200 meters**.

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