A train travelling at 30 km an hour took 13 1/2 sec in passing a certain point ,Find the length of train ------

Options

A. 113 metres
B. 112 metres
C. 112.5 metres
D. None of these

Answer

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

### Step 1: Convert the speed from km/h to m/s
The speed of the train is given as 30 km/h. We need to convert this to meters per second (m/s) using the conversion factor:
1 km/h = (1000 m) / (3600 s) = 1/3.6 m/s.

So, to convert 30 km/h to m/s:
\[ \text{Speed in m/s} = 30 \times \frac{1000}{3600} = 30 \times \frac{5}{18} = \frac{150}{18} = \frac{25}{3} \text{ m/s}. \]

### Step 2: Convert the time from seconds
The time taken for the train to pass a certain point is given as 13.5 seconds. We can express this in fractional form:
\[ 13.5 \text{ seconds} = \frac{27}{2} \text{ seconds}. \]

### Step 3: Use the formula for distance
The formula for distance (or length of the train in this case) is given by:
\[ \text{Distance} = \text{Speed} \times \text{Time}. \]

### Step 4: Substitute the values into the formula
Now we can substitute the values we have:
\[ \text{Distance} = \left(\frac{25}{3} \text{ m/s}\right) \times \left(\frac{27}{2} \text{ s}\right). \]

### Step 5: Calculate the distance
Calculating the above expression:
\[ \text{Distance} = \frac{25 \times 27}{3 \times 2} = \frac{675}{6} = 112.5 \text{ meters}. \]

### Conclusion
The length of the train is **112.5 meters**.

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