A train covers a distance of 12km in 10 minutes. If it takes 6 seconds to pass a telegraph post, then the length of the train is

Options

A. 100 metre
B. 120 metre
C. 140 metre
D. 90 metre

Answer

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

### Step 1: Convert the distance and time to find the speed of the train.
The train covers a distance of 12 kilometers in 10 minutes.

- Convert 10 minutes to hours:
\[ \text{Time in hours} = \frac{10 \text{ minutes}}{60} = \frac{1}{6} \text{ hours} \]

- Now, calculate the speed of the train in kilometers per hour (km/h):
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{12 \text{ km}}{\frac{1}{6} \text{ hours}} = 12 \times 6 = 72 \text{ km/h} \]

### Step 2: Convert the speed from km/h to m/s.
To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \):
\[ \text{Speed in m/s} = 72 \text{ km/h} \times \frac{5}{18} = 20 \text{ m/s} \]

### Step 3: Calculate the distance covered by the train in 6 seconds.
The train takes 6 seconds to pass a telegraph post, which means it covers a distance equal to its own length in that time.

- Using the speed in m/s:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 20 \text{ m/s} \times 6 \text{ s} = 120 \text{ meters} \]

### Conclusion:
The length of the train is **120 meters**.

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