If a train 225 m long passes a telegraphic pole in 9 seconds then the time taken (in seconds) by it to cross a tunnel 450 m long is:

Options

A. 8 s
B. 10 s
C. 27 s
D. none of these

Answer

To solve the problem, we need to determine the speed of the train and then use that speed to find out how long it takes to cross the tunnel.

### Step 1: Find the speed of the train.
The length of the train is 225 meters, and it passes a telegraphic pole in 9 seconds.

Speed is calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

In this case, the distance is the length of the train (225 m) and the time is 9 seconds.

\[ \text{Speed} = \frac{225 \text{ m}}{9 \text{ s}} = 25 \text{ m/s} \]

### Step 2: Calculate the total distance to cross the tunnel.
To cross the tunnel, the train must cover its own length plus the length of the tunnel.

The length of the tunnel is 450 meters, so the total distance to be covered is:
\[ \text{Total Distance} = \text{Length of Train} + \text{Length of Tunnel} \]
\[ \text{Total Distance} = 225 \text{ m} + 450 \text{ m} = 675 \text{ m} \]

### Step 3: Calculate the time taken to cross the tunnel.
Now that we have the speed of the train and the total distance to cross the tunnel, we can find the time taken using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values we have:
\[ \text{Time} = \frac{675 \text{ m}}{25 \text{ m/s}} \]

Calculating this gives:
\[ \text{Time} = 27 \text{ seconds} \]

### Final Answer:
The time taken by the train to cross the tunnel is **27 seconds**.

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