A train goes through a `1100 m` long tunnel at a constant speed of `72 km//h`. The last compartment comes out one minute after the entry of engine in the tunnel. Find the length of train (including engine).

Options

A. `80 m`
B. `100 m`
C. `1200m`
D. `1000m`

Explanation

To solve the problem, we need to find the length of the train given that it passes through a 1100 m long tunnel at a constant speed of 72 km/h, and the last compartment exits the tunnel one minute after the engine enters.

### Step-by-Step Solution:

1. **Convert the speed from km/h to m/s:**
\[ \text{Speed} = 72 \, \text{km/h} = 72 \times \frac{1000 \, \text{m}}{3600 \, \text{s}} = 20 \, \text{m/s} \]

**Hint:** To convert km/h to m/s, multiply by \(\frac{1000}{3600}\) or simply by \(\frac{5}{18}\).

2. **Determine the time taken for the last compartment to exit the tunnel:**
The last compartment exits the tunnel 1 minute (60 seconds) after the engine enters.

3. **Calculate the total distance covered by the train in that time:**
\[ \text{Distance} = \text{Speed} \times \text{Time} = 20 \, \text{m/s} \times 60 \, \text{s} = 1200 \, \text{m} \]

**Hint:** Distance can be calculated using the formula \( \text{Distance} = \text{Speed} \times \text{Time} \).

4. **Set up the equation for the total distance covered:**
The total distance covered by the train when the last compartment exits the tunnel is the length of the tunnel plus the length of the train:
\[ \text{Total Distance} = \text{Length of Tunnel} + \text{Length of Train} \]
\[ 1200 \, \text{m} = 1100 \, \text{m} + L \]

5. **Solve for the length of the train (L):**
\[ L = 1200 \, \text{m} - 1100 \, \text{m} = 100 \, \text{m} \]

**Hint:** Rearranging the equation helps isolate the variable you want to solve for.

### Final Answer:
The length of the train (including the engine) is **100 meters**.