A train 120 metres long is running at a rate of 54 km/hr.Time taken by the train to cross a tunnel 130 metres long is -----

Options

A. 8 1/3 seconds
B. 16 2/3 seconds
C. 10 seconds
D. 15 seconds

Answer

To solve the problem of how long it takes for a train to cross a tunnel, we can follow these steps:

### Step 1: Understand the Problem
We have a train that is 120 meters long and it is crossing a tunnel that is 130 meters long. We need to find the time taken for the entire train to completely cross the tunnel.

### Step 2: Calculate the Total Distance
The total distance that the train needs to cover to completely cross the tunnel is the sum of the lengths of the train and the tunnel.

\[ \text{Total Distance} = \text{Length of Train} + \text{Length of Tunnel} = 120 \, \text{meters} + 130 \, \text{meters} = 250 \, \text{meters} \]

### Step 3: Convert Speed from km/hr to m/s
The speed of the train is given as 54 km/hr. We need to convert this speed into meters per second (m/s) using the conversion factor \( \frac{5}{18} \).

\[ \text{Speed in m/s} = 54 \times \frac{5}{18} = 15 \, \text{m/s} \]

### Step 4: Use the Formula for Time
We can use the formula for time, which is:

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

Substituting the values we have:

\[ \text{Time} = \frac{250 \, \text{meters}}{15 \, \text{m/s}} = \frac{250}{15} = \frac{50}{3} \, \text{seconds} \]

### Step 5: Convert Time to Mixed Number
Now we can convert \( \frac{50}{3} \) seconds to a mixed number:

\[ \frac{50}{3} = 16 \, \text{whole seconds} \, \text{and} \, \frac{2}{3} \, \text{seconds} \]

Thus, the time taken by the train to cross the tunnel is \( 16 \frac{2}{3} \) seconds.

### Final Answer
The time taken by the train to cross the tunnel is **16 \( \frac{2}{3} \) seconds**.

---