A train cross a platform in 20 second which is 180 meter-long and a man in 8 seconds What time it takes to cross a bridge of 240-meter-long. (in sec)?

Options

A. 12 sec
B. 30 sec
C. 24 sec
D. 20 sec

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Problem
We need to find the time it takes for a train to cross a bridge that is 240 meters long. We know the train crosses a platform of 180 meters in 20 seconds and a man in 8 seconds.

### Step 2: Define Variables
Let:
- \( t \) = length of the train (in meters)
- \( x \) = speed of the train (in meters per second)

### Step 3: Set Up Equations
1. **Crossing the Platform**:
The distance covered when crossing the platform is the length of the train plus the length of the platform:
\[ \text{Distance} = t + 180 \]
The time taken to cross the platform is 20 seconds. Therefore, we can write:
\[ t + 180 = 20x \quad \text{(1)} \]

2. **Crossing the Man**:
When the train crosses a man, the distance covered is just the length of the train:
\[ t = 8x \quad \text{(2)} \]

### Step 4: Solve the Equations
Now, we can solve equations (1) and (2) simultaneously.

From equation (2):
\[ x = \frac{t}{8} \]

Substituting \( x \) in equation (1):
\[ t + 180 = 20 \left(\frac{t}{8}\right) \]
\[ t + 180 = \frac{20t}{8} \]
\[ t + 180 = 2.5t \]
Rearranging gives:
\[ 180 = 2.5t - t \]
\[ 180 = 1.5t \]
\[ t = \frac{180}{1.5} = 120 \text{ meters} \]

### Step 5: Calculate the Speed of the Train
Now we can find the speed \( x \) using equation (2):
\[ t = 8x \implies 120 = 8x \implies x = \frac{120}{8} = 15 \text{ m/s} \]

### Step 6: Find the Time to Cross the Bridge
When crossing the bridge, the distance is the length of the train plus the length of the bridge:
\[ \text{Distance} = t + 240 = 120 + 240 = 360 \text{ meters} \]
Using the speed to find the time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{360}{15} = 24 \text{ seconds} \]

### Final Answer
The time taken to cross the bridge is **24 seconds**.

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