A train passes two bridges of lengths 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is:

Options

A. 80 m
B. 90 m
C. 200 m
D. 150 m

Answer

To find the length of the train, we can set up equations based on the information given in the problem. Let's denote the length of the train as \( L \).

### Step 1: Calculate the speed of the train when crossing the first bridge.
- The first bridge is 800 meters long, and the train takes 100 seconds to cross it.
- The total distance covered by the train while crossing the bridge is the length of the train plus the length of the bridge: \( L + 800 \).
- The speed of the train can be calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{L + 800}{100} \]

### Step 2: Calculate the speed of the train when crossing the second bridge.
- The second bridge is 400 meters long, and the train takes 60 seconds to cross it.
- The total distance covered while crossing this bridge is \( L + 400 \).
- The speed of the train in this case is:
\[ \text{Speed} = \frac{L + 400}{60} \]

### Step 3: Set the two speed equations equal to each other.
Since the speed of the train is constant, we can set the two equations equal:
\[ \frac{L + 800}{100} = \frac{L + 400}{60} \]

### Step 4: Cross-multiply to eliminate the fractions.
Cross-multiplying gives us:
\[ 60(L + 800) = 100(L + 400) \]

### Step 5: Distribute both sides.
Distributing the terms results in:
\[ 60L + 48000 = 100L + 40000 \]

### Step 6: Rearrange the equation to isolate \( L \).
Rearranging gives:
\[ 48000 - 40000 = 100L - 60L \]
\[ 8000 = 40L \]

### Step 7: Solve for \( L \).
Dividing both sides by 40 gives:
\[ L = \frac{8000}{40} = 200 \]

### Conclusion:
The length of the train is \( 200 \) meters.