A train is moving with a uniform speed. Train crosses a bridge of length 243 meters in 30 seconds and a bridge of length 343 meters in 36 seconds. Whatis the speed of the train?

Options

A. 60 km/hr
B. 72 km/hr
C. 64 km/h
D. 65 km/hr

Answer

To find the speed of the train, we can follow these steps:

### Step 1: Understand the Problem
The train crosses two bridges of different lengths in different times. We need to find the speed of the train, which is uniform.

### Step 2: Set Up the Equations
Let \( L \) be the length of the train.
- When the train crosses the first bridge (243 m), the total distance covered is \( 243 + L \) meters in 30 seconds.
- When the train crosses the second bridge (343 m), the total distance covered is \( 343 + L \) meters in 36 seconds.

### Step 3: Write the Speed Equations
Using the formula for speed, which is \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \), we can set up two equations:

1. For the first bridge:
\[ \text{Speed} = \frac{243 + L}{30} \]

2. For the second bridge:
\[ \text{Speed} = \frac{343 + L}{36} \]

Since the speed is the same in both cases, we can set the two equations equal to each other:
\[ \frac{243 + L}{30} = \frac{343 + L}{36} \]

### Step 4: Cross Multiply to Solve for \( L \)
Cross multiplying gives us:
\[ 36(243 + L) = 30(343 + L) \]

Expanding both sides:
\[ 36 \times 243 + 36L = 30 \times 343 + 30L \]

Calculating the products:
\[ 8748 + 36L = 10290 + 30L \]

### Step 5: Rearranging the Equation
Now, we can rearrange the equation to isolate \( L \):
\[ 8748 + 36L - 30L = 10290 \]
\[ 6L = 10290 - 8748 \]
\[ 6L = 1542 \]
\[ L = \frac{1542}{6} = 257 \text{ meters} \]

### Step 6: Calculate the Speed of the Train
Now that we have the length of the train, we can find the speed using either of the speed equations. Let's use the first one:
\[ \text{Speed} = \frac{243 + 257}{30} = \frac{500}{30} = \frac{50}{3} \text{ m/s} \]

### Step 7: Convert Speed to km/h
To convert the speed from m/s to km/h, we multiply by \( \frac{18}{5} \):
\[ \text{Speed in km/h} = \frac{50}{3} \times \frac{18}{5} = 60 \text{ km/h} \]

### Final Answer
The speed of the train is **60 km/h**.

---