A train crosses two platform having length 293 m and 425 m in 35 sec. and 47 sec. respectively. Find the length of train.

Options

A. 92 m
B. 78 m
C. 85 m
D. 99 m

Answer

To find the length of the train that crosses two platforms of lengths 293 m and 425 m in 35 seconds and 47 seconds respectively, we can follow these steps:

### Step 1: Define Variables
Let the length of the train be \( x \) meters.

### Step 2: Calculate Speed for Each Platform
The speed of the train when crossing the first platform can be expressed as:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{x + 293}{35} \]

For the second platform, the speed can be expressed as:
\[ \text{Speed} = \frac{x + 425}{47} \]

### Step 3: Set the Speeds Equal
Since the speed of the train remains constant while crossing both platforms, we can set the two expressions for speed equal to each other:
\[ \frac{x + 293}{35} = \frac{x + 425}{47} \]

### Step 4: Cross Multiply to Eliminate Fractions
Cross multiplying gives us:
\[ 47(x + 293) = 35(x + 425) \]

### Step 5: Expand Both Sides
Expanding both sides:
\[ 47x + 13751 = 35x + 14875 \]

### Step 6: Rearrange the Equation
Rearranging to isolate \( x \):
\[ 47x - 35x = 14875 - 13751 \]
\[ 12x = 1124 \]

### Step 7: Solve for \( x \)
Now, divide both sides by 12 to find \( x \):
\[ x = \frac{1124}{12} = 93.67 \text{ m} \]

### Step 8: Round to the Nearest Whole Number
Since the length of the train is typically expressed in whole meters, we can round \( 93.67 \) to \( 94 \) meters.

### Final Answer
The length of the train is approximately \( 94 \) meters.

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