In a platform, train 'A' 225 m long is stopped to allow train 'B' 375m long to pass. Speed of 'B' is 90 km per hour. time taken by train 'B' to cross train 'A' completely will be

Options

A. (a) 6.67 sec
B. (b) 9 sec
C. (c) 2.5 sec
D. (d) 24 sec

Explanation

To solve the problem of how long it takes for train B to completely cross train A, we will follow these steps:

### Step 1: Identify the lengths of the trains
- Length of train A = 225 meters
- Length of train B = 375 meters

### Step 2: Calculate the total distance to be covered
The total distance that train B needs to cover to completely pass train A is the sum of the lengths of both trains:
\[ \text{Total Distance} = \text{Length of Train A} + \text{Length of Train B} \]
\[ \text{Total Distance} = 225 \, \text{m} + 375 \, \text{m} = 600 \, \text{m} \]

### Step 3: Convert the speed of train B from km/h to m/s
The speed of train B is given as 90 km/h. To convert this speed into meters per second, we use the conversion factor (1 km/h = 5/18 m/s):
\[ \text{Speed of Train B} = 90 \, \text{km/h} \times \frac{5}{18} = 25 \, \text{m/s} \]

### Step 4: Calculate the time taken to cross
To find the time taken for train B to cross train A completely, we use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Substituting the total distance and speed:
\[ \text{Time} = \frac{600 \, \text{m}}{25 \, \text{m/s}} = 24 \, \text{seconds} \]

### Final Answer:
The time taken by train B to completely cross train A is **24 seconds**.

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