A man crosses a stationary train in 5 minutes. The same train crosses a pole in 48 seconds. What is the ratio between the speed of the man and the speed of the train respectively?

Options

A. `3:25`
B. `4:25`
C. `25:3`
D. Cannot be determined

Answer

To solve the problem, we need to find the ratio between the speed of the man and the speed of the train. Let's break it down step by step.

### Step 1: Convert the time taken by the man to seconds
The man crosses the stationary train in 5 minutes. We need to convert this time into seconds for easier calculations.

\[ \text{Time in seconds} = 5 \text{ minutes} \times 60 \text{ seconds/minute} = 300 \text{ seconds} \]

**Hint:** Remember that 1 minute = 60 seconds. Multiply the number of minutes by 60 to convert to seconds.

### Step 2: Determine the time taken by the train to cross a pole
The train crosses a pole in 48 seconds. This is already in the correct unit, so we can use this value directly.

\[ \text{Time taken by the train} = 48 \text{ seconds} \]

**Hint:** When given a time in seconds, you can use it directly without conversion.

### Step 3: Calculate the speed of the train
The speed of the train can be calculated using the formula:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

Since the train crosses a pole, the distance is equal to the length of the train. Let's denote the length of the train as \( L \).

\[ \text{Speed of the train} = \frac{L}{48 \text{ seconds}} \]

**Hint:** The distance when crossing a pole is simply the length of the train.

### Step 4: Calculate the speed of the man
The man crosses the entire length of the train in 300 seconds. Thus, the speed of the man can be calculated as:

\[ \text{Speed of the man} = \frac{L}{300 \text{ seconds}} \]

**Hint:** The distance covered by the man while crossing the train is also the length of the train.

### Step 5: Find the ratio of the speeds
Now that we have both speeds, we can find the ratio of the speed of the man to the speed of the train.

\[ \text{Ratio} = \frac{\text{Speed of the man}}{\text{Speed of the train}} = \frac{\frac{L}{300}}{\frac{L}{48}} \]

The \( L \) cancels out:

\[ \text{Ratio} = \frac{48}{300} \]

### Step 6: Simplify the ratio
To simplify \( \frac{48}{300} \):

\[ \text{Ratio} = \frac{48 \div 12}{300 \div 12} = \frac{4}{25} \]

Thus, the ratio of the speed of the man to the speed of the train is:

\[ \text{Ratio} = 4:25 \]

**Final Answer:** The ratio between the speed of the man and the speed of the train is \( 4:25 \).