A column of men ,extending 250 metres in length takes one hour to march through a street at the rate of 50 paces a minute, each pacebeing 75 cm.Find the length of the street ?

Options

A. 2 km
B. 1 km
C. 1.5 km
D. 2.5 km

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the distance covered in one minute
We know that each pace is 75 cm and the rate is 50 paces per minute.

\[ \text{Distance covered in one minute} = \text{Number of paces} \times \text{Length of each pace} \]
\[ = 50 \text{ paces/min} \times 75 \text{ cm/pace} = 3750 \text{ cm/min} \]

### Step 2: Convert the distance from cm to meters
Since 1 meter = 100 cm, we convert the distance covered in one minute to meters.

\[ \text{Distance covered in one minute in meters} = \frac{3750 \text{ cm}}{100} = 37.5 \text{ m/min} \]

### Step 3: Calculate the distance covered in one hour
Now, we need to find out how much distance is covered in one hour (which is 60 minutes).

\[ \text{Distance covered in one hour} = \text{Distance covered in one minute} \times 60 \]
\[ = 37.5 \text{ m/min} \times 60 \text{ min} = 2250 \text{ m} \]

### Step 4: Calculate the length of the street
The column of men is 250 meters long, and they take one hour to march through the street. Therefore, the total length of the street is the distance covered in one hour plus the length of the column.

\[ \text{Length of the street} = \text{Distance covered in one hour} + \text{Length of the column} \]
\[ = 2250 \text{ m} + 250 \text{ m} = 2500 \text{ m} \]

### Step 5: Convert the length of the street to kilometers
Since 1 kilometer = 1000 meters, we convert the length of the street into kilometers.

\[ \text{Length of the street in kilometers} = \frac{2500 \text{ m}}{1000} = 2.5 \text{ km} \]

### Final Answer
The length of the street is **2.5 kilometers**.

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