A man cycling at a uniform speed of 10 km/h crosses a bridge in 90 seconds. The length of the bridge is:

Options

A. 150m
B. 25m
C. 250m
D. 15m

Answer

To find the length of the bridge that a man cycling at a uniform speed of 10 km/h crosses in 90 seconds, we can follow these steps:

### Step 1: Convert Speed from km/h to m/s
The speed is given as 10 km/h. To convert this speed into meters per second (m/s), we use the conversion factor:

\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{5}{18} \]

Calculating this gives:

\[ \text{Speed in m/s} = 10 \times \frac{5}{18} = \frac{50}{18} = \frac{25}{9} \text{ m/s} \]

### Step 2: Use the Distance Formula
The distance covered can be calculated using the formula:

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

### Step 3: Substitute the Values
We know the speed is \(\frac{25}{9}\) m/s and the time is 90 seconds. Substitute these values into the distance formula:

\[ \text{Distance} = \left(\frac{25}{9}\right) \times 90 \]

### Step 4: Calculate the Distance
Now, we can simplify the calculation:

\[ \text{Distance} = \frac{25 \times 90}{9} \]

Calculating this gives:

\[ \text{Distance} = 25 \times 10 = 250 \text{ meters} \]

### Conclusion
The length of the bridge is **250 meters**.

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