A boy in a train notices that he can count 31 telephone posts in 60 seconds. The distance between two posts is 60 metres. Calculate the speed of the train?
A 90 km/hr
B. 108 km/hr
C. 60 km/hr
D. 120 km/hr

Options

A. C
B. D
C. B
D. A

Answer

To solve the problem, we need to calculate the speed of the train based on the information provided. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the given information
- The boy counts 31 telephone posts in 60 seconds.
- The distance between two posts is 60 meters.

### Step 2: Calculate the number of gaps between the posts
When counting telephone posts, if there are 31 posts, the number of gaps between them is 30 (since the first post does not have a gap before it).

### Step 3: Calculate the total distance covered
The total distance covered by the train while counting the posts can be calculated as follows:
- Number of gaps = 30
- Distance between each post = 60 meters
- Total distance = Number of gaps × Distance between each post
- Total distance = 30 × 60 = 1800 meters

### Step 4: Calculate the speed of the train
Speed is calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Using the total distance covered and the time taken:
- Distance = 1800 meters
- Time = 60 seconds
- Speed = \( \frac{1800 \text{ meters}}{60 \text{ seconds}} = 30 \text{ meters/second} \)

### Step 5: Convert speed from meters per second to kilometers per hour
To convert the speed from meters per second to kilometers per hour, we use the conversion factor:
\[ 1 \text{ m/s} = \frac{18}{5} \text{ km/hr} \]
Thus,
- Speed in km/hr = \( 30 \text{ m/s} \times \frac{18}{5} = 30 \times 3.6 = 108 \text{ km/hr} \)

### Conclusion
The speed of the train is 108 km/hr.

### Answer
B. 108 km/hr