Institution: Bangladesh Bank Exam: Officer (General) -Ansar VDP Unnayan | BD House Building Finance Corporation 28.09.2018 ||
Topic: Mathematics (সাধারণ গণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To find the average speed for the entire journey, we first need to determine the total time taken for the trip. The man covers a total distance of 100 km.

For the first 2 hours, he rides at a speed of 20 km/hr. The distance covered in this segment is:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 20 \, \text{km/hr} \times 2 \, \text{hr} = 40 \, \text{km} \]

After the first 2 hours, he has 100 km - 40 km = 60 km remaining. He covers this distance at a reduced speed of 10 km/hr. The time taken to cover the remaining distance is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{60 \, \text{km}}{10 \, \text{km/hr}} = 6 \, \text{hr} \]

Now, we can calculate the total time for the entire journey:
\[ \text{Total Time} = 2 \, \text{hr} + 6 \, \text{hr} = 8 \, \text{hr} \]

Finally, the average speed for the whole journey is calculated using the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{100 \, \text{km}}{8 \, \text{hr}} = 12.5 \, \text{km/hr} \]

Thus, the average speed for the trip is 12.5 km/hr, making option A the correct choice.