To solve this problem, the user needs to know the concept of distance, speed, and time, and the proportionality between petrol consumption and velocity. The user must calculate the time it takes to travel 100 km at a speed of 100 km/h, subtract the time it takes to travel 80 km, and add the time it takes to travel the remaining 20 km at a reduced speed due to petrol consumption.
Now, let's go through each option and explain why it is right or wrong:
Option A) 10:15: This option is incorrect. The time taken to travel 100 km at 100 km/h is 1 hour. The time taken to travel 80 km at the same speed is 0.8 hours (i.e., 48 minutes). The time taken to travel the remaining 20 km, assuming a reduced speed of 80 km/h due to petrol consumption, is 20/80=0.25 hours (i.e., 15 minutes). Therefore, the earliest time Divya can arrive at the petrol pump is 9 PM + 1 hour + 0.8 hour + 0.25 hour = 10:05 PM.
Option B) 10:20: This option is incorrect. The earliest time Divya can arrive at the petrol pump is 10:05 PM, which is earlier than 10:20 PM.
Option C) 10:30: This option is incorrect. The earliest time Divya can arrive at the petrol pump is 10:05 PM, which is earlier than 10:30 PM.
Option D) 10:00: This option is incorrect. The time taken to travel 100 km at 100 km/h is 1 hour. The time taken to travel 80 km at the same speed is 0.8 hours (i.e., 48 minutes). Therefore, Divya would arrive at the 80 km mark at 9:48 PM. The remaining 20 km would take 20/100*60 = 12 minutes, so she would arrive at the petrol pump at 10 PM, not 10:00 PM.
Therefore, the correct answer is:
The Answer is: A. 10:15