UGC NET Questions (Paper – 1)

In the first hour, from 8:00 to 9:00 a.m., the first bus travels 40 km. After 9:00 a.m., the second bus starts and the relative speed between the two buses is 60 − 40 = 20 km/h. To close a gap of 40 km at a relative speed of 20 km/h, the second bus needs 40 ÷ 20 = 2 hours. Adding 2 hours to 9:00 a.m. gives 11:00 a.m. as the overtaking time.

Option A:
Option A, 10:00 a.m., would correspond to only one hour of catch-up time, which would close a distance of 20 km at a relative speed of 20 km/h, leaving 20 km still between the buses.

Option B:
Option B, 10:30 a.m., gives 1.5 hours of catch-up and would close 30 km of the gap, not the full 40 km, so the faster bus would still be behind.

Option C:
Option C, 11:00 a.m., correctly accounts for the full 2 hours needed at a relative speed of 20 km/h to cover the initial 40 km head start, exactly matching the required condition for overtaking.

Option D:
Option D, 11:30 a.m., overshoots the required catch-up time; by then, the second bus would have been ahead of the first bus for half an hour already.