D
Geetha starts with 12 kmph.
Distance covered in first 1 hour = 12 km
she increases her speed in every hour by 1 km.
Speed in 2nd hour = 13 km/hr
Distance covered in 2nd hour = 13 km
Remaining distance = 27.8 - (12+13) = 2.8 km
Speed in the third hour = 14 km/hr
Time taken to cover 2.8 km at 14 km/hr = 2.8/14 = 1/5 hour.
Therefore, total time = 1 + 1 + 1/5 hours = 2 1/5 hours.
Hence the answer is 2 1/5 hours.