IMO D.

average speed s = total distance travelled d / total time taken t

1) s+5=120/(t-0.5)

2) .2s=120/.85t

Since we also know that s=120/t

we can figure out what s is even with one of the conditions.

IMO A..what is OA?

OA is A but i would ask for a lil more explanation.

A) Incase of A we get a quadratic equation(check attached pic)

B) My understanding for eliminating B :

120=1.2s*0.75*t
Now, we know s*t=120
120=1.2s*0.75*120/s
which results in cancellation of average speed s throughout so we cannot answer. Is it why we are eliminating this?

I don't think that the equation would be a Quadratic one.
The distance traveled in both the case will be 120 k.m
For x=avg speed and t- time

120 =x.h
from A
we get,
120=(x+5)(1/2)h
so equating both we get value of x.
so A doesn't leads to a ny Quadratic equation.

Correct me if i am wrong