Let after time 't' man catches the bus.
After time 't' bus has covered the distance = 12(1)t2=t22
Therefore the total distance man has to cover = 48+t22
Therefore, vt=s
⇒10t=48+t22⇒20t=96+t2⇒t2−20t+96=0⇒(t−12)(t−8)=0⇒t=12 or t=8
Therefore, minimum time in which man catches the bus is 8 seconds.