Only a single rail track exists between station A and B on a railway line. One hour after the north bound superfast train N leaves station A for station B, a south passenger train S reaches station A from station B. The speed of the superfast train is twice that of a normal express train E, while the speed of a passenger train s is half that of E. On a particular day N leaves station B from station A, $20$ minutes behind the normal schedule. In order to maintain the schedule both N and S increased their speed. If the superfast train doubles its speed, what should be the ration (approximately) of the speed of passenger train to that of the superfast train so that the passenger train S reaches exactly at the scheduled time at the station A on that day.
- $1:3$
- $1:4$
- $1:5$
- $1:6$