Let A be Aakash's speed and S be Sagear's speed in kph. They each run 2km so, in the first run, Aakash takes 2/A hours=120/A minutes and Sagear takes 2/S hours=120/S minutes.
120/S-120/A=2 because Sagear takes 2 minutes more than Aakash.
120(1/S-1/A)=2, 60(A-S)/AS=1, 60A-60S=AS, 60A-AS=60S,
A(60-S)=60S, A=60S/(60-S).
In the second run Sagear's speed is S+2 and Aakash's speed is A-2.
120/(A-2)-120/(S+2)=2, 120(1/(A-2)-1/(S+2))=2, 60(1/(A-2)-1/(S+2))=1,
60(S+2-(A-2))/[(A-2)(S+2)]=1,
60(S+2-A+2)=(A-2)(S+2)=AS+2A-2S-4,
60S-60A+240=AS+2A-2S-4,
62S-62A=AS-244.
Substitute for A:
62S-3720S/(60-S)=60S2/(60-S)-244,
3720S-62S2-3720S=60S2-14640+244S,
122S2+244S-14640=0, S2+2S-120=0=(S+12)(S-10), therefore S=10kph and A=60S/(60-S)=600/50=12kph.
Therefore Aakash's speed was 12kph and Sagear's speed was 10kph in the first run.
CHECK
1st run: tA=2/12=⅙hr=10min; tS=2/10=⅕hr=12min.
2nd run: tA=2/10hr=12min; tS=2/12hr=10min.
Difference in times is 2min for each run. Solution confirmed.