Arun and Bhaskar run a race of 3 km. First, Arun gives Bhaskar a head start of 400 m and beats him by 30 seconds. While coming back, Arun gives Bhaskar a lead of 2.5 minutes and gets beaten by 500 m. What is the difference between the times in minutes in which Arun and Bhaskar can run the race for one side separately?

Correct option is B

Given: 

Arun and Bhaskar run a race of 3 km.

Formula used:

Distance = Speed × Time
Solution:
Case I:
Arun : Bhaskar
Distance → 3000 : 2600
Time → t : t +0.5
Case II:
Arun : Bhaskar
Distance → 3000 : 2500
Time → $$\frac{5}{6} t : \frac{5}{6} t +2.5$$​​
Now, according to question
​$$\frac{2600}{(t+o.5)}= \frac{3000}{(\frac{5}{6} t +2.5)} \\\ \\=> 15t + 7.5 = \frac{65t}{6}+32.5 \\\ \\=> 25 = 15t - \frac{65t}{6} \\\ \\=> 25 = \frac{25t}{6} \\\ \\=>t=6$$​​
∴ required difference = $$\frac{5}{6} t +2.5- t = 2.5 - \frac{t}{6} = 1.5$$​ minutes