Relax, chances of such questions is quite rare in IIMA PGPX interview. This is more geared towards consulting cases in placement.
Though this one is tough and WILL be unsettling whereever you get it

So I would simply approach it as:
Just off the hand assumptions
Those who play football: professional clubs/country×players/club + recreational ones
Total countries: 200???
players/club: 30?
now all countries are not equally passionate about football. So number of clubs/country, high football penetration= 100 clubs/country, mid 50/country, low is 10/ctry?? Just assumptions here
Also I'd assume countries are 200 and 10% are high football penetration, 30% are mid, 60% are low so it comes to
= (20x100+60x50+120x10 )X 30
=(2000+3000+1200) x 30
= 186000 ppl play football
Okay, so next is important to see the 1PM IST thing. At this hour US is sleeping, and maybe Europe is waking up. So the number of active players at this moment is going to be SE Asia and ME only largely. So take US out. and use low% of EU which is anyway high penetration. So the effective number would be lower. Say by 70-80% lower?? So maybe only 30-40K players active.
=30000 players at 1pm IST are active
1 ball per 4 players?? very rough including all sorts, hobbyist and prof player.
so balls in action = 7500 ??
Assume a ball is 10% time in air = 750 balls in air at 1pm IST
Best,
Abhijeet Singh
LinkedIn:
https://www.linkedin.com/in/abhijeetdelhi/Founder, MBASurf.com
+91-9999 898 737 (WA only)