Xavier Aptitude Test 2011 Paper

(d) No. of teams in the bottom group = 10
No. of matches played among the bottom group teams = ‌10C2= 45
∴ No. of points that bottom group gets
playing amongst themselves = 45 (1 pt per match).
It is given in the question that the bottom teams get 45 points from their matches against the top group , i.e.45 out 10 n points where n is the no. of teams in the top group.
No. of points that the top group gets from the matches played among themselves = nC2
No. of points that the top group gets against the bottom group = 10 n – 45
nC2=10n−45
n(n+1)=20n−90
n2−21n+90=0
(n−6)(n−15)=0
If n=6, the top group would get nC2+10n−45
If n=6, the top group would get nC2+10n−45
=nC2+10(6)−45=30 points or an average of 5 points per team the bottom group would get

(45+45)

10

or an avg of 9. This is not possible as points of the top group should be higher than that of the bottom group.
∴ n=15.
∴ Total no. of teams =25