Indian Institute of Foreign Trade 2010 Solved Paper

Let the number of professors, associate professors and assistant professors be x, y and z respectively and their average ages be a, b and c respectively.
xa+yb+zc=2160.....(1)
Average age =36
∴x+y+z=60
xa+yb=39(x+y)
11(yb+zc)=360(y+z)
3(xa+zc)=110(x+z)
  [ ∵ Average increases by 5]
Eq 2- Eq 1
We get x+6y+7z=300
Lets solve the options one by one
Option A: x=16,y=24,z=20
16+6×24+7*20=300 which satisfies the equations.
So either A or C can be the answer.
Now check for the values of a, b, c
a=45, b=35, c=30
ax+by+cz=45×16+35×24+30×20
=2160
Hence, option A is the correct answer.