In a B-school there are three levels of faculty positions i.e Professor, Associate Professor and Assistant Professor. It is found that the sum of the ages of all faculty present is 2160, their average age is 36; the average age of the Professor and Associate Professor is 39; Of the Associate Professor and Assistant professor is 360/11 ; Of the Professor and Assistant Professor is 110/3. Had each Professor been 1 year older, each Associate Professor 6 year older and each Assistant professor 7 year older, then their average age would increase by 5 year. What will be the number of faculty at each level and their average ages ?
Answer: A Let the number of professor, associate and assistant professor be a,b and c respectively. Let their average ages = p,q and r respectively. So, ap+bq+cr = 2160.............(i) a+b+c = 2160/36 = 60............(ii) (ap+bq)/(a+b) = 39...............(iii) (bq+cr)/(b+c) = 360/11 ...........(iv) (ap+cr)/(a+c) = 110/3.............(v) a(p+1) + b(q+6) + c(r+7) = 2460...........(vi) On solving the equations we get, a= 16, b = 24, c = 20, p=45, q = 35, r =30.