[spoiler]The concept of weighted average comes here and there is a little nuance that has to be observed. For example, it was told in the question that the weighted average of Navy(avg wt 83) and Army(avg wt 76) is 79.

Now let us take the number of persons in the Navy to be N and in the Army to be A

and weighted average is 79 means

(76A+83N)/(A+N)=79 and this means 76A+83N=79A+79N and this means 4N=3A and N:A=3:4 -- 1

This is extremely important for every weighted average problem, the ratio of the number of elements in a particular group is the reverse ratio of the difference in the average weights[/spoiler]

The ratio of the number of Navy to the Number of Army=reverse ratio of the differences with the average weights
means Difference in the weighted average weight and the average weight of Army(79-76):Difference in the weighted average weight and the average weight of Navy(83-79)=3:4

in a similar way, ratio of the number of Army(A) and Airforce(F){A:F}=(85-81)/(81-76)=4:5 -- 2

From the 1 and 2, N:A:F=3:4:5

So total weighted average= (83x3+76x4+85x5)/(3+4+5)=81.5

harsh.champ wrote:Three wings of defence: Navy, Army, and Airforce conduct their weight measurements.
The average weight in Navy is 83 kgs.
The average weight in Army is 76 kgs.
The average weight in Airforce is 85 kgs.
The average weight of all the soldiers in Navy and Army together is 79 kgs.
The average weight of all the soldiers in Army and Airforce together is 81 kgs.

What is the average weight for all the three wings taken together?

A. 81 kgs
B. 81.5 kgs
C. 82 kgs
D. 82.5 kgs
E. 83 kgs
Let x,y,z be the no. of navy , army ,airforce respectively
so total navy = 83x total army = 76y total airforce = 85z
83x + 76y = 79(x+y) --> 4x = 3y--> x= 3/4 y
76y + 85z= 81(y+z) --> 4z = 5y --> z=5/4 y
avg total of three wings = (83x+76y + 85z)/(x+y+z)=(83x3/4 + 76 + 85 x5/4)/(3/4+1+5/4) = (249+304 +425)/12 = 81.5
Ans is B.