Find the ratio of students and then find the average.

Follow the screenshot.

Ans B

I´ve found another way. Maybe more complicated but still another option.

You know that the average of X and Y is 79, so you need to calculate:

(83x+76y)/(x+y)=79
It gives you the x:y ratio: 4:3

On the other hand, you have the average of Y and Z, meaning you calculate the same as previous:
(76y+85z)/(y+z)=81
It gives you the y:z ratio, which is 5:4

Combining both, you will realize that the ratio x:y:z is 12:15:20
In detail: 12= 4*3 (x*y), 15= 3*5 (y1*y2) and, finally, 20= 5*4 (y2*z).

The statement is asking you to find the average of x, y and, z. Now you have everything you need to do it:
(83*12+76*15+85*20)/(12+15+20)
Being x=12, y=15 and z=20, as I said before.

This results in 81,5 approx., which is answer B.