Question

Three Maths classes; X, Y, and Z take an algebra test.
The average score in class X is 83.
The average score in class Y is 76.
The average score in class Z is 85.
The average score of all students in class X and Y together is 79.
The average score of all students in classes Y and Z together is 81.
What is the average of all the three classes?

• A. 81
• B. 81.5
• C. 82
• D. 84.5

Answer 1

The correct option is B 81.5

Let no. of students in classes X, Y and Z = x, y and z respectively.
$\frac{83x+76y}{x+y}=79$ ...(1)
and $\frac{76y+85z}{y+z}=81$ ...(2)
We have to find $\frac{83x+76y+85z}{x+y+z}$
From (1) $4x=3yory=\frac{4x}{3}$;
From (2) $5y=4zorz=\frac{5}{4}y=\frac{5}{4}\times \frac{4}{3}x=\frac{5}{3}x$
$\therefore$ Required average $=\frac{83x+76\times \frac{4x}{3}+85\times \frac{5}{3}x}{\frac{3x}{3}+\frac{4x}{3}+\frac{5x}{3}}$
$=\frac{83+\frac{729}{3}}{4}=81.5$