Three maths classes: X, Y, and Z take an algebra test. The average score of class X is 83. The average score of class Y is 76. The average score of class Z is 85. The average score of class X and Y is 79 and the average score of class Y and Z is 81. What is the average score of the combined classes X, Y, and Z?

1. 81
2. 81.5
3. 82
4. 84.5

Answer: 81.5

Explanation: According to question,
(i) (83x + 76y)/( x + y )​=79
⇒ x = 43y​
(ii) (76y + 85z)/(y + z)​ = 81
z = 45y​
Average of all 3 = (83x + 76y + 85z​)/(x + y + z)
​=81.5