Question : Three science classes (A, B, and C) take a life science test. The average score for class A is 83. The average score for B is 76. The average score in class C is 85. The average score of classes A and B is 79 and the average score of classes B and C is 81. Then the average score of classes A, B, and C is:
Option 1: 81.5
Option 2: 81
Option 3: 80.5
Option 4: 80
Correct Answer: 81.5
Solution :
Let the number of students in the classes be a, b, and c respectively.
According to the question: 83a + 76b = 79 (a + b) ⇒ 4a – 3b = 0 ⇒ a : b = $3 : 4$
Also, 76b + 85c = 81 (b + c) ⇒ 5b – 4c = 0 ⇒ b : c = $4 : 5$
Hence, a : b : c = $3 : 4 : 5$ ⇒ a = 3k, b = 4k, and c = 5k.
So, the average for all the three classes = $\frac{(83 × 3k + 76 × 4k + 85 × 5k)}{(3k + 4k + 5k)}$ = 81.5
Hence, the correct answer is 81.5.
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