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Q.
Three maths classes: A, B and C take an algebra test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and average score of class B and C is 81. What is the average score of classes A, B, C ?
A.
81
B.
78
C.
80.5
D.
81.5
View Answer
Correct choice: D
Explanation:
Let the number of students in classes A, B and C be P, Q and R respectively. Then, total score of A = 83P, total score of B = 76Q, total score of C = 85R. Also given that, (83P + 76Q) / (P + Q) = 79 =>4P = 3Q. (76Q + 85R)/(Q + R) = 81 =>4R = 5Q, =>Q = 4P/3 and R = 5P/3 Therefore, average score of A, B, C = ( 83P + 76Q + 85R ) / (P + Q + R) = 978/12 = 81.5
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