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Question

 Three Science classes: A, B, and C, take a test

1. The average score in class A is 83

2. The average score in class B is 76

3. The average score in class C is 85

4. The average score of all students in classes A and B together is 79

5. The average score of all students in classes B and C together is 81

What is the average for all three classes?


  1. 81  

  2. 82

  3. 84.5

  4. 81.5


Solution

The correct option is D

81.5


(b) Let the no. of students in the classes are a, b, c respectively then 83x + 76y

= 79 (x + y) ⇒ 4x – 3y = 0 ⇒ x : y = 3 : 4

and 76y + 85z = 81 (y + z) ⇒ 5y – 4z = 0 ⇒ y : z = 4 : 5.

Hence x : y : z = 3 : 4 : 5 ⇒ x = 3k, y = 4k and z = 5k.

Now average for all the three classes is

(83 × 3k + 76 × 4k + 85 × 5k)/(3k + 4k + 5k) = 81.5.

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