Three Science classes A, B and C take a Life Science test.

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Three Science classes A, B and C take a Life Science 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. Then the average score of classes A, B and C is

Let Students in class A ⇒ p
Students in class B ⇒ q
Students in class C ⇒ r
For classes A and B,

83p + 76q	= 79
p + q

⇒ 83p + 76q = 79p + 79q
⇒ 83p – 79p = 79q – 76q
⇒ 4p = 3q
For classes B and C

76q + 85r	= 81
q + r

⇒ 76q + 85r = 81q + 81r
⇒ 5q = 4r
∴ 20p = 15q = 12r

⇒	20p	=	15q	=	12r
	60		60		60

⇒	p	=	q	=	r
	3		4		5

Required average =	83 × 3 + 76 × 4 + 85 × 5
	3 + 4 + 5

Required average =	249 + 304 + 425
	12

Required average =	978
	12

Required average = 81.5