SSC CGL Tier II 25 Oct 2015 Paper 1

Question : 22 of 100

Marks: +1, -0

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

81.5
81
80.5
80

Validate

Solution:

(1) Students in class A ⇒ x
Students in class B ⇒ y
Students in class C ⇒ z
For classes A and B,

{83 x+76 y}/{x+y}=79

⇒ 83 x+76 y=79 x+79 y

⇒ 83 x-79 x=79 y-76 y

⇒ 4 x=3 y

For classes B and C

{76 y+85 z}/{y+z}=81

⇒ 76 y+85 z=81 y+81 z

⇒5 y=4 z

∴ 20 x=15 y=12 z

⇒{20 x}/{60}= {15 y}/{60}= {12 z}/{60}

⇒{x}/{3}= {y}/{4}= {z}/{5}

∴ Required average

= {83× 3+76× 4+85 × 5}/{3+4+5}

= {249+304+425}/{12}

= {978}/{12} =81.5

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