The average score of boys in an examination of a school is 71 and that of girls is 73. The average score of school in that examination is 71.8. The ratio of the number of boys to the number of girls appeared in the examination, is 

The average score of boys in an examination of a school is 71 and that of girls is 73. The average score of school in that examination is 71.8. The ratio of the number of boys to the number of girls appeared in the examination, is 

  1. A

    3:2

  2. B

    3:4

  3. C

    1:2

  4. D

    2:1

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    Solution:

    Let there be n1 boys and n2 girls in the school. 

    Let X1¯ and X2¯ be the average scores of boys and girls  respectively and X be the average of both boys and girls. Then, 

    X1¯=71,X2¯=63,X¯=71.8 X¯=n1X1¯+n2X2¯n1+n2 71.8=n1×71+n2×73n1+n2 71.8n1+n2=71n1+73n2 71.8n1+71.8n2=71n1+73n2 0.8n1=1.2n2 8n1=12n2n1n2=128=32

    Hence, n1:n2=3:2

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