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Statistics question

2007 · Shift 0 · Q39
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Statistics question

2007 · Shift 0 · Q39

JEE MainMathematicsStatisticsMCQ+4 / −1
The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is
  1. A
    80
  2. B
    60
  3. C
    40
  4. D
    20
View written solutionFree

Correct answer: A

  1. Let the number of boys be bbb and the number of girls be ggg.

  2. Given averages:

    • Average marks of boys =52= 52=52
    • Average marks of girls =42= 42=42
    • Combined average =50= 50=50

  3. Total marks of boys and girls together: 52b+42g52b + 42g52b+42g

  4. Since the combined average is 505050, we have: 52b+42gb+g=50\frac{52b + 42g}{b+g} = 50b+g52b+42g​=50

  5. Solve the equation: 52b+42g=50b+50g52b + 42g = 50b + 50g52b+42g=50b+50g 52b−50b=50g−42g52b - 50b = 50g - 42g52b−50b=50g−42g 2b=8g2b = 8g2b=8g b=4gb = 4gb=4g

  6. So the ratio of boys to girls is: b:g=4:1b:g = 4:1b:g=4:1

  7. Therefore, percentage of boys in the class is: 44+1×100=45×100=80%\frac{4}{4+1} \times 100 = \frac{4}{5} \times 100 = 80\%4+14​×100=54​×100=80%

  8. Hence, the correct option is A.

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