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21 September, 09:13

There are 50 students in an auditorium, of which 2x are boys and y are girls. After (y - 6) boys leave the auditorium and (2x - 5) girls enter the auditorium, the probability of selecting a girl at random becomes 9/13. Find the value of x and of y?

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  1. 21 September, 10:21
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    Total number of students=50

    Number of boys=2x

    Number of girls=y

    total will be:

    2x+y=50

    ⇒y=50-2x

    when (y-6) boys left the auditorium the new number of boys was:

    2x - (y-6)

    =2x-y+6

    but y=50-2x

    thus the new number will be:

    2x - (50-2x) + 6

    =4x-44

    when (2x-5) girls left the auditorium the remaining number will be:

    y - (2x-5)

    =y-2x+5

    but

    y=50-2x

    thus the new number of girls will be:

    50-2x-2x+5

    =55-4x

    new total number of students:

    (55-4x) + (4x-44)

    =11

    probability of selecting a girl at random will be:

    (55-4x) / 11=9/13

    13 (55-4x) = 9*11

    715-52x=99

    616=52x

    x=12

    thus

    y=50-12=38

    thus

    x=12 and y=38
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