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    Question

    Mohit is a teacher and he teach some students in two

    (Morning & evening) slots. There are 5 boys and тАШxтАЩ girls in morning slot, while there are тАШxтАЩ boys and 8 girls in evening slot. If one student is chosen at random from any slot, then the probability of being girl is 5/9. Which of the following can be the value of тАШxтАЩ?┬а I. 10 II. 4 III. 3 IV. 5 V. 6
    A Only I Correct Answer Incorrect Answer
    B Only V Correct Answer Incorrect Answer
    C Both I and IV Correct Answer Incorrect Answer
    D Both II and III Correct Answer Incorrect Answer
    E Both I and II Correct Answer Incorrect Answer

    Solution

    Probability for being girl from morning slot = (1/2) ├Ч (x/(x+5)) Probability for being girl from evening slot┬а = (1/2) ├Ч (8/(x+8))┬а ATQ тАУ 1/2 [x/(x+5)+(8/(x+8))]=5/9 10/9=(x(x+8)+8(x+5))/(x+8)(x+5)┬а┬а 10/9=(x2+8x+8x+40)/(x2+13x+40)┬а 10x2+130x+400=9x2+144x+360┬а x2тАУ14x+40=0┬а x2тАУ10xтАУ4x+40=0┬а┬а x(x тАУ10)┬а тАУ4(x тАУ10)=0┬а┬а x=10,4┬а┬а So, both I and II follow

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