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    Question

    Mohit is a teacher and he teach some students in two (Morning & evening) slots. There are 5 boys and ‘x’ girls in morning slot, while there are ‘x’ 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 ‘x’? 

    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) × (x/(x+5)) Probability for being girl from evening slot  = (1/2) × (8/(x+8))  ATQ – 1/2 [x/(x+5)+(8/(x+8))]=5/9 10/9=(x(x+8)+8(x+5))/(x+8)(x+5)   10/9=(x2+8x+8x+40)/(x2+13x+40)  10x2+130x+400=9x2+144x+360  x2–14x+40=0  x2–10x–4x+40=0   x(x –10)  –4(x –10)=0   x=10,4   So, both I and II follow

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