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10th Class Mathematics Real Numbers Question Bank Case Based MCQs - Real Number

  • question_answer
     
    Directions: Q. 16 to 20
    A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Madiematics are 60, 84 and 108 respectively.      
    Based am die above information answer the following questions.
    In each room the same number of participants are 10 be sealed and all of them being in the sine subject, hence maximum number participants that can accommodated in each room are

    A) 14

    B) 12

    C) 16

    D) 18

    Correct Answer: B

    Solution :

    Given, number of students in each subject are
    Hindi = 60, English = 84,
    Mathematics = 108.
    The prime factors of each subject students are
    \[60=2\times 2\times 3\times 5={{2}^{2}}\times 3\times 5\]
    \[84=2\times 2\times 3\times 7={{2}^{2}}\times 3\times 7\]\[108=2\times 2\times 3\times 3\times 3={{2}^{2}}\times {{3}^{3}}\]
    The maximum number of participants that can accommodated in each room
    = HCF (60, 84, 108)
    = Product of the smallest power of each common prime factor involved in the numbers
    \[={{2}^{2}}\times 3=12\]


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