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    Question

    In a school with 400 students, the average of the age of

    the boys is 16 years and that of the girls is 12 years. If the average age of the school is 14 years 9 months. Then the number of girls in the school is.
    A 275 Correct Answer Incorrect Answer
    B 175 Correct Answer Incorrect Answer
    C 137 Correct Answer Incorrect Answer
    D 125 Correct Answer Incorrect Answer

    Solution

    Let the average age of Boys be ‘x’ According to question, x × 16 + (400 - x) × 12 = 400 × 14(3/4) 16x + 4800 - 12x = 400 × 59/4 4x + 4800 = 5900 4x = 1100 x = 275 Number of girls = 400 - 275 = 125 Alternate Method: By Alligation, Boys                       Girls 16                            12              59/4 59/4 - 12          :      16 - (59/4) 11/4                 :           5/4 11                    :           5 So Number of girls = 5/(5+11) of 400 = 5/16 of 400 = 125  

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