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    Question

    The average age of a group of 70 students is

    14 years. If three students whose ages are 22 years, 20years, ________ years are replaced with three new students whose ages are 19 years, ______ years, and 32 years, then the new average age is increased by 0.4 years. The value given in the option, which of the following will correctly fill the banks.  I. 17, 36  II. 22, 41  III. 15, 34 
    A Only I Correct Answer Incorrect Answer
    B Only II, III Correct Answer Incorrect Answer
    C Only I, III Correct Answer Incorrect Answer
    D Only I, II Correct Answer Incorrect Answer
    E All I, II, III Correct Answer Incorrect Answer

    Solution

    The average age increased by 0.4 years .   So, the difference of sum of ages of new student to the age of old student = 70*0.4 = 28 years   (19+32+__x___) - (20+22+__y_ _) = 28   (x-y) + (51 -4 2 ) = 28    x-y = 19    So, option I, II, and III all satisfy the above relation    Hence, all three will be the answer

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