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JCECE Engineering JCECE Engineering Solved Paper-2014

  • question_answer
    If the \[AM\] of two numbers is greater than \[GM\] of the numbers by \[2\] and the ratio of the numbers is\[4:1\], then the numbers are

    A) \[4,\,\,1\]                                           

    B) \[12,\,\,3\]

    C) \[16,\,\,4\]                         

    D)  None of these

    Correct Answer: C

    Solution :

    Let required numbers are \[a\] and\[b\]. Now,\[AM=\frac{a+b}{2}\]and\[GM=\sqrt{ab}\] According to the question,                 \[AM=GM+2\] \[\Rightarrow \]               \[\frac{a+b}{2}=\sqrt{ab}+2\]                    ... (i) and        \[\frac{a}{b}=\frac{4}{1}\] \[\Rightarrow \]               \[a=4b\]                                                               ... (ii) On solving Eqs. (i) and (ii), we get                 \[a=16,\,\,b=4\]


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