11th Class Mathematics Other Series Question Bank Critical Thinking

  • question_answer If the A.M. of two numbers is greater than G.M. of the numbers by 2 and the ratio of the numbers is \[4:1\], then the numbers are [RPET 1988]

    A) 4, 1

    B) 12, 3

    C) 16, 4

    D) None of these

    Correct Answer: C

    Solution :

      Suppose that required numbers are \[a\] and \[b\]. Now  A.M.\[=\frac{a+b}{2}\] and G.M.\[=\sqrt{ab}\] Under conditions, A.M.=G.M.+ 2 \[\Rightarrow \]\[\frac{a+b}{2}=\sqrt{ab}+2\]      ......(i) and \[\frac{a}{b}=\frac{4}{1}\]\[\Rightarrow \]\[a=4b\]                .....(ii) From (ii) and (i), we get  \[a=16\] and \[b=4\].

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