Railways Mathematics Ratio Proportion and Partnership Sample Paper Ratio, Proportion & Partnership Sample Test Paper-6

  • question_answer The third proportional between \[({{a}^{2}}-{{b}^{2}})\] and \[({{a}^{2}}+{{b}^{2}})\] is

    A)  \[\frac{a+b}{a-b}\]      

    B)  \[\frac{a-b}{a+b}\]

    C)  \[\frac{{{(a-b)}^{2}}}{a+b}\] 

    D)  \[\frac{{{(a+b)}^{3}}}{a-b}\]

    Correct Answer: D

    Solution :

    [d] Let x be the required third proportional \[\therefore \] \[\frac{{{a}^{2}}-{{b}^{2}}}{{{(a+b)}^{2}}}=\frac{{{(a+b)}^{2}}}{x}\] \[\Rightarrow \] \[x=\frac{{{(a+b)}^{4}}}{{{a}^{2}}-{{b}^{2}}}=\frac{{{(a+b)}^{3}}(a+b)}{(a+b)(a-b)}=\frac{{{(a+b)}^{3}}}{(a-b)}\]

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