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8th Class Mathematics Cubes and Cube Roots Question Bank Cubes and Cube Roots

  • question_answer
    Three numbers are in the ratio 2 : 3 : 5 to one another. The sum of their cubes is 54880. The numbers are____.

    A)  14, 21, 35                  

    B)         12, 15, 17      

    C)         14, 18, 21                  

    D)         21, 28, 32

    Correct Answer: A

    Solution :

    Let the numbers be \[2x,\text{ }3x\] and \[5x\]. So, \[{{(2x)}^{3}}+{{(3x)}^{3}}+{{(5x)}^{3}}=54880\] \[=\text{ }8{{x}^{3}}+\text{ }27{{x}^{3}}+125{{x}^{3}}=54880\] \[\Rightarrow 160{{x}^{3}}=54880\Rightarrow {{x}^{3}}=\frac{54880}{160}=343\] \[\Rightarrow x=\sqrt[3]{343}=7\] So, numbers are 14, 21 and 35


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