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SSC Sample Paper SSC CGL - Sample Paper-19

  • question_answer
    The LCM of two numbers is 495 and their HCF is 5. If the sum of the numbers is 100, then their difference is

    A) 10                    

    B) 46

    C) 70                    

    D) 90

    Correct Answer: A

    Solution :

    Suppose, 1st number is x, then 2nd number \[=100-x\] \[\therefore \] \[\text{LCM}\times \text{HCT =1st number}\times \text{2nd number}\] \[\Rightarrow \]   \[495\times 5=x(100-x)\] \[\Rightarrow \]   \[495\times 5=100x-{{x}^{2}}\] \[\Rightarrow \]   \[{{x}^{2}}-55x-45x-2475=0\] \[\Rightarrow \]   \[(x-45)(x-55)=0\] \[\Rightarrow \]   \[x=45\] or \[x=55\] Then, difference \[=55-45=10\]   


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