The LCM and HCF of two numbers are 45 and 3 respectively

The LCM and HCF of two numbers are 45 and 3 respectively, their sum is 24, what is their difference?
(a) 2
(b) 4
(c) 6
(d) 8

Anurag Mishra Professor Asked on 29th February 2016 in Maths.
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  • 1 Answer(s)
    Best answer

    Answer: (C) 6 

    Solution:-
    Let the two numbers be a & b

    The LCM and HCF of two numbers are 45 and 3, 
    Then, the product of two numbers = 45 x 3 
     ab = 135     …………..(1) 

    The sum of two numbers  (a + b) = 24
    Square on both side, 
    (a + b)^2 = 24^2
    a^2 + b^2 + 2 ab = 576
    a^2 + b^2 = 576 – 2 x 135                  {From equation (1)  ab = 135}
    a^2 + b^2 = 576 – 270
     a^2 + b^2 = 306  ………………. (2) 

    Difference of two both numbers  = a – b
    (a – b)^2  = a^2 + b^2 – 2 ab
    From equation (1) ab = 1  &  equation (2)  a^2 + b^2 = 306, 
    Then,   (a – b)^2  = 306 – 2 x 135
     (a – b)^2 = 306 – 270
     (a – b)^2 = 36
    Square root on both side, 
    a – b = 6 

    Then, the difference between of two numbers is 6. 

    Hence, the correct answer is option (C) 6. 

    Anurag Mishra Professor Answered on 1st March 2016.
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