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    Question

    The LCM of two numbers is 20 times their HCF, and the

    sum of the LCM and the HCF is 504. If the difference of the numbers is 24, then find the sum of the numbers.
    A 210 Correct Answer Incorrect Answer
    B 180 Correct Answer Incorrect Answer
    C 225 Correct Answer Incorrect Answer
    D 216 Correct Answer Incorrect Answer

    Solution

    Let the HCF =x then, LCM=20x ATQ-20x+x =504 21x =504 X =24. LCM=480 HCF=24 Hence, the product of HCF and LCM = 480 × 24 = 11520 Let the numbers be P and Q (P > Q). Hence, PQ = 11520 According to the question, P - Q = 24   (P - Q)2=242   (P - Q) + 4PQ = 24 + 4PQ (Adding 4PQ on both side)   (P - Q) + 4PQ = 24 + 4 × 11520 ( ∵ PQ = 11520) (P + Q)2 = 46656   (P + Q) = 216

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