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    Question

    The sum of the LCM and HCF of two numbers is 370 and the

    difference between the LCM and HCF is 354. If one of the numbers is 59, find the other number.
    A 49 Correct Answer Incorrect Answer
    B 24 Correct Answer Incorrect Answer
    C 38 Correct Answer Incorrect Answer
    D 56 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the LCM and the HCF of the two numbers be 'a' and 'b', respectively

    We have, (a + b) = 370 and (a - b) = 354

    So, a + b + (a - b) = 370 + 354

    Or, 2a = 724

    Or, a = 724 ÷ 2 = 362

    So, b = 370 - 362 = 8

    We know that product of the two numbers is equal to the product of their LCM and HCF

    Let the two numbers be 'x' and 'y' where x = 59

    So, 362 × 8 = 59y

    So, y = (362 × 8) ÷ 59 = 49

    So, the other number is 49

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