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    Question

    The LCM of two numbers is 15 times their HCF.

    The sum of HCF and LCM of these numbers is 352. If one of the numbers is 110, find the other number.
    A 64 Correct Answer Incorrect Answer
    B 66 Correct Answer Incorrect Answer
    C 68 Correct Answer Incorrect Answer
    D 70 Correct Answer Incorrect Answer
    E none of these Correct Answer Incorrect Answer

    Solution

    Let HCF be x [if gte msEquation 12]>x [if !msEquation]-->[endif]-->, then LCM = 15x [if gte msEquation 12]>x [if !msEquation]-->[endif]--> It is given LCM + HCF = 352 [if gte msEquation 12]>x [if !msEquation]-->[endif]-->=> x + 15x [if gte msEquation 12]>x [if !msEquation]-->[endif]--> = 352 ⇒ 16x [if gte msEquation 12]>x [if !msEquation]-->[endif]--> = 352 [if gte msEquation 12]>∴ [if !msEquation]-->[endif]--> => x = 22 HCF = 22 and LCM = 15x = 15 × 22 = 330 Product of two numbers = Product of their HCF and LCM ⇒ 110 × other number = 22 × 330 => Other number = (22 × 330)/110 = 66

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