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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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