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      Question

      The digits of a two-digit number ‘N’ are

      reversed to form a new number ‘M’. If M < N and N – M = 54, then which of the following maybe ‘N’?
      A 51 Correct Answer Incorrect Answer
      B 79 Correct Answer Incorrect Answer
      C 61 Correct Answer Incorrect Answer
      D 71 Correct Answer Incorrect Answer

      Solution

      ATQ; Let the original number = N = ‘10a + b’ So, the new number = M = ‘10b + a’ ATQ; N = M + 54 So, 10a + b = 10b – a + 54 Or, 9a – 9b = 54 Or, a – b = 6 So, possible pairs of ‘a’ and ‘b’ = (9, 3), (8, 2), (7, 1) So, possible values of ‘N’ = 93, 82, 71 Alternate Solution From option ‘a’: N = 39 So, M = 93 Since, M > N {not possible} N = 71 So, M = 17 Also, N – M = 71 – 17 = 54

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