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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 = 27, then which of the following maybe ‘N’?
    A 51 Correct Answer Incorrect Answer
    B 75 Correct Answer Incorrect Answer
    C 61 Correct Answer Incorrect Answer
    D 27 Correct Answer Incorrect Answer

    Solution

    ATQ; Let the original number = N = ‘10a + b’ So, the new number = M = ‘10b + a’ ATQ; N = M + 27 So, 10a + b = 10b – a + 27 Or, 9a – 9b = 27 Or, a – b = 3 So, possible pairs of ‘a’ and ‘b’ = (9, 6), (8, 5), (7, 4), (6, 3), (5, 2), (4, 1) So, possible values of ‘N’ = 96, 85, 74, 63, 52, 41 Alternate Solution From option ‘a’: N = 69 So, M = 96 Since, M > N {not possible} N = 41 So, M = 14 Also, N – M = 41 – 14 = 27

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