Question
The digits of a two-digit number ‘N’ are reversed to
form a new number ‘M’. If M < N and N – M = 45, then which of the following maybe ‘N’?Solution
ATQ; Let the original number = N = ‘10a + b’ So, the new number = M = ‘10b + a’ ATQ; N = M + 45 So, 10a + b = 10b – a + 45 Or, 9a – 9b = 45 Or, a – b = 5 So, possible pairs of ‘a’ and ‘b’ = (9, 4), (8, 3), (7, 2), (6, 1) So, possible values of ‘N’ = 94, 83, 72, 61 Alternate Solution From option ‘a’: N = 49 So, M = 94 Since, M > N {not possible} N = 61 So, M = 16 Also, N – M = 61 – 16 = 45
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