Question
The digits of a two-digit number βNβ are reversed to
form a new number βMβ. If M < N and N β M = 27, then which of the following maybe βNβ?Solution
ATQ; Let the original number = N = β10a + bβ So, the new number = M = β10b + aβ ATQ; N = M + 27 So, 10a + b = 10b β a + 27 Or, 9a β 9b = 27 Or, a β b = 3 So, possible pairs of βaβ and βbβ = (9, 6), (8, 5), (7, 4), (6, 3), (5, 2), (4, 1) So, possible values of βNβ = 96, 85, 74, 63, 52, 41 Alternate Solution From option βaβ: N = 69 So, M = 96 Since, M > N {not possible} N = 41 So, M = 14 Also, N β M = 41 β 14 = 27
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