Question
A two-digit number when divided by the sum of its digits
gives quotient 5 and remainder 2. If the digits differ by 1, find the number.Solution
ATQ, Let the number be 10a + b, sum of digits = a + b Given: 10a + b = 5(a + b) + 2 10a + b = 5a + 5b + 2 5a - 4b = 2 ...(1) Digits differ by 1. Try a = b - 1 (since tens digit likely larger): Put a = b - 1 in (1): 5(b - 1) - 4b = 2 5b - 5 - 4b = 2 b - 5 = 2 b = 7 Then a = 6 Number = 67 Check: Sum digits = 6 + 7 = 13 67 = 5*13 + 2 (correct)
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