Question
Sum of digits of a two-digit number is 9. When 27 is
subtracted from the number, its digits get interchanged. Find the original number.Solution
ATQ, Let ones and tens digit of the number be a and b respectively. So, original number = 10b + a. Reverse number = 10a + b. So, a + b = 9 --------- (I) And, 10b + a − 27 = 10a + b. Or, 9b − 9a = 27. Or, b − a = 3 ---------- (II). On adding equation I and II, We get, a + b + b − a = 9 + 3. Or, 2b = 12. Or, b = 6. On putting value of b in equation I, We get, 6 + a = 9. Or, a = 3. Required number = 10 × 6 + 3 = 63.
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