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      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.
      A 47 Correct Answer Incorrect Answer
      B 77 Correct Answer Incorrect Answer
      C 63 Correct Answer Incorrect Answer
      D 55 Correct Answer Incorrect Answer

      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 βˆ’ 27 = 10a + b. Or, 9b βˆ’ 9a = 27. Or, b βˆ’ a = 3 ---------- (II). On adding equation I and II, We get, a + b + b βˆ’ 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 Γ— 6 + 3 = 63.

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