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      Question

      The digits of a two-digit number add up to 9. If 27 is

      subtracted from the number, the digits switch places. What is the number?
      A 63 Correct Answer Incorrect Answer
      B 56 Correct Answer Incorrect Answer
      C 73 Correct Answer Incorrect Answer
      D 65 Correct Answer Incorrect Answer

      Solution

      ATQ,
      Let the digits be 'a' (ones) and 'b' (tens).

      Original number = 10b + a

      Reversed = 10a + b
      Given:

      a + b = 9 --------- (I)

      And, 10b + a - 27 = 10a + b

      β‡’ 9b - 9a = 27

      β‡’ b - a = 3 --------- (II)

      Add (I) and (II):

      a + b + b - a = 9 + 3

      β‡’ 2b = 12 β‡’ b = 6

      Then a = 3

      Required number = 10 Γ— 6 + 3 = 63

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