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    Question

    A two-digit number has digits summing up to 10. On

    subtracting 36 from the number, the digits get interchanged. What is the original 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 ones digit = 'a', tens digit = 'b'

    Number = 10b + a, Reversed = 10a + b

    a + b = 10 --------- (I)

    10b + a - 36 = 10a + b

    ⇒ 9b - 9a = 36

    ⇒ b - a = 4 --------- (II)

    Add (I) and (II):

    a + b + b - a = 10 + 4

    ⇒ 2b = 14 ⇒ b = 7

    Then a = 3

    Required number = 10 × 7 + 3 = 73

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