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    Question

    A two-digit number decreases by 54 when its digits are

    reversed. If the sum of its digits is 10, what is the original number?
    A 17 Correct Answer Incorrect Answer
    B 71 Correct Answer Incorrect Answer
    C 82 Correct Answer Incorrect Answer
    D 28 Correct Answer Incorrect Answer

    Solution

    For the original number, let the unit digit and ten’s digit be β€˜y’ and β€˜x’, respectively.

    So, the original number = (10x + y)

    Now, if the digits are reversed, the new number = (10y + x).

    ATQ, (10x + y) – (10y + x) = 54

    Or, 9x – 9y = 54

    So, x – y = 6……….(i)

    And, given that, x + y = 10………(ii)

    By adding equation (i) and equation (ii), we get,

    2x = 16

    So, β€˜x’ = 8

    And, β€˜y’ = 2

    So, the original number = 10x + y = 10 Γ— 8 + 2 = 80 + 2 = 82

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