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    Question

    If the digits of a two-digit number are reversed, the

    resulting number is 36 less than twice the original number. If the sum of the digits is 9, what is the original number?
    A 25 Correct Answer Incorrect Answer
    B 45 Correct Answer Incorrect Answer
    C 65 Correct Answer Incorrect Answer
    D 75 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the tens digit and unit digit be тАШxтАЩ and тАШyтАЩ respectively. So, the original number = (10x + y) According to the question: 10y + x = 2 ├Ч (10x + y) тАУ 36 Or, 10y + x = 20x + 2y тАУ 36 Or, 19x тАУ 8y = 36 тАж.. (i) Also, x + y = 9 тАж.. (ii) Multiply equation (ii) by 8: 8x + 8y = 72 тАжтАжтАжтАжтАжтАжтАж.(iii) Add equations (i) and (iii): 27x = 108 x = 4 So, y = 9 тАУ 4 = 5 [from equation (ii)] Original number = 10 ├Ч 4 + 5 = 45

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