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    Question

    A two-digit number is such that the sum of its digits is

    10. If 36 is added to the number, the digits interchange their places. Find the number.
    A 28 Correct Answer Incorrect Answer
    B 37 Correct Answer Incorrect Answer
    C 46 Correct Answer Incorrect Answer
    D 55 Correct Answer Incorrect Answer

    Solution

    Let the number be 10x + y, where x and y are its digits. From the problem, x + y = 10 and 10x + y + 36 = 10y + x. Simplifying the second equation: 9x - 9y = -36 → x - y = -4. Solving x + y = 10 and x - y = -4, we get x = 3 and y = 7. The number is 10x + y = 37. Correct Option: b

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