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A two-digit number when divided by the sum of its digits gives a quotient of 7 and a remainder of 3. When the number is reversed and then divided by the sum of its digits it gives a quotient of 3 and a remainder of 7. What is the sum of the digits of the number?
    Correct answer is '10'. Can you explain this answer?
    Verified Answer
    A two-digit number when divided by the sum of its digits gives a quoti...
    Let the tens digit of the number be x and the units digit be y.
    The number is (10x + y)
    When the number is divided by the sum of its digits it gives a quotient of 7 and a remainder of 3.
    10x + y = 7(x + y) + 3 ...(i)
    When the number is reversed and then divided by the sum of its digits it gives a quotient of 3 and a remainder of 7.
    10y + x = 3(x + y) + 7 ...(ii)
    Solving (i) and (ii), we get, x = 7 and y = 3
    The required number is 73 and the sum of its digits is 10.
    Answer: 10
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    Most Upvoted Answer
    A two-digit number when divided by the sum of its digits gives a quoti...
    Introduction:
    In this problem, we are given a two-digit number and we have to find the sum of its digits. We are also given that when the number is divided by the sum of its digits, it gives a quotient of 7 and a remainder of 3. When the number is reversed and then divided by the sum of its digits, it gives a quotient of 3 and a remainder of 7.

    Solution:
    Let the two-digit number be xy. Then, its value is given by 10x + y.

    When this number is divided by the sum of its digits (x+y), we get a quotient of 7 and a remainder of 3. This can be represented by the following equation:

    10x + y = 7(x+y) + 3
    10x + y = 7x + 7y + 3
    3x = 6y + 3
    x = 2y + 1

    Now, when the number is reversed, it becomes yx. Its value is given by 10y + x.

    When this number is divided by the sum of its digits (x+y), we get a quotient of 3 and a remainder of 7. This can be represented by the following equation:

    10y + x = 3(x+y) + 7
    10y + x = 3x + 3y + 7
    7y = 2x + 7
    y = (2/7)x + 1

    From equations (1) and (2), we can see that x and y are both integers. Therefore, we can substitute y = (2/7)x + 1 in equation (1) to get:

    x = 5

    Therefore, the two-digit number is 51 and the sum of its digits is 5+1 = 6.

    Conclusion:
    The sum of the digits of the given number is 6.
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    A two-digit number when divided by the sum of its digits gives a quotient of 7 and a remainder of 3. When the number is reversed and then divided by the sum of its digits it gives a quotient of 3 and a remainder of 7. What is the sum of the digits of the number?Correct answer is '10'. Can you explain this answer?
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