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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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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
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
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.
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 quoti...
When a two digit number is divided by the sum of its digit and cotaint is 7 and the remainder is 6 full stops if one of the digit of the number is 3 then what is the difference between of the digit
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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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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? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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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?, a detailed solution for 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? has been provided alongside types of 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? theory, EduRev gives you an
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