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The sum of the digits of a two digit number is 7 the number obtained by interchanging the digits exceeds the original number by 27 find the number?
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The sum of the digits of a two digit number is 7 the number obtained b...
Understanding the Problem
To solve the problem, let's denote the two-digit number as "10a + b," where "a" is the tens digit and "b" is the units digit.
Key Equations Derived from the Problem
- The sum of the digits is given as:
- a + b = 7
- The number obtained by interchanging the digits is:
- 10b + a
- The relationship between the two numbers is:
- (10b + a) - (10a + b) = 27
Forming the Equations
From the second equation, we can simplify:
- 10b + a - 10a - b = 27
- This simplifies to:
- 9b - 9a = 27
- Dividing through by 9 gives:
- b - a = 3
Solving the Equations
Now we have a system of two equations:
1. a + b = 7
2. b - a = 3
We can solve these equations step by step:
- From the second equation, we can express "b" in terms of "a":
- b = a + 3
- Substitute this into the first equation:
- a + (a + 3) = 7
- 2a + 3 = 7
- 2a = 4
- a = 2
- Now substituting "a" back into the equation for "b":
- b = 2 + 3 = 5
Conclusion
The digits of the original number are:
- a = 2
- b = 5
Thus, the two-digit number is:
- 10a + b = 10(2) + 5 = 25
Therefore, the two-digit number you are looking for is: 25.
To solve the problem, let's denote the two-digit number as "10a + b," where "a" is the tens digit and "b" is the units digit.
Key Equations Derived from the Problem
- The sum of the digits is given as:
- a + b = 7
- The number obtained by interchanging the digits is:
- 10b + a
- The relationship between the two numbers is:
- (10b + a) - (10a + b) = 27
Forming the Equations
From the second equation, we can simplify:
- 10b + a - 10a - b = 27
- This simplifies to:
- 9b - 9a = 27
- Dividing through by 9 gives:
- b - a = 3
Solving the Equations
Now we have a system of two equations:
1. a + b = 7
2. b - a = 3
We can solve these equations step by step:
- From the second equation, we can express "b" in terms of "a":
- b = a + 3
- Substitute this into the first equation:
- a + (a + 3) = 7
- 2a + 3 = 7
- 2a = 4
- a = 2
- Now substituting "a" back into the equation for "b":
- b = 2 + 3 = 5
Conclusion
The digits of the original number are:
- a = 2
- b = 5
Thus, the two-digit number is:
- 10a + b = 10(2) + 5 = 25
Therefore, the two-digit number you are looking for is: 25.
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The sum of the digits of a two digit number is 7 the number obtained by interchanging the digits exceeds the original number by 27 find the number?
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The sum of the digits of a two digit number is 7 the number obtained by interchanging the digits exceeds the original number by 27 find the number? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The sum of the digits of a two digit number is 7 the number obtained by interchanging the digits exceeds the original number by 27 find the number? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the digits of a two digit number is 7 the number obtained by interchanging the digits exceeds the original number by 27 find the number?.
The sum of the digits of a two digit number is 7 the number obtained by interchanging the digits exceeds the original number by 27 find the number? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The sum of the digits of a two digit number is 7 the number obtained by interchanging the digits exceeds the original number by 27 find the number? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the digits of a two digit number is 7 the number obtained by interchanging the digits exceeds the original number by 27 find the number?.
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