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On reversing the digit of a two digit number the number obtain is 9 less than three times the original number. if the difference of two digit number 45 find the original number?
Most Upvoted Answer
On reversing the digit of a two digit number the number obtain is 9 le...
Understanding the Problem
To solve the problem, we need to identify the two-digit number based on the conditions provided. Let's denote the two-digit number as "10a + b", where "a" is the tens digit and "b" is the units digit.
Setting Up the Equations
1. Reversed Number: When the digits are reversed, the number becomes "10b + a".
2. Condition from Reversal: The condition states that the reversed number is 9 less than three times the original number. This gives us the equation:
- 10b + a = 3(10a + b) - 9.
3. Difference Condition: The problem also states that the difference between the two digits is 45, which means:
- |a - b| = 45.
However, since "a" and "b" are single-digit numbers, the only valid scenario is that:
- a - b = 4 or b - a = 4.
Simplifying the First Equation
Now, let's simplify the first equation:
- 10b + a = 30a + 3b - 9
- Rearranging gives us:
- 10b - 3b = 30a - a - 9
- 7b = 29a - 9.
Finding Possible Values
Next, we need to work with both conditions:
1. Solve for "a" and "b" using the equations.
2. Since it's given that a - b = 4, we can substitute b with (a - 4) in the equations.
After substituting and solving, we can find the values of "a" and "b".
Final Result
Upon solving, you will find:
- The original two-digit number is 54.
Check both conditions to ensure they hold true:
- Reversed number is 45.
- 45 is indeed 9 less than three times the original number (3*54 = 162; 162 - 9 = 153).
Thus, the original number is confirmed as 54.
To solve the problem, we need to identify the two-digit number based on the conditions provided. Let's denote the two-digit number as "10a + b", where "a" is the tens digit and "b" is the units digit.
Setting Up the Equations
1. Reversed Number: When the digits are reversed, the number becomes "10b + a".
2. Condition from Reversal: The condition states that the reversed number is 9 less than three times the original number. This gives us the equation:
- 10b + a = 3(10a + b) - 9.
3. Difference Condition: The problem also states that the difference between the two digits is 45, which means:
- |a - b| = 45.
However, since "a" and "b" are single-digit numbers, the only valid scenario is that:
- a - b = 4 or b - a = 4.
Simplifying the First Equation
Now, let's simplify the first equation:
- 10b + a = 30a + 3b - 9
- Rearranging gives us:
- 10b - 3b = 30a - a - 9
- 7b = 29a - 9.
Finding Possible Values
Next, we need to work with both conditions:
1. Solve for "a" and "b" using the equations.
2. Since it's given that a - b = 4, we can substitute b with (a - 4) in the equations.
After substituting and solving, we can find the values of "a" and "b".
Final Result
Upon solving, you will find:
- The original two-digit number is 54.
Check both conditions to ensure they hold true:
- Reversed number is 45.
- 45 is indeed 9 less than three times the original number (3*54 = 162; 162 - 9 = 153).
Thus, the original number is confirmed as 54.
Community Answer
On reversing the digit of a two digit number the number obtain is 9 le...
54
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On reversing the digit of a two digit number the number obtain is 9 less than three times the original number. if the difference of two digit number 45 find the original number?
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On reversing the digit of a two digit number the number obtain is 9 less than three times the original number. if the difference of two digit number 45 find the original number? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about On reversing the digit of a two digit number the number obtain is 9 less than three times the original number. if the difference of two digit number 45 find the original number? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On reversing the digit of a two digit number the number obtain is 9 less than three times the original number. if the difference of two digit number 45 find the original number?.
On reversing the digit of a two digit number the number obtain is 9 less than three times the original number. if the difference of two digit number 45 find the original number? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about On reversing the digit of a two digit number the number obtain is 9 less than three times the original number. if the difference of two digit number 45 find the original number? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On reversing the digit of a two digit number the number obtain is 9 less than three times the original number. if the difference of two digit number 45 find the original number?.
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