Class 10 Exam > Class 10 Questions > On reversing the digit of a two digit number ...
Start Learning for Free
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
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup