UPSC Exam > UPSC Questions > The sum of the digits of a two-digit number ...
Start Learning for Free
The sum of the digits of a two-digit number is 11. If 45 is added to the number, then the digits are reversed. Find the number.
- a)65
- b)56
- c)38
- d)74
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The sum of the digits of a two-digit number is 11. If 45 is added to ...
The given problem can be solved by using algebraic equations. Let's break down the problem into smaller steps:
The sum of the digits of a two-digit number is 11. Let's assume the two-digit number as '10x + y', where x represents the tens digit and y represents the units digit. So we have the equation:
x + y = 11
If 45 is added to the number, the digits are reversed. This means that the new number would be '10y + x'. So we have the equation:
(10x + y) + 45 = 10y + x
Let's simplify the equation by combining like terms:
10x + y + 45 = 10y + x
Simplifying further:
9x - 9y = 45
Dividing both sides of the equation by 9:
x - y = 5
We now have a system of equations:
x + y = 11
x - y = 5
Adding the two equations together, we get:
2x = 16
Dividing both sides by 2, we find that x = 8.
Substituting the value of x in the first equation, we can find y:
8 + y = 11
Simplifying further, we find that y = 3.
Now that we have the values of x and y, we can determine the two-digit number:
10x + y = 10(8) + 3 = 80 + 3 = 83
Therefore, the number is 83.
Conclusion:
The two-digit number in this problem is 83. Therefore, the correct answer is option C) 38.
Step 1: Understanding the first statement
The sum of the digits of a two-digit number is 11. Let's assume the two-digit number as '10x + y', where x represents the tens digit and y represents the units digit. So we have the equation:
x + y = 11
Step 2: Understanding the second statement
If 45 is added to the number, the digits are reversed. This means that the new number would be '10y + x'. So we have the equation:
(10x + y) + 45 = 10y + x
Step 3: Simplifying the equation
Let's simplify the equation by combining like terms:
10x + y + 45 = 10y + x
Simplifying further:
9x - 9y = 45
Dividing both sides of the equation by 9:
x - y = 5
Step 4: Solving the equations
We now have a system of equations:
x + y = 11
x - y = 5
Adding the two equations together, we get:
2x = 16
Dividing both sides by 2, we find that x = 8.
Substituting the value of x in the first equation, we can find y:
8 + y = 11
Simplifying further, we find that y = 3.
Step 5: Finding the number
Now that we have the values of x and y, we can determine the two-digit number:
10x + y = 10(8) + 3 = 80 + 3 = 83
Therefore, the number is 83.
Conclusion:
The two-digit number in this problem is 83. Therefore, the correct answer is option C) 38.
Free Test
FREE
| Start Free Test |
Community Answer
The sum of the digits of a two-digit number is 11. If 45 is added to ...
Given
x + y = 11………(i)
10x + y + 45 = 10y + x ……….. (ii)
From equation (i) and (ii), we get
X = 3 and y =8
So, the number is 38.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
The sum of the digits of a two-digit number is 11. If 45 is added to the number, then the digits are reversed. Find the number.a) 65b) 56c) 38d) 74Correct answer is option 'C'. Can you explain this answer?
Question Description
The sum of the digits of a two-digit number is 11. If 45 is added to the number, then the digits are reversed. Find the number.a) 65b) 56c) 38d) 74Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sum of the digits of a two-digit number is 11. If 45 is added to the number, then the digits are reversed. Find the number.a) 65b) 56c) 38d) 74Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the digits of a two-digit number is 11. If 45 is added to the number, then the digits are reversed. Find the number.a) 65b) 56c) 38d) 74Correct answer is option 'C'. Can you explain this answer?.
The sum of the digits of a two-digit number is 11. If 45 is added to the number, then the digits are reversed. Find the number.a) 65b) 56c) 38d) 74Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sum of the digits of a two-digit number is 11. If 45 is added to the number, then the digits are reversed. Find the number.a) 65b) 56c) 38d) 74Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the digits of a two-digit number is 11. If 45 is added to the number, then the digits are reversed. Find the number.a) 65b) 56c) 38d) 74Correct answer is option 'C'. Can you explain this answer?.
Solutions for The sum of the digits of a two-digit number is 11. If 45 is added to the number, then the digits are reversed. Find the number.a) 65b) 56c) 38d) 74Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of The sum of the digits of a two-digit number is 11. If 45 is added to the number, then the digits are reversed. Find the number.a) 65b) 56c) 38d) 74Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The sum of the digits of a two-digit number is 11. If 45 is added to the number, then the digits are reversed. Find the number.a) 65b) 56c) 38d) 74Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The sum of the digits of a two-digit number is 11. If 45 is added to the number, then the digits are reversed. Find the number.a) 65b) 56c) 38d) 74Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The sum of the digits of a two-digit number is 11. If 45 is added to the number, then the digits are reversed. Find the number.a) 65b) 56c) 38d) 74Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The sum of the digits of a two-digit number is 11. If 45 is added to the number, then the digits are reversed. Find the number.a) 65b) 56c) 38d) 74Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup