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The sum of the digits in a three digit number is 12.If the digits are reversed the numbers is increased by 495 but reversing only of the ten's and unit digits increases the number by 36.The number is?
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The sum of the digits in a three digit number is 12.If the digits are ...
Understanding the Problem
We have a three-digit number represented as ABC, where A, B, and C are its digits. The following conditions are given:
- The sum of the digits is 12: A + B + C = 12.
- Reversing all digits (CBA) increases the number by 495: CBA - ABC = 495.
- Reversing only the tens and units digits (ACB) increases the number by 36: ACB - ABC = 36.
Setting Up the Equations
1. Digit Representation:
- The original number: 100A + 10B + C.
- The reversed number: 100C + 10B + A.
- The partially reversed number: 100A + 10C + B.
2. Equations from Conditions:
- From condition 1: A + B + C = 12.
- From condition 2: (100C + 10B + A) - (100A + 10B + C) = 495
Simplifies to: 99C - 99A = 495, or C - A = 5.
- From condition 3: (100A + 10C + B) - (100A + 10B + C) = 36
Simplifies to: 9C - 9B = 36, or C - B = 4.
Solving the Equations
From C - A = 5 and C - B = 4, we can express A and B in terms of C:
- A = C - 5
- B = C - 4
Substituting into the sum of digits equation:
(C - 5) + (C - 4) + C = 12
This simplifies to:
3C - 9 = 12
=> 3C = 21
=> C = 7.
Now substituting C back:
- A = 7 - 5 = 2
- B = 7 - 4 = 3.
Conclusion
The digits are A = 2, B = 3, C = 7, thus the three-digit number is 237.
We have a three-digit number represented as ABC, where A, B, and C are its digits. The following conditions are given:
- The sum of the digits is 12: A + B + C = 12.
- Reversing all digits (CBA) increases the number by 495: CBA - ABC = 495.
- Reversing only the tens and units digits (ACB) increases the number by 36: ACB - ABC = 36.
Setting Up the Equations
1. Digit Representation:
- The original number: 100A + 10B + C.
- The reversed number: 100C + 10B + A.
- The partially reversed number: 100A + 10C + B.
2. Equations from Conditions:
- From condition 1: A + B + C = 12.
- From condition 2: (100C + 10B + A) - (100A + 10B + C) = 495
Simplifies to: 99C - 99A = 495, or C - A = 5.
- From condition 3: (100A + 10C + B) - (100A + 10B + C) = 36
Simplifies to: 9C - 9B = 36, or C - B = 4.
Solving the Equations
From C - A = 5 and C - B = 4, we can express A and B in terms of C:
- A = C - 5
- B = C - 4
Substituting into the sum of digits equation:
(C - 5) + (C - 4) + C = 12
This simplifies to:
3C - 9 = 12
=> 3C = 21
=> C = 7.
Now substituting C back:
- A = 7 - 5 = 2
- B = 7 - 4 = 3.
Conclusion
The digits are A = 2, B = 3, C = 7, thus the three-digit number is 237.
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The sum of the digits in a three digit number is 12.If the digits are reversed the numbers is increased by 495 but reversing only of the ten's and unit digits increases the number by 36.The number is?
Question Description
The sum of the digits in a three digit number is 12.If the digits are reversed the numbers is increased by 495 but reversing only of the ten's and unit digits increases the number by 36.The number is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The sum of the digits in a three digit number is 12.If the digits are reversed the numbers is increased by 495 but reversing only of the ten's and unit digits increases the number by 36.The number is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the digits in a three digit number is 12.If the digits are reversed the numbers is increased by 495 but reversing only of the ten's and unit digits increases the number by 36.The number is?.
The sum of the digits in a three digit number is 12.If the digits are reversed the numbers is increased by 495 but reversing only of the ten's and unit digits increases the number by 36.The number is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The sum of the digits in a three digit number is 12.If the digits are reversed the numbers is increased by 495 but reversing only of the ten's and unit digits increases the number by 36.The number is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the digits in a three digit number is 12.If the digits are reversed the numbers is increased by 495 but reversing only of the ten's and unit digits increases the number by 36.The number is?.
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