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The numbers of the digits in a three digit number is 12. If the digits are reversed the number 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 numbers of the digits in a three digit number is 12. If the digits...
Understanding the Problem
To find the three-digit number based on the given conditions, let's denote the number as ABC, where A, B, and C are its digits.
Conditions Given
- The sum of the digits is 12:
A + B + C = 12
- Reversing the entire number increases it by 495:
100C + 10B + A = 100A + 10B + C + 495
This simplifies to:
99C - 99A = 495
Hence, C - A = 5
- Reversing only the ten’s and unit digits increases the number by 36:
100A + 10C + B = 100A + 10B + C + 36
This simplifies to:
9C - 9B = 36
Hence, C - B = 4
Formulating the Equations
Now we have two equations from the conditions:
1. C - A = 5
2. C - B = 4
From these, we can express A and B in terms of C:
- A = C - 5
- B = C - 4
Now substitute A and B into the digit sum equation:
(C - 5) + (C - 4) + C = 12
Solving for C
- 3C - 9 = 12
- 3C = 21
- C = 7
Now substituting C back to find A and B:
- A = 7 - 5 = 2
- B = 7 - 4 = 3
Conclusion
Thus, the three-digit number is 237.
Verification
- Sum of digits: 2 + 3 + 7 = 12
- Reversed number: 732, and 732 - 237 = 495
- Reversed tens and units: 273, and 273 - 237 = 36
All conditions are satisfied, confirming the number is indeed 237.
To find the three-digit number based on the given conditions, let's denote the number as ABC, where A, B, and C are its digits.
Conditions Given
- The sum of the digits is 12:
A + B + C = 12
- Reversing the entire number increases it by 495:
100C + 10B + A = 100A + 10B + C + 495
This simplifies to:
99C - 99A = 495
Hence, C - A = 5
- Reversing only the ten’s and unit digits increases the number by 36:
100A + 10C + B = 100A + 10B + C + 36
This simplifies to:
9C - 9B = 36
Hence, C - B = 4
Formulating the Equations
Now we have two equations from the conditions:
1. C - A = 5
2. C - B = 4
From these, we can express A and B in terms of C:
- A = C - 5
- B = C - 4
Now substitute A and B into the digit sum equation:
(C - 5) + (C - 4) + C = 12
Solving for C
- 3C - 9 = 12
- 3C = 21
- C = 7
Now substituting C back to find A and B:
- A = 7 - 5 = 2
- B = 7 - 4 = 3
Conclusion
Thus, the three-digit number is 237.
Verification
- Sum of digits: 2 + 3 + 7 = 12
- Reversed number: 732, and 732 - 237 = 495
- Reversed tens and units: 273, and 273 - 237 = 36
All conditions are satisfied, confirming the number is indeed 237.
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Question Description
The numbers of the digits in a three digit number is 12. If the digits are reversed the number 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 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The numbers of the digits in a three digit number is 12. If the digits are reversed the number 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 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The numbers of the digits in a three digit number is 12. If the digits are reversed the number is increased by 495 but reversing only of the ten's and unit digits increases the number by 36. The number is?.
The numbers of the digits in a three digit number is 12. If the digits are reversed the number 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 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The numbers of the digits in a three digit number is 12. If the digits are reversed the number 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 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The numbers of the digits in a three digit number is 12. If the digits are reversed the number 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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