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The sum of the digits of two digit number id 10 if 18 be subtracted from it the digits in the resulting number will be equal the number is?
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The sum of the digits of two digit number id 10 if 18 be subtracted fr...
Problem Overview
To find the two-digit number based on the given conditions, we can break down the problem into manageable steps.
Step 1: Understand the Constraints
- The sum of the digits of the two-digit number is 10.
- If 18 is subtracted from the number, the digits of the resulting number will be equal.
Step 2: Represent the Two-Digit Number
- Let the two-digit number be represented as 10a + b, where:
- a = tens digit
- b = units digit
Step 3: Formulate the Equations
- From the first condition:
a + b = 10
- From the second condition:
10a + b - 18 = 10b + a
This simplifies to:
9a - 9b = 18
Further simplifying gives:
a - b = 2
Step 4: Solve the Equations
Now, we have the following system of equations:
- a + b = 10
- a - b = 2
To solve:
1. Add both equations:
- 2a = 12
- a = 6
2. Substitute a back into the first equation:
- 6 + b = 10
- b = 4
Step 5: Final Result
The digits are:
- Tens digit (a) = 6
- Units digit (b) = 4
Thus, the two-digit number is 64.
Verification
- Sum of digits: 6 + 4 = 10 (Correct)
- Number after subtracting 18: 64 - 18 = 46
- Digits of 46: 4 and 6 (Equal to the digits of 64, but swapped)
Hence, the two-digit number is indeed 64.
To find the two-digit number based on the given conditions, we can break down the problem into manageable steps.
Step 1: Understand the Constraints
- The sum of the digits of the two-digit number is 10.
- If 18 is subtracted from the number, the digits of the resulting number will be equal.
Step 2: Represent the Two-Digit Number
- Let the two-digit number be represented as 10a + b, where:
- a = tens digit
- b = units digit
Step 3: Formulate the Equations
- From the first condition:
a + b = 10
- From the second condition:
10a + b - 18 = 10b + a
This simplifies to:
9a - 9b = 18
Further simplifying gives:
a - b = 2
Step 4: Solve the Equations
Now, we have the following system of equations:
- a + b = 10
- a - b = 2
To solve:
1. Add both equations:
- 2a = 12
- a = 6
2. Substitute a back into the first equation:
- 6 + b = 10
- b = 4
Step 5: Final Result
The digits are:
- Tens digit (a) = 6
- Units digit (b) = 4
Thus, the two-digit number is 64.
Verification
- Sum of digits: 6 + 4 = 10 (Correct)
- Number after subtracting 18: 64 - 18 = 46
- Digits of 46: 4 and 6 (Equal to the digits of 64, but swapped)
Hence, the two-digit number is indeed 64.
Community Answer
The sum of the digits of two digit number id 10 if 18 be subtracted fr...
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The sum of the digits of two digit number id 10 if 18 be subtracted from it the digits in the resulting number will be equal the number is?
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The sum of the digits of two digit number id 10 if 18 be subtracted from it the digits in the resulting number will be equal the number is? 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 two digit number id 10 if 18 be subtracted from it the digits in the resulting number will be equal the number is? 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 two digit number id 10 if 18 be subtracted from it the digits in the resulting number will be equal the number is?.
The sum of the digits of two digit number id 10 if 18 be subtracted from it the digits in the resulting number will be equal the number is? 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 two digit number id 10 if 18 be subtracted from it the digits in the resulting number will be equal the number is? 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 two digit number id 10 if 18 be subtracted from it the digits in the resulting number will be equal the number is?.
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