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The sum of digits of a two digit number is 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 digits of a two digit number is 10. If 18 be subtracted fro...
Understanding the Problem
To find the two-digit number that meets the conditions given, we need to analyze the clues provided:
1. Sum of Digits: The sum of the digits of the two-digit number equals 10.
2. Subtraction Result: When 18 is subtracted from this number, the resulting digits are equal.
Defining the Variables
Let the two-digit number be represented as 10a + b, where:
- a = the tens digit
- b = the units digit
Setting Up the Equations
From the problem, we can derive the following equations:
- Equation 1: a + b = 10
- Equation 2: (10a + b) - 18 = 10c + c (where c is the common digit after subtraction)
This simplifies to:
10a + b - 18 = 11c
Finding Solutions
Now, we can substitute Equation 1 into our equations:
1. From a + b = 10, we can express b as:
b = 10 - a
2. Substitute b into Equation 2:
10a + (10 - a) - 18 = 11c
Simplifying gives:
9a - 8 = 11c
Now we can test integer values for a (1 to 9):
- If a = 8:
9(8) - 8 = 72 - 8 = 64, which is not divisible by 11.
- If a = 7:
9(7) - 8 = 63 - 8 = 55, which gives c = 5.
Therefore, b = 10 - 7 = 3.
So, the number is:
73
Conclusion
The two-digit number that meets the conditions is 73.
To find the two-digit number that meets the conditions given, we need to analyze the clues provided:
1. Sum of Digits: The sum of the digits of the two-digit number equals 10.
2. Subtraction Result: When 18 is subtracted from this number, the resulting digits are equal.
Defining the Variables
Let the two-digit number be represented as 10a + b, where:
- a = the tens digit
- b = the units digit
Setting Up the Equations
From the problem, we can derive the following equations:
- Equation 1: a + b = 10
- Equation 2: (10a + b) - 18 = 10c + c (where c is the common digit after subtraction)
This simplifies to:
10a + b - 18 = 11c
Finding Solutions
Now, we can substitute Equation 1 into our equations:
1. From a + b = 10, we can express b as:
b = 10 - a
2. Substitute b into Equation 2:
10a + (10 - a) - 18 = 11c
Simplifying gives:
9a - 8 = 11c
Now we can test integer values for a (1 to 9):
- If a = 8:
9(8) - 8 = 72 - 8 = 64, which is not divisible by 11.
- If a = 7:
9(7) - 8 = 63 - 8 = 55, which gives c = 5.
Therefore, b = 10 - 7 = 3.
So, the number is:
73
Conclusion
The two-digit number that meets the conditions is 73.
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The sum of digits of a two digit number is 10. If 18 be subtracted from it the digits in the resulting number will be equal. The number is?
Question Description
The sum of digits of a two digit number is 10. If 18 be subtracted from it the digits in the resulting number will be equal. 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 digits of a two digit number is 10. If 18 be subtracted from it the digits in the resulting number will be equal. 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 digits of a two digit number is 10. If 18 be subtracted from it the digits in the resulting number will be equal. The number is?.
The sum of digits of a two digit number is 10. If 18 be subtracted from it the digits in the resulting number will be equal. 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 digits of a two digit number is 10. If 18 be subtracted from it the digits in the resulting number will be equal. 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 digits of a two digit number is 10. If 18 be subtracted from it the digits in the resulting number will be equal. The number is?.
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