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The sum of digits of a two-digit number is 9. If 9 is subtracted from the number, its digits are interchanged.
Q. What is the half of that number?
- a)26
- b)27
- c)28
- d)29
Correct answer is option 'B'. Can you explain this answer?
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The sum of digits of a two-digit number is 9. If 9 is subtracted from ...
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The sum of digits of a two-digit number is 9. If 9 is subtracted from ...
Understanding the Problem
To solve the problem, we need to identify a two-digit number whose digits add up to 9, and when 9 is subtracted from it, the digits are reversed.
Step 1: Define the Two-Digit Number
Let the two-digit number be represented as:
- 10a + b, where
- a = tens digit
- b = units digit
Step 2: Set Up the Equations
From the problem, we have the following conditions:
- The sum of the digits is 9:
- a + b = 9
- When 9 is subtracted from the number, the digits are interchanged:
- 10a + b - 9 = 10b + a
Step 3: Simplify the Second Equation
Rearranging the second equation gives:
- 10a + b - 9 = 10b + a
- This simplifies to:
- 9a - 9b = 9
- or, a - b = 1
Step 4: Solve the Equations
Now we have a system of equations:
1. a + b = 9
2. a - b = 1
Adding these equations:
- (a + b) + (a - b) = 9 + 1
- 2a = 10
- a = 5
Now substitute a = 5 into a + b = 9:
- 5 + b = 9
- b = 4
Step 5: Find the Number
The two-digit number is:
- 10a + b = 10(5) + 4 = 54
Step 6: Calculate Half of the Number
Now, to find half of the number:
- Half of 54 = 27
Conclusion
Thus, the half of that number is 27, confirming that the correct answer is option 'B'.
To solve the problem, we need to identify a two-digit number whose digits add up to 9, and when 9 is subtracted from it, the digits are reversed.
Step 1: Define the Two-Digit Number
Let the two-digit number be represented as:
- 10a + b, where
- a = tens digit
- b = units digit
Step 2: Set Up the Equations
From the problem, we have the following conditions:
- The sum of the digits is 9:
- a + b = 9
- When 9 is subtracted from the number, the digits are interchanged:
- 10a + b - 9 = 10b + a
Step 3: Simplify the Second Equation
Rearranging the second equation gives:
- 10a + b - 9 = 10b + a
- This simplifies to:
- 9a - 9b = 9
- or, a - b = 1
Step 4: Solve the Equations
Now we have a system of equations:
1. a + b = 9
2. a - b = 1
Adding these equations:
- (a + b) + (a - b) = 9 + 1
- 2a = 10
- a = 5
Now substitute a = 5 into a + b = 9:
- 5 + b = 9
- b = 4
Step 5: Find the Number
The two-digit number is:
- 10a + b = 10(5) + 4 = 54
Step 6: Calculate Half of the Number
Now, to find half of the number:
- Half of 54 = 27
Conclusion
Thus, the half of that number is 27, confirming that the correct answer is option 'B'.
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