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The digit in the tens place of a two digit number is 6 more than the digit in the units place. The sum of the number and the number obtained by reversing the digits is 66. Find the number.?
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The digit in the tens place of a two digit number is 6 more than the d...
To solve the problem of finding the two-digit number, we will break it down step by step.
Step 1: Define the digits
Let the digit in the units place be represented as \( x \).
Then, the digit in the tens place can be expressed as \( x + 6 \).
Thus, the two-digit number can be written as:
\[ 10(y) + x = 10(x + 6) + x = 10x + 60 + x = 11x + 60 \]
Step 2: Reverse the digits
When the digits are reversed, the units place becomes the tens place, and vice versa. Therefore, the reversed number is:
\[ 10x + (x + 6) = 10x + x + 6 = 11x + 6 \]
Step 3: Set up the equation
According to the problem, the sum of the number and its reverse is equal to 66:
\[ (11x + 60) + (11x + 6) = 66 \]
This simplifies to:
\[ 22x + 66 = 66 \]
Step 4: Solve for \( x \)
Subtract 66 from both sides:
\[ 22x = 0 \]
\[ x = 0 \]
Step 5: Find the digits
Now, substitute \( x \) back to find the digits:
- Units place: \( x = 0 \)
- Tens place: \( x + 6 = 0 + 6 = 6 \)
So, the two-digit number is:
\[ 60 + 0 = 60 \]
Final Answer
The two-digit number is 60.
Step 1: Define the digits
Let the digit in the units place be represented as \( x \).
Then, the digit in the tens place can be expressed as \( x + 6 \).
Thus, the two-digit number can be written as:
\[ 10(y) + x = 10(x + 6) + x = 10x + 60 + x = 11x + 60 \]
Step 2: Reverse the digits
When the digits are reversed, the units place becomes the tens place, and vice versa. Therefore, the reversed number is:
\[ 10x + (x + 6) = 10x + x + 6 = 11x + 6 \]
Step 3: Set up the equation
According to the problem, the sum of the number and its reverse is equal to 66:
\[ (11x + 60) + (11x + 6) = 66 \]
This simplifies to:
\[ 22x + 66 = 66 \]
Step 4: Solve for \( x \)
Subtract 66 from both sides:
\[ 22x = 0 \]
\[ x = 0 \]
Step 5: Find the digits
Now, substitute \( x \) back to find the digits:
- Units place: \( x = 0 \)
- Tens place: \( x + 6 = 0 + 6 = 6 \)
So, the two-digit number is:
\[ 60 + 0 = 60 \]
Final Answer
The two-digit number is 60.
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The digit in the tens place of a two digit number is 6 more than the digit in the units place. The sum of the number and the number obtained by reversing the digits is 66. Find the number.?
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The digit in the tens place of a two digit number is 6 more than the digit in the units place. The sum of the number and the number obtained by reversing the digits is 66. Find the number.? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The digit in the tens place of a two digit number is 6 more than the digit in the units place. The sum of the number and the number obtained by reversing the digits is 66. Find the number.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The digit in the tens place of a two digit number is 6 more than the digit in the units place. The sum of the number and the number obtained by reversing the digits is 66. Find the number.?.
The digit in the tens place of a two digit number is 6 more than the digit in the units place. The sum of the number and the number obtained by reversing the digits is 66. Find the number.? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The digit in the tens place of a two digit number is 6 more than the digit in the units place. The sum of the number and the number obtained by reversing the digits is 66. Find the number.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The digit in the tens place of a two digit number is 6 more than the digit in the units place. The sum of the number and the number obtained by reversing the digits is 66. Find the number.?.
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