Question

Two times a two-digit number is 9 times the number obtained by reversing the digits and sum of the digits is 9. The number is ........

• A. 54
• B. 72
• C. 63
• D. 81

Hint:

For problems involving two-digit numbers, represent the number as \( 10x + y \), where \( x \) and \( y \) are the digits, and use algebra to form equations based on the given conditions.

Answer 1

The Correct Option is D

Let the number be \( 10x + y \), where \( x \) is the tens digit and \( y \) is the units digit. Given: - Two times the number is 9 times the number obtained by reversing the digits. This gives us the equation: \[ 2(10x + y) = 9(10y + x) \] Simplify the equation: \[ 20x + 2y = 90y + 9x \] \[ 20x - 9x = 90y - 2y \] \[ 11x = 88y \] \[ x = 8y \] - The sum of the digits is 9: \[ x + y = 9 \] Substitute \( x = 8y \) into the above equation: \[ 8y + y = 9 \] \[ 9y = 9 \] \[ y = 1 \] Substitute \( y = 1 \) into \( x = 8y \): \[ x = 8 \times 1 = 8 \] Thus, the number is \( 10x + y = 10(8) + 1 = 81 \).

Step 2: Final Answer The correct answer is (d) 81. Final Answer: The correct answer is (d) 81.