Question

The sum of the digits of a 2-digit number is 12. When the digits of the number are interchanged, the number becomes 15 more than twice the original number. The original number is:

• A. 39
• B. 48
• C. 57
• D. 75

Hint:

To solve problems with two-digit numbers, express the number using variables for its digits and form equations based on the given conditions.

Answer 1

The Correct Option is A

Step 1: Let the number be represented as \( 10a + b \), where \( a \) is the tens digit and \( b \) is the ones digit.
The sum of the digits is 12, so we have: \[ a + b = 12. \] When the digits are interchanged, the new number is \( 10b + a \). We are also told that this new number is 15 more than twice the original number, so: \[ 10b + a = 2(10a + b) + 15. \]

Step 2: Solve the system of equations.
Simplify the second equation: \[ 10b + a = 20a + 2b + 15. \] \[ 10b - 2b = 20a - a + 15. \] \[ 8b = 19a + 15. \] Now, solve these two equations: \[ a + b = 12 \text{and} 8b = 19a + 15. \] Substitute \( b = 12 - a \) into the second equation: \[ 8(12 - a) = 19a + 15. \] \[ 96 - 8a = 19a + 15. \] \[ 96 - 15 = 19a + 8a. \] \[ 81 = 27a. \] \[ a = 3. \] Substitute \( a = 3 \) into \( a + b = 12 \): \[ 3 + b = 12 $\Rightarrow$ b = 9. \] Thus, the original number is \( 10a + b = 10 \times 3 + 9 = 39 \).

Step 3: Conclusion.
The correct answer is (A) 39.