2021 · Q32
A two-digit number is such that the product of the digits is 8. If 63 is added to this number, the digits interchange their places. What is the sum of the digits in the number ?
Elementary MathematicsNumber System
- A6
- B7
- C8
- D9
Explanation
Let the number be 10a + b with ab = 8. Adding 63 interchanges the digits: 10a + b + 63 = 10b + a, so 9(b − a) = 63 and b − a = 7. With ab = 8, the digits are 1 and 8 (8 − 1 = 7), so the number is 18. The sum of the digits is 9, option (d).