2020 · Q11
A two-digit number is 9 more than four times of the number obtained by interchanging its digits. If the product of digits in the two-digit number is 8, then what is the number?
Elementary MathematicsNumber System
- A81
- B42
- C24
- D18
Explanation
Let the number be 10a + b. The condition gives 10a + b = 9 + 4(10b + a), i.e. 6a − 39b = 9, or 2a − 13b = 3, with ab = 8. Trying b = 1 gives 2a = 16, so a = 8; check: 81 = 9 + 4 × 18. Hence the number is 81.