2016 · Q21
Let a two-digit number be k times the sum of its digits. If the number formed by interchanging the digits is m times the sum of the digits, then the value of m is
Elementary MathematicsNumber System
- A9 - k
- B10 - k
- C11 - k
- Dk - 1
Explanation
Let the number be 10a+b = k(a+b) and its reversal 10b+a = m(a+b). Adding the two equations gives 11(a+b) = (k+m)(a+b). Since a+b ≠ 0, k+m = 11, so m = 11−k, option C.