Problem: If an integer of two digits is k times the sum of its digits, the number formed by interchanging the digits is the sum of the digits multiplied by:
Answer Choices:
A. (9−k)
B. (10−k)
C. (11−k)
D. (k−1)
E. (k+1)
Solution:
Given 10u+t=k(u+t). Let 10t+u=m(u+t).
∴11(t+u)=(k+m)(u+t);∴k+m=11;∴m=11−k.