Question

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

• A. $(9-k)$
• B. $(10-k)$
• C. $(11-k)$
• D. $(k-1)$
• E. $(k+1)$

Answer 1

Answer: (C)

$(11-k)$

Given $10u+t=k(u+t)$. Let $10t+u=m(u+t)$.
$\therefore 11(t+u)=(k+m)(u+t);\therefore k+m=11;\therefore m=11-k$.