If a number of two digits is k times the sum of its digits, then the number formed by interchanging the digits is the sum of the digits multiplied by :

Answer: Option B

Let the ten's digit be x and the unit's digit be y
Then, number = 10x + y
$$\begin{array}{rl}& \therefore 10x+y=k\left(x+y\right)\\ & \Rightarrow k=\frac{10x+y}{x+y}\end{array}$$
Number formed by interchanging the digits = 10y + x
Let, 10y + x = h(x + y)
Then,
$$\begin{array}{rl}& h=\frac{10y+x}{x+y}\\ & =\frac{11\left(x+y\right)-\left(10x+y\right)}{x+y}\\ & =11-\frac{10x+y}{x+y}\\ & =11-k\end{array}$$