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 :

Solution (By Examveda Team)

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