The sum of three numbers is 116. The second number and the third number are in the ratio of 9 : 16 while the first number and the third number are in the ratio of 1 : 4. Find the second number.

$$\eqalign{ & {\text{Second}}:{\text{Third}} \cr & = {\text{9}}:{\text{16}} \cr & {\text{Third}}:{\text{first}} \cr & = {\text{4}}:{\text{1}} \cr & {\text{ = 16}}:{\text{4}}{\text{}} \cr & \therefore {\text{Second}}:{\text{Third}}:{\text{first}} \cr & = {\text{9}}:{\text{16}}:{\text{4}}{\text{}} \cr & {\text{Second number}} \cr & = \left( {{\text{116}} \times \frac{{\text{9}}}{{{\text{29}}}}} \right) \cr & = {\text{36}} \cr} $$