The ratio between the ages of Neelam and Shiny is 5 : 6 respectively. If the ratio between the one-third age of Neelam and half of Shiny's age is 5 : 9, then what is Shiny's age = ?

Answer: Option D

Let Neelam's age be 5x years and
Shiny's age be 6x years
$$\begin{array}{rl}& \left(\frac{1}{3}\times 5x\right):\left(\frac{1}{2}\times 6x\right)=5:9\\ & \Rightarrow \frac{5x}{3\times 3x}=\frac{5}{9}\end{array}$$
Thus, Shiny's age cannot be determined