X and Y enter into a partnership with capitals in the ratio 5 : 6 and at the end of 8 months, X withdraws. If they receive profit in the ratio of 5 : 9. Find how long Y's capital was used.

Answer: Option D

Let the capitals of Y was used for T months
According to the question,
$$\begin{array}{rl}& \frac{5\times 8}{6\times \text{T}}\text{ = }\frac{5}{9}\\ & \Rightarrow \text{T}=\text{12 months}\end{array}$$
Hence capital of Y was used for = 12 months