### Swati and Rajni enter into a partnership with their capitals in the ratio 5 : 6. At the end of 7 months Swati withdraws her capital. If they receive the profit in the ratio of 5 : 9, find how long was Rajni’s capital used ?

A. 10 months B. 12 months C. 14 months D. None of these Answer: Option D
Suppose, Swati invested Rs. 5x for 7 months And Rajni invested Rs. 6x for y months Then, $\begin{array}{l} \Rightarrow \Large\frac{5 x \times 7}{6 x \times y}=\frac{5}{9} \\ \Rightarrow 30 y=315 \\ \Rightarrow y=10 \large\frac{1}{2} \end{array}$ Hence, Rajni’s capital was used for $10 \frac{1}{2}$ months.