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 ?

Suppose,
Swati invested Rs. 5x for 7 months
And
Rajni invested Rs. 6x for y months
Then,
$$\eqalign{ & \Rightarrow \frac{{5x \times 7}}{{6x \times y}} = \frac{5}{9} \cr & \Rightarrow 30y = 315 \cr & \Rightarrow y = 10\frac{1}{2} \cr} $$
Hence, Rajni's capital was used for $${\text{10}}\frac{1}{2}$$ months