A began a business with Rs. 85000, he was joined afterwards by B with Rs. 42500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?

$$\eqalign{ & {\text{Suppose B joined for }}x{\text{ months}} \cr & {\text{Then,}} \cr & \Rightarrow \frac{{85000 \times 12}}{{42500 \times x}} = \frac{3}{1} \cr & \Rightarrow x = \frac{{85000 \times 12}}{{42500 \times 3}} \cr & \Rightarrow x = 8 \cr & {\text{So, B joined for 8 months}} \cr} $$