A began a business with Rs. 85,000. He was joined afterwards by B with Rs. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?

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