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? 

The profit ratio is

 $\begin{array}{rcl}85000·\left(12\right):42500·\left(12-x\right)& =& 850\left(12\right):425\left(12-x\right)\\ & =& 170\left(12\right):85\left(12-x\right)\\ & =& \left(120\right):5\left(12-x\right)\\ & =& 24:12-x\end{array}$

Given that the ratio is $3:17$

Hence,

$\begin{array}{rcl}\frac{24}{12-x}& =& 3\\ 12-x& =& 8\\ x& =& 4\end{array}$

Thereor,e the number of months that $B$ is in the businiess is $12-4=8 months$