A invested Rs. 76,000 in a business. After few months, B joined him Rs. 57,000. At the end of the year, the total profit was divided between them in ratio 2 : 1. After bow many months did B join?

Suppose B joined after x months. Then, B's money was invested for
                          (12 - x)(76000 x 12)/(57000 x (12-x) =2/1
                      
                           912000=114000(12-x)

                           114 (12 - x) = 912ó12-x=8óx=4

Hence, B joined after 4 months.