Madhu started a business and he invested in 76000, After some month, Amar came to join with him and invest 57000.The end of the year the total profit was divided among them into ratio form 2 : 1.Find after how many months Amar join.

we can assume that Amar join into business after x months. So Amar money was invest into  (12 – x ) months.

$\frac{76000\times 12}{57000\times (12-x)}=\frac{2}{1}$

--> 912000 = 114000 ( 12 – x ) = 114 ( 12 – x ) = 912

--> x = 4

After 4 months amar join the business.