Joyanta started a business and he invested in 38000, After some month, Omar came to join with him and invest 28500. The end of the year the total profit was divided among them into ratio form 16 : 8. Find after how many months did Omar join.

Question: Joyanta started a business and he invested in 38000, After some month, Omar came to join with him and invest 28500. The end of the year the total profit was divided among them into ratio form 16 : 8. Find after how many months did Omar join.

Solution:
we can assume that Omar join into business after x months.
So Omar money was invested for (12 - x) months.

(38000 × 12)/{28500 × (12 - x)} = 2/1 (The given ratio of 16 : 8 is equivalent to 2 :1)
⇒ 456000 = 28500(12 - x)
⇒ 456000 = 57000(12 - x)
⇒ 57(12 - x) = 456
⇒ 12 - x = 8
∴ x = 4

After 4 months Omar join the business.