Two persons A and B enter into a partnership with a total initial investment of 'X'. A leaves the business after 3 months, and at the same time C joins with an investment of ₹1,000. If the ratio of the profit shares of A, B, and C at the end of one year is 3 : 8 : 3, find the difference between the initial investments of A and B.

Three partners invested in a business in the ratio 8:5:4. They invested their capital for 3 months, 10 months, and 9 months respectively. What was the ratio of their profits?

A started a business with an investment of ₹21,000 and after a few months, B joined him with an investment of ₹15,000. At the end of the year, the total profit was divided between them in the ratio 12 : 5. After how many months did B join the business?