'A' started a business alone. After 6 months, 'B' joined the business whose investment was Rs. 2,000 more than that of 'A'. After a further 6 months, 'A' decreased his investment by Rs. 2,000. If the ratio of the profit share of 'A' to 'B' at the end of 18 months is 5:6, then find the initial investment of 'A'.

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?