X, Y and Z enter into a partnership. X invests some money at the beginning. Y invests thrice the amount of X after 4 months from the start, and Z invests double the amount of Y after 9 months from the start. If the annual profit is Rs. 4,50,000, then what is the share of Y?

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?