Arjun and Suman entered into a partnership to open a boutique hotel with initial investments of Rs. 20,000 and Rs. 30,000 respectively. After 6 months, Kabir joined them with an investment of Rs. 40,000, and at the same time Arjun invested an additional Rs. 4000. If at the end of two years, Suman received Rs. 15,000 as her share of profit, what was the total profit earned?

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?