Vivek started a business with Rs. 25,000 and is joined afterwards by Ramu with Rs. 60,000. After how many months did Ramu join if the profits at the end of the year are divided equally?

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?