Two individuals, A and B, rented a pasture. A grazes 12 horses for 5 months and 20 sheep for 4 months. B grazes 15 cows for 6 months and 30 sheep for 3 months. If 3 horses consume as much as 5 cows, and 6 cows consume as much as 10 sheep, find the fraction of the total rent that A should pay.

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?