In what ratio should the profit of Rs.8000 be divided if X starts a business with an investment of Rs.20000, Y invests Rs.7500 for 4 months and Z invests Rs.15000 after 3 months from the start of the business.

The profit in a business is divided among the partners in the ratio of their investment multiplied by the time for which they invested.

1. X invested Rs.20000 for the entire year. So, his share in the profit will be proportional to 20000*12 = 240000.

2. Y invested Rs.7500 for 4 months. So, his share in the profit will be proportional to 7500*4 = 30000.

3. Z invested Rs.15000 but only after 3 months from the start of the business. So, he effectively invested for 12-3 = 9 months. So, his share in the profit will be proportional to 15000*9 = 135000.

So, the ratio in which the profit of Rs.8000 should be divided is 240000:30000:135000.

This simplifies to 8:1:4.5 after dividing each term by 30000.

So, X should get 8/13.5 of the profit, Y should get 1/13.5 of the profit, and Z should get 4.5/13.5 of the profit.

Therefore, X should get Rs. (8/13.5)*8000 = Rs. 4740.74, Y should get Rs. (1/13.5)*8000 = Rs. 592.59, and Z should get Rs. (4.5/13.5)*8000 = Rs. 2666.67.

The profit in a business is divided among the partners in the ratio of their investment multiplied by the time for which they invested.

1. X's investment is Rs. 20000 for 12 months (assuming the business runs for a year). So, X's share = 20000 * 12 = 240000

2. Y's investment is Rs. 7500 for 4 months. So, Y's share = 7500 * 4 = 30000

3. Z's investment is Rs. 15000 but he invested 3 months after the start of the business, so he invested for 9 months. So, Z's share = 15000 * 9 = 135000

So, the ratio in which the profit of Rs. 8000 should be divided is X:Y:Z = 240000:30000:135000 = 8:1:4.5

Therefore, X gets 8/13.5 * 8000 = Rs. 4740.74, Y gets 1/13.5 * 8000 = Rs. 592.59, and Z gets 4.5/13.5 * 8000 = Rs. 2666.67.