1. In a business, if the capital ratio of A, B, and C is 2:3:5 and their time of investment ratio is 3:4:5, then in what ratio will the profit be distributed?

(a) 3:4:5 (b) 5:8:9 (c) 8:9:11 (d) 6:12:15

2. In a business, three friends have their capital investment in the ratio 2:3:4. If in the following year they increase their capital by 10%, 15%, and 20%, respectively, in what ratio will the profit be distributed among them at the end of the second year?

(a) 44 : 69 : 96 (b) 69 : 44 : 96 (c) 96 : 69 : 44 (d) 45 : 96 : 63

3. If the ratio of the capital investments of A, B, and C is \(\cfrac{1}{2} : \cfrac{1}{3} : \cfrac{1}{4}\) and the total profit is ₹520, then C's share of the profit will be

(a) ₹120 (b) ₹160 (c) ₹180 (d) ₹140

4. Two friends start a partnership business by investing ₹40,000 and ₹50,000 respectively. They agree that 50% of the profit will be shared equally, and the remaining 50% will be divided in the ratio of their investments. If the first friend’s share of the profit is ₹800 less than the second friend’s share, then what is the first friend’s profit?

5. Three friends purchase a bus by investing ₹1,20,000, ₹1,50,000, and ₹1,10,000 respectively. The first friend works as the driver, while the other two work as conductors. They decide that \(\frac{2}{5}\) of the income will be distributed based on work in the ratio 3 : 2 : 2, and the remaining amount will be divided according to their capital investment. If the total income in a certain month is ₹29,260, determine how much each person will receive.

6. A and B jointly started a business at the beginning of the year with investments of ₹18,000 and ₹21,000, respectively. After 6 months, A invested an additional ₹3,000 in the business. If their total profit at the end of the year is ₹7,200, what is the ratio of A and B's individual profit shares?

(a) 13 : 12 (b) 14 : 13 (c) 13 : 14 (d) 14 : 11

7. In a business, the investment duration ratio of A, B, and C is 5:6:4, and the profit ratio is 5:3:12. What is the ratio of their capital investments?

(a) 2:3:1 (b) 2:1:3 (c) 3:1:2 (d) 1:2:3

8. The ratio of the principal investments of A and B is 11:9. The difference in their entitled profits will be 10%.

9. In a joint business, the capital of three friends is ₹200, ₹150, and ₹250, respectively. After the same period, their profit ratio will be –?

(a) 5:3:4 (b) 4:3:5 (c) 3:5:4 (d) 5:4:3

10. A, B, and C started a business by investing ₹6,500, ₹5,200, and ₹9,100 respectively. After exactly one year, they made a profit of ₹14,400. If \(\cfrac{2}{3}\) of the profit is divided equally among them and the remaining part is shared in the ratio of their investments, find out how much profit each person will receive.

11. In a partnership business, if the capital ratio of three members is \(a : b : c\) and the time invested is in the ratio \(x : y : z\), then their profit ratio will be \(ax : by : cz\).

12. In a joint business involving three individuals, the ratio of invested capital is 3:4:6, and the ratio of profit earned is 3:2:9. Then, the ratio of their invested time will be ..........

13. Kaushik and Sanjay started a joint business by investing ₹12,500 and ₹8,500 respectively. They agreed that 40% of the profit would be equally distributed between them, and the remaining profit would be shared in the ratio of their capitals. If Kaushik received ₹1,950 as profit, what was Sanjay's share of the profit?

14. In a partnership business, three friends invested capital amounts of ₹4,500, ₹6,000, and ₹9,000 respectively. After a certain period, their profit shares will be in the same ratio as their investments: \[ \text{Profit Ratio} = 4500 : 6000 : 9000 = 3 : 4 : 6 \] So, their respective shares of profit will be in the ratio 3 : 4 : 6.

15. Pallavi invests ₹500 for 9 months, and Rajiya invests ₹600 for 5 months in a business. The profit will be distributed between them in the ratio –

(a) 3:2 (b) 5:6 (c) 6:5 (d) 9:5

16. In a partnership business, the capital ratio between A and B is 2:3, and the capital ratio between B and C is 6:5. If A's profit share is ₹400, what will be C's profit share?

(a) ₹ 500 (b) ₹ 600 (c) ₹ 700 (d) ₹ 800

17. In a business, the ratio of Lalu and Bhulu's capital is 3:2. If Bhulu's investment period is 4 months, for how many months should Lalu invest so that the profit ratio becomes 9:4?

18. A and B started a joint business by investing ₹6,200 and ₹10,000 respectively. They agreed that A would receive 20% of the profit for managing the business, and 10% of the remaining profit would be kept aside as savings. The rest of the profit would be divided between A and B in proportion to their capital investments. If the total profit at the end of the year is ₹45,000, how much money will A receive in total?

19. In a partnership business, the capitals of three friends are ₹200, ₹150, and ₹250 respectively. After the same period of time, their profit-sharing ratio will be ______.

20. A, B, and C together start a business and make a profit of ₹36,400. The ratio of capital between A and B is 5:3, and the ratio between B and C is 5:4. What will be A’s share of the profit?

21. In a business, the capitals of three friends are respectively \(x^2\) Taka, \(xy\) Taka, and \(xa^2\) Taka. After the same period, their profit ratio will be ______.

22. A, B, and C made a total profit of ₹15,000 in a joint business. If the capital ratio between A and B is 2:3 and between B and C is 2:5, then how much profit will B receive?

(a) 4500 (b) 9000 (c) 2400 (d) 3600

23. In a business, Rahul and Amit's capital investment ratio is 4:5. If 10% of the profit is retained as business capital and the remaining amount is distributed, and Rahul receives ₹16,000, what was the total profit?

(a) ₹ 50,000 (b) ₹ 40,000 (c) ₹ 55,000 (d) ₹ 80,000

24. In a business, A's capital is twice that of B, and B's capital is four times that of C. What will be the profit-sharing ratio of A, B, and C?

(a) 1 : 4 : 8 (b) 2 : 4 : 8 (c) 8 : 2 : 4 (d) 8 : 4 : 1

25. In a business, the capital ratio of A and C is 2:1, and the capital ratio of A and B is 3:2. If the annual profit is ₹1,57,300, what will be B's share of the profit?

(a) ₹ 48,000 (b) ₹ 58,400 (c) ₹ 48,400 (d) ₹68,000

26. A, B, and C start a business where their capital ratio is \(\cfrac{1}{2} : \cfrac{1}{3} : \cfrac{1}{4}\). After 4 months, A withdraws half of their capital, and after another 8 months, the total profit is ₹2,024. How much will A receive?

(a) ₹ 900 (b) ₹ 836 (c) ₹ 700 (d) ₹ 736

27. John invests 800 INR for 5 months, and Paul invests 500 INR for 6 months in a business. The ratio in which the profit will be distributed between them is? (Question)

(a) 3:2 (b) 5:6 (c) 4:3 (d) 8:5

28. In a business, the capital ratio of A and B is \(1:\frac{4}{5}\). If A's profit is 80 rupees, then B's profit will be 100 rupees.

29. A invests 500 rupees for 9 months, and B invests 600 rupees for 5 months in the business. In what ratio will the profit be distributed between them?

30. If the capital ratio of A, B, and C is \(\frac{1}{6}:\frac{1}{5}:\frac{1}{4}\), then the profit distribution will be in the ratio 4:5:6.