1. 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

2. 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

3. At the beginning of the year, Srikanta and Sadananda started a business with investments of 24,000 taka and 30,000 taka, respectively. After 5 months, Srikanta invested an additional 4,000 taka in the business. If the total profit at the end of the year is 27,716 taka, determine how much profit each person will receive.

4. A joint business. On January 1st, A, B, and C invest 4,000 rupees, 5,000 rupees, and 6,000 rupees, respectively. On May 1st, A invests an additional 2,000 rupees in the business. On September 1st, C withdraws half of their capital. By December 31st, if the total profit is 6,900 rupees, how much profit will each person receive?

5. At the beginning of the year, Mr. Pradip and Mrs. Amina invested ₹24,000 and ₹30,000, respectively, in a business. After five months, Mr. Pradip added ₹4,000 more to his capital. At the end of the year, the total profit was ₹27,716. Determine how much profit each person will receive.

6. Three friends—A, B, and C—started a business by investing \(x\), \(2x\), and \(y\) taka respectively. If the profit at the end of the term is \(z\) taka, then what will be A’s share of the profit?

(a) ₹ \(\cfrac{xz}{3x+y}\) (b) ₹ \(\cfrac{2xz}{3x+y}\) (c) ₹ \(\cfrac{z}{2x+y}\) (d) ₹\(\cfrac{xyz}{3x+y}\)

7. At the beginning of the year, Arun and Ajay jointly started a business with investments of ₹24,000 and ₹30,000 respectively. After a few months, Arun added ₹12,000 more to the business capital. At the end of the year, the total profit from the business was ₹14,030, and Arun received ₹7,130 as his share of the profit. Determine how many months later Arun invested the additional ₹12,000.

8. At the beginning of the year, Samir and Idrish started a joint business with investments of ₹24,000 and ₹30,000 respectively. A few months later, Samir added another ₹12,000 to the business. At the end of the year, the total profit was ₹14,030, and Samir received ₹7,130 as his share of the profit. Find out how many months later Samir added the extra ₹12,000.

9. 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

10. A, B, and C started a business together with capital investments of ₹6,000, ₹8,000, and ₹9,000 respectively. After a few months, A invested an additional ₹3,000 into the business. At the end of the year, the total profit was ₹30,000, and C received ₹10,800 as his share of the profit. When did A invest the additional ₹3,000?

11. 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?

12. Anisur invested ₹500 for 9 months and David invested ₹600 for 5 months in a joint business. Their profit-sharing ratio will be _____ .

13. In a joint business venture, Samir, Idrish, and Anthony invested ₹4000, ₹5000, and ₹6000 respectively. After 4 months, Anthony withdrew half of his capital. At the end of the year, the total profit was ₹3900. Determine how much profit each person will receive.

14. 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?

15. At the beginning of the year, A and B jointly started a business by investing ₹24,000 and ₹30,000 respectively. After five months, A added another ₹12,000 to the business. At the end of the year, the total profit from the business was ₹14,030. Determine each person's share of the profit.

16. In a joint business, Sumedha, Rabeya, and Rina invest 4,000 rupees, 5,000 rupees, and 6,000 rupees, respectively. After 4 months, Sumedha adds another 2,000 rupees, and after another 4 months, Rina withdraws half of her capital. If the total profit at the end of the year is 6,900 rupees, how much profit will each person receive?

17. Niyamat Chacha and Korobi Didi jointly started a business with initial investments of 30,000 INR and 50,000 INR, respectively. After 6 months, Niyamat Chacha invested an additional 40,000 INR, while Korobi Didi withdrew 10,000 INR for personal needs. At the end of the year, if the total profit is 19,000 INR, determine how much each of them will receive.

18. Niyamat Chacha and Korobi Didi jointly started a business by investing ₹30,000 and ₹50,000 respectively. After 6 months, Niyamat Chacha invested an additional ₹40,000, while Korobi Didi withdrew ₹10,000 for personal use. At the end of the year, if the total profit is ₹19,000, calculate how much profit each person will receive.

19. 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 ..........

20. Ashish invested ₹600 for 5 months and Tarun invested ₹500 for 9 months to start a business. The ratio in which the profit will be distributed between them is —

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

21. Masud, Nibedita, and Kabir jointly started a business by investing ₹6000, ₹8000, and ₹9000 respectively. After 4 months, Masud invested an additional amount of money. By the end of the year, the total profit was ₹3000, and Kabir received a share of ₹1080. How much money did Masud invest after 4 months?

22. A and B start a joint business. At the end of the year, they share the profit in the ratio 2 : 3. If A invested ₹40,000, then how much did B invest?

(a) ₹ 50000 (b) ₹ 60000 (c) ₹ 40000 (d) ₹ 70000

23. At the beginning of the year, in a joint business, the capital ratio of A and B is 2:3, and the capital ratio of B and C is 4:5. If at the end of the year, C's share of the profit is ₹300, then how much profit should A receive?

24. At the beginning of the year, Pradip Babu and Amina Bibi started a business with ₹24,000 and ₹30,000 respectively. After 5 months, Pradip Babu added ₹4,000 more to his capital. At the end of the year, the total profit was ₹27,716. How much profit will each of them receive?

25. At the beginning of the year, Souvik and Rahul started a business by investing ₹24,000 and ₹30,000 respectively. After 5 months, Souvik added an additional ₹4,000 to his capital. At the end of the year, the total profit was ₹27,716. Calculate how much profit each of them will receive.

26. At the beginning of the year, Arun and Asraf started a joint business by investing ₹24,000 and ₹30,000 respectively. A few months later, Arun added another ₹12,000 to the business capital. At the end of the year, the business made a profit of ₹14,300, and Arun received ₹7,130 as his share of the profit. Determine how many months later Arun added the additional amount.

27. A, B, and C started a business by investing ₹6,000, ₹8,000, and ₹10,000 respectively, with the condition that A would manage the business. For this, A would receive \(\frac{3}{20}\) of the total profit. The remaining profit would be divided among the three in proportion to their capital. If C received ₹391 more than B, what was the total profit?

28. Amal and Bimal started a business. Amal invested ₹500 for 9 months, while Bimal invested some amount for 6 months. The total profit of the business is ₹69, and Bimal received ₹46 as his share. What was Bimal's investment in the business?

(a) ₹ 1500 (b) ₹ 3000 (c) ₹ 4500 (d) ₹ 6000

29. On January 1, 2015, \( A \) invested 800 rupees in a business, \( B \) invested 600 rupees on May 1, and \( C \) invested 500 rupees on July 1. If the total profit for the year is 3480 rupees, then how much will \( A \) receive?

(a) ₹ 1920 (b) ₹ 2019 (c) ₹9201 (d) ₹ 2000

30. In a business, if two individuals invest \(x\) rupees and \(y\) rupees for 9 months and 6 months respectively, then their profit share ratio will be?

(a) \(2x:3y\) (b) \(3x:2y\) (c) \(x:y\) (d) \(2y:5x\)