1. 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.

2. 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.

3. 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.

4. 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.

5. 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?

6. Initially, Arun and Ajay started a joint business with investments of ₹24,000 and ₹30,000, respectively. After a few months, Arun added ₹12,000 more to the business. At the end of the year, the business made a profit of ₹14,030, and Arun received ₹7,130 as his share of the profit. How many months later did Arun invest the additional amount in the business?

7. 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.

8. 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?

9. Nivedita and Uma started a business by investing ₹3,000 and ₹5,000 respectively. After 6 months, Nivedita added ₹4,000 more to her investment, while Uma withdrew ₹1,000. At the end of one year, the total profit was ₹6,175. Calculate the profit share of both.

10. A and B started a business by investing ₹3000 and ₹5000, respectively. After 6 months, A added ₹4000 more, but after another 6 months, A withdrew ₹1000. At the end of the year, the total profit was ₹6175. Determine how the profit should be distributed between A and B.

11. At the beginning of the year, Pradeep Babu and Amina Bibi started a business with ₹24,000 and ₹30,000 respectively. After five months, Pradeep Babu added ₹4,000 more to the capital. At the end of the year, if there is a profit of ₹27,716, calculate how much profit each person will receive.

12. 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.

13. 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?

14. At the beginning of the year, Rabeya and Megha started a business with capital investments of ₹24,000 and ₹30,000 respectively. After five months, Rabeya added ₹4,000 more to her capital. At the end of the year, the business earned a profit of ₹27,716. Determine how much profit each person receives.

15. Sabba, Deepak, and Pritha started a business together by investing ₹6000, ₹8000, and ₹9000 respectively. A few months later, Sabba invested an additional ₹3000. At the end of the year, the total profit was ₹3000, and Pritha received ₹1080 as her share of the profit. Determine when Sabba invested the additional ₹3000.

16. In a joint business, B's capital was \(1\frac{1}{2}\) times A's capital. After 4 months, B withdrew half of his capital, and after another 2 months, A withdrew one-fourth of his capital. At the end of the year, the total profit was ₹6,360. Determine the share of each person's profit.

17. Sabbah, Deepak, and Pritha started a joint business by investing ₹6000, ₹8000, and ₹9000 respectively. A few months later, Sabbah invested an additional ₹3000. At the end of the year, the total profit was ₹3000, and Pritha received ₹1080 as her share of the profit. Determine when Sabbah made the additional investment of ₹3000.

18. At the beginning of the year, Srikanta and Saifuddin purchased a minibus and started operating it by investing ₹2,40,000 and ₹3,00,000 respectively. Four months later, their friend Peter joined them with ₹81,000. Srikanta and Saifuddin withdrew amounts proportional to their original investments from Peter’s contribution. At the end of the year, the total profit was ₹39,150. How much profit will each of them receive?

19. Mr. Nilesh and Ms. Rahima jointly started a business with initial capital investments of 30,000 rupees and 50,000 rupees, respectively. After 6 months, Mr. Nilesh invested an additional 40,000 rupees, while Ms. Rahima withdrew 10,000 rupees for personal use. At the end of the year, if the total profit was 19,000 rupees, how much profit will each of them receive?

20. 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.

21. A, B, and C started a business with initial capitals of 6,000 rupees, 8,000 rupees, and 9,000 rupees, respectively. A invested an additional 3,000 rupees after a few months. At the end of the year, the total profit was 3,000 rupees, and C received a share of 1,080 rupees from the profit. Determine how many months later A made the additional investment of 3,000 rupees.

22. At the beginning of the year, Srikanta and Saifuddin purchased a minibus and started operating it with investments of ₹2,40,000 and ₹3,00,000 respectively. After four months, their friend Peter joined them by contributing ₹81,000. Srikanta and Saifuddin withdrew amounts from the business in proportion to their original capital. At the end of the year, if there is a profit of ₹39,150, calculate how much profit each person will receive.

23. A, B, and C started a joint business by investing ₹500, ₹300, and ₹1200 respectively. After one year, the total profit was ₹3200. How much will B receive from the profit?

(a) ₹ 800 (b) ₹ 1920 (c) ₹ 480 (d) ₹ 840

24. 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

25. 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.

26. Supriya, Uma, and Megha started a business with initial investments of 6000 rupees, 8000 rupees, and 9000 rupees, respectively. After a few months, Supriya invested an additional 3000 rupees. At the end of the year, the total profit was 3000 rupees, and Megha received a profit share of 1080 rupees. Determine when Supriya invested the additional 3000 rupees.

27. 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.

28. Three friends contributed ₹8,000, ₹10,000, and ₹12,000 respectively and started a business by also taking a loan from the bank. At the end of the year, they made a profit of ₹13,400. After repaying the bank’s annual installment of ₹5,000 from the profit, they divided the remaining amount among themselves in proportion to their capital contributions. How much will each of them receive from the remaining profit?

29. Deepak, Uma, and Pritha started a business together with capital investments of 6000 rupees, 4000 rupees, and 9000 rupees, respectively. After a few months, Deepak invested an additional 3000 rupees. At the end of the year, the total profit was 3000 rupees, and Pritha received a dividend of 1080 rupees. Determine when Deepak invested the additional 3000 rupees.

30. Rajib started a business with a capital of ₹3750. After 6 months, Sayan joined the business with a capital of ₹1500. At the end of the year, if the total profit is ₹6900, determine each person's share of the profit.