1. 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?

2. Three friends invested capital amounts of ₹6500, ₹5200, and ₹9100 respectively to start a business. After exactly one year, the business made a profit of ₹14,400. If \(\frac{2}{3}\) of this profit is divided equally among them and the remaining portion is shared according to their capital ratio, calculate how much profit each person receives.

3. 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?

4. 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.

5. 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?

6. 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

7. 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

8. Jayanta, Ajit, and Kunal jointly started a partnership business with a total investment of ₹15,000. At the end of the year, their respective profits were ₹800, ₹1000, and ₹1200. How much did Jayanta invest in the business?

(a) ₹ 5000 (b) ₹ 7000 (c) ₹ 4000 (d) none of the above

9. In a joint business, Sudip invested 10,000 rupees for 6 months, and Subhendu invested some amount for 8 months. If Subhendu receives \(\cfrac{4}{9}\) of the profit, then how much did he invest?

(a) ₹ 4000 (b) ₹6000 (c) ₹ 7000 (d) ₹ 8000

10. In a business, the capital ratio of Raju and Asim is \( 4:5 \), and their profit ratio is \( 2:3 \). If Raju invested for 10 months, then for how long did Asim invest?

(a) 1 years (b) 2 years (c) 6 month (d) 3 years

11. 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.

12. 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.

13. 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.

14. 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.

15. Jayanta, Ajit, and Kunal jointly started a partnership business with a total capital of ₹15,000. At the end of the year, they earned profits of ₹800, ₹1,000, and ₹1,200 respectively. Profit ratio = 800 : 1000 : 1200 = 4 : 5 : 6 Total capital = ₹15,000 Sum of ratio parts = 4 + 5 + 6 = 15 Jayanta’s capital = ₹\(\frac{4}{15} × 15,000 = 4,000\) Ajit’s capital = ₹\(\frac{5}{15} × 15,000 = 5,000\) Kunal’s capital = ₹\(\frac{6}{15} × 15,000 = 6,000\)

16. In a business, Sujay and Palash invested capital in the ratio 4:5 and shared profit in the ratio 2:3. If Sujay invested money for 10 months, how long did Palash invest his money?

17. 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.

18. 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?

19. 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?

20. 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.

21. In a partnership business, A, B, and C have invested in the ratio \( \frac{1}{6}:\frac{1}{5}:\frac{1}{4} \). At the end of the year, if the total profit is ₹3700, how much profit will B receive?

22. 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.

23. 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?

24. Rohit, Anish, and Soham started a business with capital investments of 1500 rupees, 1000 rupees, and 1750 rupees, respectively. At the end of the year, if the total profit is 425 rupees, how much profit did Anish receive?

(a) ₹ 100 (b) ₹ 150 (c) ₹ 200 (d) ₹ 400

25. 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?

26. 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.

27. In a joint business, three friends invested in the ratio 6 : 4 : 3. After 4 months, the first friend withdrew half of his capital. Four months later, the total profit became ₹61,050. How much profit does each of them receive?

28. Three friends collected ₹8000, ₹10000, and ₹12000 respectively and started a business after borrowing some amount from the bank. At the end of the year, they made a profit of ₹13,400. From this profit, they repaid the bank’s yearly installment of ₹5000. The remaining amount was divided among them in proportion to their capital investment. Write the calculation showing how much profit each friend will receive.

29. Puja, Uttam, and Meher started a partnership business by investing ₹5,000, ₹7,000, and ₹10,000 respectively, under the following conditions: (i) Monthly business operating expenses are ₹125. (ii) Puja and Uttam will each receive ₹200 per month for bookkeeping duties. At the end of the year, if the total profit is ₹6,960, calculate how much profit each person will receive.