1. 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.

2. 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?

3. 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.

4. 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?

5. 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.

6. 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?

7. 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?

8. 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?

9. 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.

10. A and B started a business by investing ₹12,500 and ₹8,500 respectively. They agreed that 40% of the profit would be shared equally, and the remaining 60% would be divided in proportion to their capital investments. If A's profit is ₹1950, what is B's profit?

11. 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.

12. 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.

13. 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.

14. 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?

15. 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) ₹\(\cfrac{xyz}{3x+y}\)

16. 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.

17. Amal and Bimal started a business. Amal invested ₹500 for 9 months, and Bimal invested some amount for 6 months in the business. The total profit in the business was ₹69, out of which Bimal received ₹46. The amount of capital invested by Bimal in the business is –

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

18. 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?

19. P started a business with a capital of ₹12,000. After a few months, Q joined the same business with a capital of ₹16,000. After 9 months from Q’s joining, both P and Q received equal amounts of profit. For how many months was P involved in the business?

(a) 6 months (b) 3 months (c) 9 months (d) 12 months

20. 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

21. Gautam and Samaresh started a joint business with ₹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 proportion to their investments. If Gautam received ₹1,950 as his share of the profit, determine Samaresh’s profit amount.

22. A and B start a business by investing 24,000 currency units and 30,000 currency units, respectively, at the beginning of the year. After 5 months, A contributes an additional 4,000 currency units. If the annual profit is 27,716 currency units, determine each person's share of the profit.

23. 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.

24. 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.

25. 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.

26. 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.

27. Two friends started a joint business with investments of ₹40,000 and ₹50,000 respectively. They agreed that 50% of the profit would be shared equally between them, and the remaining 50% would be divided in proportion to their capital contributions. If the first friend’s profit share is ₹800 less than the second friend’s, calculate the amount received by the first friend.

28. Amal and Bimal started a business together. Amal invested ₹500 for 9 months, and Bimal invested an unknown amount for 6 months. The total profit from the business was ₹69, and Bimal received ₹46 from the profit. Find Bimal’s capital investment in the business.

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

29. 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.