1. 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?

2. A and B started a business by investing ₹15,000 and ₹45,000 respectively. After 6 months, B received ₹3,030 as profit. What is A’s share of the profit?

3. 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?

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, 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.

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. 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?

8. 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.

9. 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?

10. 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.

11. 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.

12. In a partnership business, the capital ratio of A, B, and C is \(\frac{1}{6}:\frac{1}{5}:\frac{1}{4}\). If the total profit at the end of the year is 7400 rupees, what will be B's share of the profit?

13. 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.

14. In a right-angled quadrilateral, if the number of vertices is denoted by \(x\), the number of sides by \(y\), and the number of diagonals by \(z\), then what is the value of \(x + 3y - 5z\)?

(a) 14 (b) 44 (c) 20 (d) 24

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. 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.

17. 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?

18. 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?

19. 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

20. 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

21. 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

22. 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.

23. 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.

24. In a joint business, the total profit is 15,000 taka. If the first person's capital is 6,000 taka and their share of the profit is 9,000 taka, then what is the capital of the second person?

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. 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.

27. 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.

28. 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.

29. 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.

30. In a joint business, A contributes \(\frac{1}{2}\), B contributes \(\frac{1}{6}\), and the remaining portion is contributed by C. If the total profit in the business is ₹18,000, what is A’s share of the profit?