1. The current price of a machine is rupees 2P, and if its price decreases by 2r% each year, then after 2n years, the price of the machine will be: (a) \(P\left(1-\cfrac{r}{100}\right)^n\) (b) \(2P\left(1-\cfrac{r}{50}\right)^n\) (c) \(P\left(1-\cfrac{r}{50}\right)^{2n}\) (d) \(2P\left(1-\cfrac{r}{50}\right)^{2n}\)

2. Asit and Dipak invested ₹22,500 and ₹35,000 respectively in a joint business. If the total profit is ₹13,800, then Dipak's share of the profit will be — (a) ₹ 8400 (b) ₹ 8600 (c) ₹ 8200 (d) ₹ 8000

3. ₹4000 was distributed among A, B, and C. If A receives ₹4, B receives ₹5, and C receives ₹7, then A would receive ₹8. So, how much money will A actually receive? (a) ₹ 1120 (b) ₹ 1600 (c) ₹ 1280 (d) None of the above

4. 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

5. In a partnership business, Ratan, Suresh, and Ramesh invested in the ratio \(\frac{1}{6} : \frac{1}{5} : \frac{1}{4}\). If the profit at the end of the year is ₹3700, what is Ramesh's share of the profit? (a) ₹ 1400 (b) ₹ 1200 (c) ₹ 1500 (d) ₹ 1600

6. If Bimal invests ₹600 per month for 5 months and Tapan invests ₹500 per month for 9 months in a business, what will be the ratio of their profits? (a) 2:3 (b) 3:2 (c) 1:3 (d) 1:2

7. In a business, if A invests ₹5000 for 4 months, and B invests ₹4000 for 12 months, the ratio of A and B's investments will be – (a) 5:4 (b) 2:3 (c) 5:6 (d) 3:2

8. 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

9. Pallavi invests ₹500 for 9 months, and Rajiya invests ₹600 for 5 months in a business. The profit will be distributed between them in the ratio – (a) 3:2 (b) 5:6 (c) 6:5 (d) 9:5

10. A and B started a business together. A invested ₹500 for 9 months, and B invested his capital for 6 months. The total profit was ₹69, and B received ₹46 as his share of the profit. What was B’s capital? (a) ₹ 1550 (b) ₹ 1525 (c) ₹ 1500 (d) ₹1575

11. 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

12. 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) ₹\(\cfrac{xyz}{3x+y}\)

13. In a partnership business, the capital ratio of Ratan, Hira, and Ramesh is \(\cfrac{1}{6}:\cfrac{1}{5}:\cfrac{1}{4}\). If the total profit at the end of the year is 3700 rupees, what is Ramesh's share of the profit? (a) 1400 rupees (b) 1200 rupees (c) 1500 rupees (d) 1600 rupees

14. A and B made a profit in a joint business; if A’s capital was ₹600 and his share of the profit was ₹90, and B’s share of the profit was ₹60, then what was B’s capital? (a) ₹ 600 (b) ₹ 1000 (c) ₹ 400 (d) ₹ 800

15. A, B, and C made a joint business profit of ₹1,500. If A's capital : B's capital = 2 : 3 and B's capital : C's capital = 2 : 5, then C's share of the profit is... (a) ₹ 900 (b) ₹ 1000 (c) ₹ 1100 (d) ₹ 1200

16. 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

17. Amal invests ₹500 for 9 months, and Bimal invests ₹600 for 5 months in a business. Find the ratio in which the profit is distributed. (a) 3:02 (b) 5:06 (c) 6:05 (d) 9:05

18. A, B, and C started a joint business. A's invested amount is 3 times that of B, and C invested \(\frac{2}{3}\) of what B invested. What will be the ratio of the capital contributions of A, B, and C? (a) 6:2:3 (b) 2:6:3 (c) 3:6:2 (d) 6:3:2

19. If the profit-sharing ratio of two friends in a partnership business is \(\cfrac{1}{2}:\cfrac{1}{3}\), then their capital ratio is—? (a) 2 : 3 (b) 3:2 (c) 1:1 (d) 5:3

20. Fatima, Shreya, and Smita jointly started a business with a total investment of ₹6000. After one year, Fatima, Shreya, and Smita receive profits of ₹50, ₹100, and ₹150, respectively. Smita's investment in the business is: - (a) ₹ 1000 (b) ₹ 2000 (c) ₹ 3000 (d) ₹ 4000

21. A started a business with ₹10,000. After 6 months, B invested ₹20,000. At the end of the year, their profit shares will be equal. True / False

22. If the partners invest their capital for the same duration, it is called a mixed partnership business. True / False

23. A partnership business requires a minimum of 3 people. True / False

24. Toton invested 500 rupees for 9 months, and Mamon invested 600 rupees for 5 months in a business. Their profit ratio is 2:3. True / False

25. A partnership business requires at least 3 people. True / False

26. 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.

27. If A invests ₹500 for 9 months and B invests ₹600 for 5 months in a business, their profit ratio will be _____.

28. In a partnership business, if the capital ratio of three members is \(a : b : c\) and the time invested is in the ratio \(x : y : z\), then their profit ratio will be \(ax : by : cz\).

29. In a partnership business, the capital ratio of Ila, Rahima, and Bela is 3:8:5. If Ila’s profit is ₹600 less than Bela’s, then what was the total profit of the business?

30. In a certain business, A's capital is one and a half times that of B's capital. If B receives ₹1,500 as profit at the end of the year, how much profit will A receive?

31. In a partnership business, the total profit is 1400 rupees. If A's capital is 6000 rupees and his profit is 600 rupees, what is B's capital?

32. A, B, and C jointly started a business with ₹1,80,000. A invested ₹20,000 more than B, and B invested ₹20,000 more than C. Distribute the profit of ₹10,800 among them.

33. In a business, Pintu invested \(1\frac{1}{2}\) times the amount Aman did, and David invested \(2\frac{1}{2}\) times the amount Aman did. The ratio of the capital contributions of Aman, Pintu, and David will be: _____

34. In a joint business venture, one of the two friends invests ₹\(xyz\) for \(y\) months, while the other invests ₹\(y^2z\) for \(x\) months. At the end of the contract, their profit-sharing ratio will be \(x : y\).

35. In a business, A and B invested in the ratio of 3:2. After donating 5% of the total profit, B’s share of the profit is ₹798. What is the total profit?

36. In a joint business, both Samar and Mahim initially invested ₹20,000 each. After 6 months, Samar added ₹5,000 to his investment, while Mahim withdrew ₹5,000. If the total profit at the end of the year is ₹32,000, calculate each of their shares of the profit.

37. 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?

38. In a partnership business, the total profit is ₹1200. One partner invested ₹6000 and earned a profit of ₹900. Then, the capital invested by the other partner is ______.

39. 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?

40. In a partnership business, if the ratio of my sister's capital to mine is 2:3 and the ratio of my capital to my elder sister's is 7:9, then what is the ratio of my sister's, mine, and my elder sister's capital?

41. 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?

42. The ratio of the capital invested by three people is 4:7:9, and the profit of the first person is ₹100 less than the profit of the third person. What is the amount of profit earned by the second person?

43. 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 3700 currency units, determine C's profit.

44. In a business, the capital contributions of A, B, and C are in the ratio \[ \cfrac{1}{x} : \cfrac{1}{y} : \cfrac{1}{z} \] If there is a loss of ₹z at the end of the year, determine C's share of the loss.

45. 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.

46. 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?

47. 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?

48. In a business, if the ratio of the investments of A and B is \(\cfrac{1}{7} : \cfrac{1}{4}\), and the total profit at the end of the year is ₹11,000, determine their respective shares of the profit.

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

50. 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?

51. 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?

52. "A and B make a profit of ₹1,050 in a business. If A's capital is ₹900 and his share of the profit is ₹630, what is B's capital?"

53. Three individuals invested capital amounts of ₹200, ₹150, and ₹250 respectively. At the end of the year, if the first individual received a profit of ₹40, what was the total profit earned by the business? .

54. 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.

55. If Raima invests 600 rupees for 5 months and Susmita invests 500 rupees for 9 months in a business, their profit share ratio will be ______.

56. In a partnership business, the capital ratio of three individuals is 3:8:5, and the profit of the first person is ₹60 less than the profit of the third person. Find the total profit of the business.

57. Let the interest rate be \( r\% \). \(\therefore\) According to the question, \[ 5000\left(1+\cfrac{r}{100}\right)^2 = 5408 \] \[ \left(1+\cfrac{r}{100}\right)^2 = \cfrac{5408}{5000} = \cfrac{676}{625} \] \[ \left(1+\cfrac{r}{100}\right)^2 = \left(\cfrac{26}{25}\right)^2 \] \[ 1+\cfrac{r}{100} = \cfrac{26}{25} \] \[ \cfrac{r}{100} = \cfrac{26}{25} - 1 = \cfrac{1}{25} \] \[ r = \cfrac{100}{25} = 4 \] \(\therefore\) The interest rate is \( 4\% \).

58. 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?

59. 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.

60. 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?

61. In a partnership business, the capital ratio of Sameer, Idrish, and Anthony is \(\frac{1}{6} : \frac{1}{5} : \frac{1}{4}\). If the total profit at the end of the year is ₹3,700, find Anthony's share of the profit.