1. 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.

2. The capital ratio of three people is 4:8:9, and the difference in profit between the first and third person is ₹200. What is the profit share of the second person?

3. In a partnership business, the capital ratio of three individuals is 3:8:5, and the profit of the first person is 70 rupees less than the profit of the third person. What was the total profit in the business?

4. In a business, the ratio of the capital investments of three friends is 5:8:12. If the profit of the first person is Rs. 700 less than the profit of the third person, find the profit of the second person.

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

6. In a joint business, the capital ratio of three individuals is 5:8:3, and the second person's profit is ₹100 more than the third person's. What is the total profit in the business?

7. 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.

8. 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?

9. In a partnership business, the capital contributions of three individuals are in the ratio 3:8:5. If the profit of the first person is ₹60 less than that of the third person, what was the total profit of the business?

10. In a partnership business, the capital ratio among three individuals is 3 : 8 : 5. If the first person’s profit is ₹60 less than the third person’s profit, calculate the total profit of the business.

11. In a partnership business between two people, the total profit is 150 rupees. If the first person's capital is 600 rupees and his profit is 90 rupees, what is the capital of the second person?

12. In a business, the ratio of capital invested by Raju and Asif is 5:4, and if Raju receives ₹80 from the total profit, Asif receives ₹100.

13. 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

14. In a partnership business, the capital ratio of three individuals is \(\cfrac{1}{4}:\cfrac{1}{3}:\cfrac{1}{8}\). If the second person's profit is ₹500 more than the third person's profit, then the total profit in the business was –?

15. 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 \(ax : by : cz\).

16. 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.

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. 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? .

19. 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 ______.

20. 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.

21. 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?

22. 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?

23. Three friends purchased a bus by investing ₹1,20,000, ₹1,50,000, and ₹1,10,000 respectively. The first person worked as the driver, and the other two worked as conductors. They agreed to divide \(\frac{2}{5}\) of the total monthly income based on work in the ratio 3:2:2, and the remaining amount based on their capital investment. If the monthly income is ₹29,260, calculate how much each person will receive.

24. 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.

25. In a joint business involving three individuals, the ratio of invested capital is 3:4:6, and the ratio of profit earned is 3:2:9. Then, the ratio of their invested time will be ..........

26. \[ \frac{1}{(x - 1)(x - 2)} + \frac{1}{(x - 2)(x - 3)} + \frac{1}{(x - 3)(x - 4)} = \frac{1}{6} \] This is a mathematical equation involving rational expressions. Here's the English translation of the statement: **"The sum of the following three fractions equals one-sixth:"** - The first fraction is: one divided by \((x - 1)(x - 2)\) - The second fraction is: one divided by \((x - 2)(x - 3)\) - The third fraction is: one divided by \((x - 3)(x - 4)\) And their total is equal to \(\frac{1}{6}\).

27. 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.

28. In a partnership business, the ratio of the capital contributions of A, B, and C is 3:8:5. If A’s profit is ₹6,000 less than C’s profit, then what is the total profit of the business?

29. In a joint business, A invests ₹600 more per month than B. B invests for \(7\cfrac{1}{2}\) months, while A invests for 2 months longer than B. If the total profit is ₹620 and B receives ₹140 less than A, what is the amount of B's capital investment?

(a) ₹ 2400 (b) ₹ 2700 (c) ₹ 3000 (d) ₹ 3500

30. In a partnership business, the capital ratio of A, B, and C is 3:4:5. If A's profit share is 60 rupees less than C's profit share, then what was the total profit in the business?