1. 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.

2. 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.

3. Under the condition that no interest will be charged if the money is repaid within two years, three friends borrowed ₹6000, ₹8000, and ₹5000 respectively from a cooperative bank to jointly purchase four cycle rickshaws. After two years, after deducting all expenses, their total income amounted to ₹30,400. They divided this income in proportion to their capital contributions and then repaid their individual bank loans. Now, calculate how much money each person will have left in hand and what the ratio of the remaining amounts will be.

4. 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 ..........

5. 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

6. In a partnership business, the capital ratio between A and B is 2:3, and the capital ratio between B and C is 6:5. If A's profit share is ₹400, what will be C's profit share?

(a) ₹ 500 (b) ₹ 600 (c) ₹ 700 (d) ₹ 800

7. If the ratio of the heights of two right circular cylinders is 1:2 and the ratio of their base circumferences is 3:4, then the ratio of their volumes will be 9:32.

8. 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?

9. In a business, if the capital ratio of A, B, and C is 2:3:5 and their time of investment ratio is 3:4:5, then in what ratio will the profit be distributed?

(a) 3:4:5 (b) 5:8:9 (c) 8:9:11 (d) 6:12:15

10. 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

11. The ratio of the total surface area of a sphere and a hemisphere with a unit radius will be 4:3.

12. The ratio of the base radii of a right circular cylinder and a right circular cone is 3:4, and the ratio of their heights is 2:3. What will be the ratio of the volumes of the cylinder and the cone?

13. The ratio of the capital investments of A, B, and C is 2:3:5, and the ratio of their investment durations is 3:4:5. Then, the profit will be distributed in the ratio _____.

14. "Four cylindrical concrete pillars each have a diameter of 17.5 cm and are to be plastered all around with a 3.5 cm thick layer of sand-cement mixture. If the mortar is prepared by mixing sand and cement in a 4:1 ratio, calculate and write how many cubic decimetres of cement will be required."

15. If the ratio of the radii of two vertical solid circular cylinders is 2:3, and the ratio of their heights is 5:3, then the ratio of their curved surface areas will be –

(a) 2:5 (b) 8:7 (c) 10:9 (d) 16:9

16. In a business, the ratio of Lalu and Bhulu's capital is 3:2. If Bhulu's investment period is 4 months, for how many months should Lalu invest so that the profit ratio becomes 9:4?

17. 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?

18. In a partnership business, if the capital ratio between Samir and Idris is 2:3, and the capital ratio between Idris and Jasmin is 4:5, then determine the capital ratio among all three of them.

19. In a partnership business, the capital ratio of Ram and Rahim is 3:4, and the capital ratio of Rahim and Jud is 5:6. If the annual profit is ₹590, how much will Rahim receive?

20. If the ratio of the heights of two right circular cones is 1:4 and the ratio of their radii is 2:1, then the ratio of their volumes will be ______.

21. 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

22. 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?

23. If the ratio of the radii of two solid right circular cones is 2:3 and the ratio of their heights is 5:3, then the ratio of their volumes will be 27:30.

24. 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

25. A, B, and C start a business where their capital ratio is \(\cfrac{1}{2} : \cfrac{1}{3} : \cfrac{1}{4}\). After 4 months, A withdraws half of their capital, and after another 8 months, the total profit is ₹2,024. How much will A receive?

(a) ₹ 900 (b) ₹ 836 (c) ₹ 700 (d) ₹ 736

26. In a business, the capital ratio of A and B is \(1:\frac{4}{5}\). If A's profit is 80 rupees, then B's profit will be 100 rupees.

27. If the capital ratio of A, B, and C is \(\frac{1}{6}:\frac{1}{5}:\frac{1}{4}\), then the profit distribution will be in the ratio 4:5:6.

28. If the volumes of two solid right circular cylinders are equal and their height ratio is 1:4, then their radius ratio will be—.

(a) \(2:1\) (b) \(\sqrt2:1\) (c) \(1:2\) (d) \(1:\sqrt2\)

29. In a partnership business, the ratio of A and B's capital is 2:3, and the ratio of B and C's capital is 4:5. If the difference in profit between A and C is ₹210, determine B's profit.

30. The ratio of the principal investments of A and B is 11:9. The difference in their entitled profits will be 10%.