1. 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
2. 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
3. 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 ..........
4. In a partnership business, the capital ratio of three friends is \(\frac{1}{4} : \frac{1}{3} : \frac{1}{2}\). If the total profit after one year is ₹3,900, what will be each of their shares of the profit?
5. 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.
6. If the profit-sharing ratio of three friends in a partnership business is \(\cfrac{1}{2} : \cfrac{1}{3} : \cfrac{1}{4}\), then the ratio of their capital investment will be?
(a) 2:3:4 (b) 2:6:3 (c) 6:4:3 (d) 1:2:1
7. 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?
8. In a partnership business, three friends invested capital amounts of ₹4,500, ₹6,000, and ₹9,000 respectively. After a certain period, their profit shares will be in the same ratio as their investments: \[ \text{Profit Ratio} = 4500 : 6000 : 9000 = 3 : 4 : 6 \] So, their respective shares of profit will be in the ratio 3 : 4 : 6.
9. 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
10. 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?
11. 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.
12. 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?
13. 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.
14. In a business, the capital ratio of Raju and Asim is \( 4:5 \), and their profit ratio is \( 2:3 \). If Raju invested for 10 months, then for how long did Asim invest?
(a) 1 years (b) 2 years (c) 6 month (d) 3 years
15. If two individuals invest \(x\) rupees and \(y\) rupees in a business for \(z\) and \(w\) units of time, respectively, then their profit ratio will be:
(a) \(xw:yz\) (b) \(xz:wy\) (c) \(xy:wz\) (d) none of the above
16. 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.
17. In a partnership business, if the profit shares of three friends are in the ratio \(\frac{1}{2}:\frac{1}{3}:\frac{1}{4}\), then their capital ratio will be—
(a) 2:3:4 (b) 2:5:4 (c) 6:4:3 (d) 1:3:4
18. In a partnership business, the capital ratio of Reena, Beena, and Sabina is 8:3:5. If Beena's profit is ₹60 less than Sabina's profit, then what was the total profit in the business?
19. 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.
20. In a partnership business, Samir, Idrish, and Antony’s capital ratio is \(\frac{1}{6} : \frac{1}{5} : \frac{1}{4}\). At the end of the year, if the total profit is ₹3,700, calculate how much profit Antony will receive.
21. 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?
22. If Kamal’s capital is \(1\cfrac{1}{2}\) times that of Amal’s, then their profit-sharing ratio will be 2:3.
23. 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
24. 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
25. 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
26. 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?
27. 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.
28. 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?
29. 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?
30. 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.
