1. 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?

2. A straight line parallel to side BC of \(\triangle\)ABC intersects AB and AC at points P and Q, respectively. If AQ = 2AP, then what is the ratio PB:QC?

(a) 1:2 (b) 2:1 (c) 1:1 (d) None of these

3. If the length, breadth, and height of a right rectangular prism are in the ratio 3:2:1 and its total surface area is 88 square centimeters, then what is its volume?

(a) 120 cubic cm (b) 64 cubic cm (c) 48 cubic cm (d) 24 cubic cm

4. A straight line parallel to side BC of triangle ∆ABC intersects sides AB and AC at points D and E respectively. If AD : BD = 3 : 5, then what is the ratio of the area of triangle ∆ADE to the area of trapezium DBCE?

5. 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

6. The volume of a cone is jointly proportional to the square of the radius of the base and its height. If the ratio of the radii of two cones is 2:3 and their heights are in the ratio 5:4, then find the ratio of their volumes.

7. 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?

8. 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?

9. The radius of a hemisphere and the height of a cone are equal. If their volumes are numerically equal, then what is the ratio of the radius of the hemisphere to the radius of the cone?

10. 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?

11. Three household kerosene oil drums contained 800 liters, 725 liters, and 575 liters of oil respectively. The oil from these three drums was poured into a rectangular container, which then had a liquid depth of 7 decimeters. If the ratio of the length to the breadth of the rectangular container is 4:3, calculate and write the length and breadth of the container. Also, if the depth of the container were 5 decimeters instead, determine whether it could hold 1620 liters of oil.

12. 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.

13. 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?

14. In a partnership business, if A, B, and C's capital ratio is 3:8:5 and A’s profit is 80 rupees less than C’s profit, then what was the total profit of the business?

15. 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

16. If the ratio of principal to interest-principal in a year is 8:9, then what is the annual simple interest rate?

(a) 12\(\cfrac{1}{2}\)% (b) 15\(\cfrac{1}{2}\)% (c) 12% (d) 15%

17. If the ratio of the principal and the total amount is 10:11, what is the annual interest rate?

(a) 10% (b) 11% (c) \(10\cfrac{1}{11}\)% (d) 12%

18. The volume of a right rectangular prism is 960 cubic centimeters. If the ratio of its length, width, and height is 6:5:4, what is the total surface area of the prism?

(a) 590 square cm (b) 592 square cm (c) 295 square cm (d) 596 square cm

19. A's amount is \(\cfrac{3}{4}\) of B's amount, and B's amount is \(1\cfrac{1}{5}\) times C's amount. What is the ratio of A's amount to C's amount?

(a) 19:20 (b) 10:9 (c) 9:10 (d) 20:19

20. If the volumes of two cones are in the ratio 2:3 and the ratio of their base radii is 1:2, then what is the ratio of their heights?

(a) 3:8 (b) 8:3 (c) 3:4 (d) 4:3

21. PQRS is a cyclic quadrilateral in which side QR is extended up to point T. If the measures of angles ∠SRQ and ∠SRT are in the ratio 4:5, then find the measures of ∠SPQ and ∠SRQ.

22. In a partnership business, A, B, and C invest capital in the ratio \(\frac{2}{3}:\frac{4}{5}:\frac{3}{4}\). If the total profit is ₹26,600, what is B's share of the profit?

23. The total surface area of a solid hemisphere and the curved surface area of a solid sphere are equal. What is the ratio of the radius of the hemisphere to the radius of the sphere?

24. If the ratio of the volumes of two cubes is 8:27, then what will be the ratio of their total surface areas?

25. A solid sphere and a solid cone have the same diameter, and their total surface areas are equal. What is the ratio of the cone's height to its diameter?

26. If the bases of two triangles lie on the same straight line and the other vertex of both triangles is common, then the ratio of their areas is ______to the ratio of the lengths of their bases.

27. A solid lead sphere with a diameter of 12 cm is melted down to form three smaller solid spheres. If the diameters of the smaller spheres are in the ratio 3 : 4 : 5, then what is the radius of each of the smaller spheres?

28. 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?

29. If the ratio of cost price to selling price is 10:11, then what will be the percentage profit?

(a) 10% (b) 20% (c) 25% (d) 15%

30. 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