Ratio & Proportion, Alligation & Ages
1. If A:B = 3:4 and B:C = 2:5, find A:B:C.
2. In what ratio should rice costing ₹40 per kg be mixed with rice costing ₹60 per kg to get a mixture worth ₹50 per kg?
3. The present ages of A and B are in the ratio 3:5. After 10 years, their ages will be in the ratio 2:3. Find their present ages.
4. Three partners A, B, and C invest in the ratio 2:3:4. If the total profit is ₹27,000, find A's share.
5. A number is divided into two parts in the ratio 3:2. If the larger part is 60, find the smaller part.
6. Tea costing ₹80 per kg is mixed with tea costing ₹120 per kg. In what ratio should they be mixed to get a mixture worth ₹100 per kg?
7. A father is 4 times as old as his son. After 20 years, he will be twice as old as his son. Find their present ages.
8. If x varies directly as y, and x = 12 when y = 4, find x when y = 10.
9. Milk costing ₹25 per liter is mixed with milk costing ₹35 per liter to get a mixture worth ₹30 per liter. Find the ratio of mixing.
10. The ratio of present ages of two persons is 5:7. Five years ago, their ages were in the ratio 1:2. Find the sum of their present ages.
11. A invests ₹5000 for 12 months and B invests ₹8000 for 6 months. Find the ratio of their profits.
12. If x varies inversely as y, and x = 8 when y = 6, find x when y = 12.
13. Sugar costing ₹45 per kg is mixed with sugar costing ₹55 per kg to get a mixture worth ₹48 per kg. Find the ratio of mixing.
14. A mother is 3 times as old as her daughter. After 12 years, she will be twice as old as her daughter. Find their present ages.
15. If a:b = 2:3 and b:c = 4:5, find a:b:c.
16. Oil costing ₹70 per liter is mixed with oil costing ₹90 per liter to get a mixture worth ₹85 per liter. Find the ratio of mixing.
17. The present ages of two friends are in the ratio 4:5. Eight years ago, their ages were in the ratio 2:3. Find their present ages.
18. Three partners invest in the ratio 3:4:5. If the total profit is ₹36,000, find the share of the second partner.
19. If y varies directly as the square of x, and y = 18 when x = 3, find y when x = 6.
20. Coffee costing ₹120 per kg is mixed with coffee costing ₹160 per kg to get a mixture worth ₹140 per kg. Find the ratio of mixing.
21. A father is 3 times as old as his son. Fifteen years ago, the father was 4 times as old as his son. Find their present ages.
22. Three numbers are in the ratio 2:3:4. If their sum is 180, find the numbers.
23. A invests ₹6000 for 8 months and B invests ₹9000 for 4 months. Find the ratio of their profits.
24. If z varies inversely as the square of x, and z = 12 when x = 2, find z when x = 4.
25. Wheat costing ₹30 per kg is mixed with wheat costing ₹50 per kg to get a mixture worth ₹35 per kg. Find the ratio of mixing.
26. The present ages of two persons are in the ratio 7:9. Four years hence, their ages will be in the ratio 4:5. Find their present ages.
27. If p:q = 5:6 and q:r = 3:4, find p:q:r.
28. Ghee costing ₹200 per kg is mixed with ghee costing ₹300 per kg to get a mixture worth ₹220 per kg. Find the ratio of mixing.
29. A brother is twice as old as his sister. Six years ago, he was thrice as old as his sister. Find their present ages.
30. Three partners invest in the ratio 1:2:3. If the total profit is ₹24,000, find the share of the third partner.
31. If m varies directly as the cube of n, and m = 24 when n = 2, find m when n = 3.
32. Pulses costing ₹60 per kg are mixed with pulses costing ₹80 per kg to get a mixture worth ₹65 per kg. Find the ratio of mixing.
33. The present ages of A and B are in the ratio 2:3. Ten years hence, their ages will be in the ratio 3:4. Find their present ages.
34. A invests ₹4000 for 9 months and B invests ₹6000 for 6 months. Find the ratio of their profits.
35. If a varies inversely as the cube of b, and a = 8 when b = 2, find a when b = 4.
36. Spices costing ₹100 per kg are mixed with spices costing ₹150 per kg to get a mixture worth ₹120 per kg. Find the ratio of mixing.
37. A grandfather is 6 times as old as his grandson. Twenty years ago, he was 10 times as old as his grandson. Find their present ages.
38. Three numbers are in the ratio 3:5:7. If their sum is 225, find the largest number.
39. A invests ₹7000 for 10 months and B invests ₹5000 for 14 months. Find the ratio of their profits.
40. If x varies jointly as y and z, and x = 48 when y = 4 and z = 6, find x when y = 8 and z = 3.
41. Nuts costing ₹180 per kg are mixed with nuts costing ₹220 per kg to get a mixture worth ₹200 per kg. Find the ratio of mixing.
42. The present ages of two persons are in the ratio 6:8. Five years ago, their ages were in the ratio 5:7. Find their present ages.
43. If u:v = 4:7 and v:w = 2:3, find u:v:w.
44. Honey costing ₹250 per kg is mixed with honey costing ₹350 per kg to get a mixture worth ₹300 per kg. Find the ratio of mixing.
45. An uncle is 5 times as old as his nephew. Ten years hence, he will be 3 times as old as his nephew. Find their present ages.
46. Three partners invest in the ratio 5:7:8. If the total profit is ₹40,000, find the share of the second partner.
47. If p varies directly as q and inversely as r, and p = 18 when q = 6 and r = 2, find p when q = 9 and r = 3.
48. Almonds costing ₹400 per kg are mixed with almonds costing ₹600 per kg to get a mixture worth ₹480 per kg. Find the ratio of mixing.
49. A teacher is 4 times as old as her student. Eight years ago, she was 6 times as old as her student. Find their present ages.
50. Three numbers are in the ratio 4:6:9. If their sum is 114, find the smallest number.