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Mixtures and Alligation questions

Mixing prices and concentrations.

1. A 100 litre mixture has milk and water with 90% milk. If 15 litres of water is added, what percentage of the new mixture is water?

  1. 20.74%
  2. 16.31%
  3. 17.39%
  4. 21.74%
Answer

D. 21.74% Water = 10 L. After adding: 25 of 115 L = 21.74%.

2. In what ratio must rice costing ₹60/kg be mixed with rice costing ₹90/kg so that the mixture costs ₹70/kg?

  1. 1:2
  2. 1:1
  3. 6:9
  4. 2:1
Answer

D. 2:1 By alligation: (90 − 70):(70 − 60) = 20:10 = 2:1.

3. A 40 litre mixture has milk and water with 90% milk. If 20 litres of water is added, what percentage of the new mixture is water?

  1. 39%
  2. 38%
  3. 40%
  4. 44%
Answer

C. 40% Water = 4 L. After adding: 24 of 60 L = 40%.

4. In what ratio must rice costing ₹50/kg be mixed with rice costing ₹100/kg so that the mixture costs ₹90/kg?

  1. 1:1
  2. 1:4
  3. 5:10
  4. 4:1
Answer

B. 1:4 By alligation: (100 − 90):(90 − 50) = 10:40 = 1:4.

5. A 120 litre mixture has milk and water with 70% milk. If 5 litres of water is added, what percentage of the new mixture is water?

  1. 34.8%
  2. 32.8%
  3. 33.8%
  4. 30.8%
Answer

B. 32.8% Water = 36 L. After adding: 41 of 125 L = 32.8%.

6. In what ratio must rice costing ₹20/kg be mixed with rice costing ₹40/kg so that the mixture costs ₹30/kg?

  1. 1:2
  2. 2:1
  3. 1:1
  4. 2:4
Answer

C. 1:1 By alligation: (40 − 30):(30 − 20) = 10:10 = 1:1.

7. A 100 litre mixture has milk and water with 80% milk. If 10 litres of water is added, what percentage of the new mixture is water?

  1. 20.45%
  2. 25.27%
  3. 29.27%
  4. 27.27%
Answer

D. 27.27% Water = 20 L. After adding: 30 of 110 L = 27.27%.

8. In what ratio must rice costing ₹60/kg be mixed with rice costing ₹120/kg so that the mixture costs ₹80/kg?

  1. 2:1
  2. 6:12
  3. 1:1
  4. 1:2
Answer

A. 2:1 By alligation: (120 − 80):(80 − 60) = 40:20 = 2:1.

9. A 70 litre mixture has milk and water with 70% milk. If 5 litres of water is added, what percentage of the new mixture is water?

  1. 41.6%
  2. 34.67%
  3. 43.34%
  4. 31.2%
Answer

B. 34.67% Water = 21 L. After adding: 26 of 75 L = 34.67%.

10. In what ratio must rice costing ₹50/kg be mixed with rice costing ₹110/kg so that the mixture costs ₹100/kg?

  1. 5:1
  2. 1:1
  3. 1:5
  4. 5:11
Answer

C. 1:5 By alligation: (110 − 100):(100 − 50) = 10:50 = 1:5.

11. A 110 litre mixture has milk and water with 80% milk. If 10 litres of water is added, what percentage of the new mixture is water?

  1. 26.67%
  2. 21.34%
  3. 27.67%
  4. 25.67%
Answer

A. 26.67% Water = 22 L. After adding: 32 of 120 L = 26.67%.

12. In what ratio must rice costing ₹60/kg be mixed with rice costing ₹100/kg so that the mixture costs ₹90/kg?

  1. 1:1
  2. 6:10
  3. 1:3
  4. 3:1
Answer

C. 1:3 By alligation: (100 − 90):(90 − 60) = 10:30 = 1:3.

13. A 120 litre mixture has milk and water with 70% milk. If 10 litres of water is added, what percentage of the new mixture is water?

  1. 31.84%
  2. 35.38%
  3. 36.38%
  4. 38.92%
Answer

B. 35.38% Water = 36 L. After adding: 46 of 130 L = 35.38%.

14. In what ratio must rice costing ₹30/kg be mixed with rice costing ₹80/kg so that the mixture costs ₹50/kg?

  1. 2:3
  2. 3:8
  3. 1:1
  4. 3:2
Answer

D. 3:2 By alligation: (80 − 50):(50 − 30) = 30:20 = 3:2.

15. A 80 litre mixture has milk and water with 75% milk. If 15 litres of water is added, what percentage of the new mixture is water?

  1. 36.84%
  2. 33.16%
  3. 35.84%
  4. 27.63%
Answer

A. 36.84% Water = 20 L. After adding: 35 of 95 L = 36.84%.

16. In what ratio must rice costing ₹50/kg be mixed with rice costing ₹70/kg so that the mixture costs ₹60/kg?

  1. 1:1
  2. 2:1
  3. 5:7
  4. 1:2
Answer

A. 1:1 By alligation: (70 − 60):(60 − 50) = 10:10 = 1:1.

17. A 120 litre mixture has milk and water with 80% milk. If 5 litres of water is added, what percentage of the new mixture is water?

  1. 18.56%
  2. 23.2%
  3. 25.2%
  4. 24.2%
Answer

B. 23.2% Water = 24 L. After adding: 29 of 125 L = 23.2%.

18. In what ratio must rice costing ₹30/kg be mixed with rice costing ₹50/kg so that the mixture costs ₹40/kg?

  1. 2:1
  2. 1:1
  3. 3:5
  4. 1:2
Answer

B. 1:1 By alligation: (50 − 40):(40 − 30) = 10:10 = 1:1.

19. A 110 litre mixture has milk and water with 90% milk. If 10 litres of water is added, what percentage of the new mixture is water?

  1. 16.5%
  2. 21.88%
  3. 19.25%
  4. 17.5%
Answer

D. 17.5% Water = 11 L. After adding: 21 of 120 L = 17.5%.

20. In what ratio must rice costing ₹30/kg be mixed with rice costing ₹70/kg so that the mixture costs ₹40/kg?

  1. 1:3
  2. 3:1
  3. 1:1
  4. 3:7
Answer

B. 3:1 By alligation: (70 − 40):(40 − 30) = 30:10 = 3:1.

21. A 40 litre mixture has milk and water with 70% milk. If 10 litres of water is added, what percentage of the new mixture is water?

  1. 35%
  2. 53%
  3. 45%
  4. 44%
Answer

D. 44% Water = 12 L. After adding: 22 of 50 L = 44%.

22. In what ratio must rice costing ₹40/kg be mixed with rice costing ₹90/kg so that the mixture costs ₹70/kg?

  1. 2:3
  2. 1:1
  3. 3:2
  4. 4:9
Answer

A. 2:3 By alligation: (90 − 70):(70 − 40) = 20:30 = 2:3.

23. A 100 litre mixture has milk and water with 75% milk. If 20 litres of water is added, what percentage of the new mixture is water?

  1. 41.25%
  2. 37.5%
  3. 30%
  4. 46.88%
Answer

B. 37.5% Water = 25 L. After adding: 45 of 120 L = 37.5%.

24. In what ratio must rice costing ₹50/kg be mixed with rice costing ₹80/kg so that the mixture costs ₹70/kg?

  1. 2:1
  2. 5:8
  3. 1:1
  4. 1:2
Answer

D. 1:2 By alligation: (80 − 70):(70 − 50) = 10:20 = 1:2.

25. A 40 litre mixture has milk and water with 75% milk. If 15 litres of water is added, what percentage of the new mixture is water?

  1. 45.45%
  2. 36.36%
  3. 47.45%
  4. 43.45%
Answer

A. 45.45% Water = 10 L. After adding: 25 of 55 L = 45.45%.

26. In what ratio must rice costing ₹60/kg be mixed with rice costing ₹80/kg so that the mixture costs ₹70/kg?

  1. 1:2
  2. 6:8
  3. 2:1
  4. 1:1
Answer

D. 1:1 By alligation: (80 − 70):(70 − 60) = 10:10 = 1:1.

27. A 60 litre mixture has milk and water with 60% milk. If 5 litres of water is added, what percentage of the new mixture is water?

  1. 44.62%
  2. 43.62%
  3. 40.16%
  4. 53.54%
Answer

A. 44.62% Water = 24 L. After adding: 29 of 65 L = 44.62%.

28. In what ratio must rice costing ₹20/kg be mixed with rice costing ₹60/kg so that the mixture costs ₹50/kg?

  1. 2:6
  2. 3:1
  3. 1:3
  4. 1:1
Answer

C. 1:3 By alligation: (60 − 50):(50 − 20) = 10:30 = 1:3.

29. A 90 litre mixture has milk and water with 80% milk. If 20 litres of water is added, what percentage of the new mixture is water?

  1. 36.55%
  2. 32.55%
  3. 35.55%
  4. 34.55%
Answer

D. 34.55% Water = 18 L. After adding: 38 of 110 L = 34.55%.

30. In what ratio must rice costing ₹40/kg be mixed with rice costing ₹80/kg so that the mixture costs ₹70/kg?

  1. 1:1
  2. 3:1
  3. 4:8
  4. 1:3
Answer

D. 1:3 By alligation: (80 − 70):(70 − 40) = 10:30 = 1:3.

31. A 90 litre mixture has milk and water with 60% milk. If 10 litres of water is added, what percentage of the new mixture is water?

  1. 47%
  2. 51%
  3. 46%
  4. 41%
Answer

C. 46% Water = 36 L. After adding: 46 of 100 L = 46%.

32. In what ratio must rice costing ₹50/kg be mixed with rice costing ₹100/kg so that the mixture costs ₹80/kg?

  1. 5:10
  2. 2:3
  3. 1:1
  4. 3:2
Answer

B. 2:3 By alligation: (100 − 80):(80 − 50) = 20:30 = 2:3.

33. A 50 litre mixture has milk and water with 60% milk. If 10 litres of water is added, what percentage of the new mixture is water?

  1. 60%
  2. 40%
  3. 50%
  4. 49%
Answer

C. 50% Water = 20 L. After adding: 30 of 60 L = 50%.

34. In what ratio must rice costing ₹40/kg be mixed with rice costing ₹100/kg so that the mixture costs ₹70/kg?

  1. 4:10
  2. 1:2
  3. 1:1
  4. 2:1
Answer

C. 1:1 By alligation: (100 − 70):(70 − 40) = 30:30 = 1:1.

35. A 60 litre mixture has milk and water with 75% milk. If 10 litres of water is added, what percentage of the new mixture is water?

  1. 42.85%
  2. 35.71%
  3. 39.28%
  4. 32.14%
Answer

B. 35.71% Water = 15 L. After adding: 25 of 70 L = 35.71%.

36. In what ratio must rice costing ₹40/kg be mixed with rice costing ₹90/kg so that the mixture costs ₹50/kg?

  1. 4:9
  2. 4:1
  3. 1:4
  4. 1:1
Answer

B. 4:1 By alligation: (90 − 50):(50 − 40) = 40:10 = 4:1.

37. A 50 litre mixture has milk and water with 60% milk. If 5 litres of water is added, what percentage of the new mixture is water?

  1. 36.36%
  2. 50%
  3. 34.09%
  4. 45.45%
Answer

D. 45.45% Water = 20 L. After adding: 25 of 55 L = 45.45%.

38. In what ratio must rice costing ₹50/kg be mixed with rice costing ₹90/kg so that the mixture costs ₹70/kg?

  1. 1:1
  2. 5:9
  3. 1:2
  4. 2:1
Answer

A. 1:1 By alligation: (90 − 70):(70 − 50) = 20:20 = 1:1.

39. A 60 litre mixture has milk and water with 70% milk. If 15 litres of water is added, what percentage of the new mixture is water?

  1. 44%
  2. 46%
  3. 42%
  4. 55%
Answer

A. 44% Water = 18 L. After adding: 33 of 75 L = 44%.

40. In what ratio must rice costing ₹30/kg be mixed with rice costing ₹60/kg so that the mixture costs ₹40/kg?

  1. 1:1
  2. 3:6
  3. 2:1
  4. 1:2
Answer

C. 2:1 By alligation: (60 − 40):(40 − 30) = 20:10 = 2:1.

41. A 80 litre mixture has milk and water with 80% milk. If 20 litres of water is added, what percentage of the new mixture is water?

  1. 38%
  2. 27%
  3. 45%
  4. 36%
Answer

D. 36% Water = 16 L. After adding: 36 of 100 L = 36%.

42. In what ratio must rice costing ₹40/kg be mixed with rice costing ₹90/kg so that the mixture costs ₹60/kg?

  1. 1:1
  2. 2:3
  3. 4:9
  4. 3:2
Answer

D. 3:2 By alligation: (90 − 60):(60 − 40) = 30:20 = 3:2.

43. A 70 litre mixture has milk and water with 90% milk. If 10 litres of water is added, what percentage of the new mixture is water?

  1. 23.25%
  2. 21.25%
  3. 19.13%
  4. 20.25%
Answer

B. 21.25% Water = 7 L. After adding: 17 of 80 L = 21.25%.

44. In what ratio must rice costing ₹60/kg be mixed with rice costing ₹120/kg so that the mixture costs ₹110/kg?

  1. 1:5
  2. 6:12
  3. 5:1
  4. 1:1
Answer

A. 1:5 By alligation: (120 − 110):(110 − 60) = 10:50 = 1:5.

45. A 110 litre mixture has milk and water with 70% milk. If 10 litres of water is added, what percentage of the new mixture is water?

  1. 37.83%
  2. 32.25%
  3. 35.83%
  4. 39.41%
Answer

C. 35.83% Water = 33 L. After adding: 43 of 120 L = 35.83%.

46. In what ratio must rice costing ₹20/kg be mixed with rice costing ₹80/kg so that the mixture costs ₹40/kg?

  1. 2:8
  2. 1:2
  3. 1:1
  4. 2:1
Answer

D. 2:1 By alligation: (80 − 40):(40 − 20) = 40:20 = 2:1.

47. A 120 litre mixture has milk and water with 80% milk. If 10 litres of water is added, what percentage of the new mixture is water?

  1. 27.15%
  2. 26.15%
  3. 31.38%
  4. 24.15%
Answer

B. 26.15% Water = 24 L. After adding: 34 of 130 L = 26.15%.

48. In what ratio must rice costing ₹30/kg be mixed with rice costing ₹90/kg so that the mixture costs ₹70/kg?

  1. 3:9
  2. 1:1
  3. 2:1
  4. 1:2
Answer

D. 1:2 By alligation: (90 − 70):(70 − 30) = 20:40 = 1:2.

49. A 100 litre mixture has milk and water with 60% milk. If 5 litres of water is added, what percentage of the new mixture is water?

  1. 51.43%
  2. 34.29%
  3. 43.86%
  4. 42.86%
Answer

D. 42.86% Water = 40 L. After adding: 45 of 105 L = 42.86%.

50. In what ratio must rice costing ₹50/kg be mixed with rice costing ₹100/kg so that the mixture costs ₹70/kg?

  1. 2:3
  2. 5:10
  3. 3:2
  4. 1:1
Answer

C. 3:2 By alligation: (100 − 70):(70 − 50) = 30:20 = 3:2.

51. A solution contains 16 litres of water and 13 litres of syrup. How many litres of water must be added to obtain 26 litres of water?

  1. 11
  2. 10
  3. 13
  4. 15
Answer

B. 10 Required water addition = (16+10)−16 = 10 litres.

52. A solution contains 100 litres of water and 13 litres of syrup. How many litres of water must be added to obtain 108 litres of water?

  1. 18
  2. 8
  3. 7
  4. 11
Answer

B. 8 Required water addition = (100+8)−100 = 8 litres.

53. A solution contains 101 litres of water and 7 litres of syrup. How many litres of water must be added to obtain 110 litres of water?

  1. 16
  2. 10
  3. 7
  4. 9
Answer

D. 9 Required water addition = (101+9)−101 = 9 litres.

54. A solution contains 49 litres of water and 10 litres of syrup. How many litres of water must be added to obtain 51 litres of water?

  1. 12
  2. 1
  3. 2
  4. 5
Answer

C. 2 Required water addition = (49+2)−49 = 2 litres.

55. A solution contains 94 litres of water and 2 litres of syrup. How many litres of water must be added to obtain 108 litres of water?

  1. 4
  2. 17
  3. 12
  4. 14
Answer

D. 14 Required water addition = (94+14)−94 = 14 litres.

56. A solution contains 116 litres of water and 8 litres of syrup. How many litres of water must be added to obtain 121 litres of water?

  1. 3
  2. 7
  3. 5
  4. 12
Answer

C. 5 Required water addition = (116+5)−116 = 5 litres.

57. A solution contains 49 litres of water and 3 litres of syrup. How many litres of water must be added to obtain 60 litres of water?

  1. 9
  2. 11
  3. 13
  4. 18
Answer

B. 11 Required water addition = (49+11)−49 = 11 litres.

58. A solution contains 112 litres of water and 4 litres of syrup. How many litres of water must be added to obtain 125 litres of water?

  1. 13
  2. 11
  3. 15
  4. 8
Answer

A. 13 Required water addition = (112+13)−112 = 13 litres.

59. A solution contains 45 litres of water and 6 litres of syrup. How many litres of water must be added to obtain 60 litres of water?

  1. 15
  2. 25
  3. 18
  4. 17
Answer

A. 15 Required water addition = (45+15)−45 = 15 litres.

60. A solution contains 101 litres of water and 19 litres of syrup. How many litres of water must be added to obtain 106 litres of water?

  1. 5
  2. 7
  3. 8
  4. 2
Answer

A. 5 Required water addition = (101+5)−101 = 5 litres.

61. A solution contains 56 litres of water and 19 litres of syrup. How many litres of water must be added to obtain 66 litres of water?

  1. 3
  2. 13
  3. 5
  4. 10
Answer

D. 10 Required water addition = (56+10)−56 = 10 litres.

62. A solution contains 116 litres of water and 17 litres of syrup. How many litres of water must be added to obtain 131 litres of water?

  1. 17
  2. 15
  3. 25
  4. 22
Answer

B. 15 Required water addition = (116+15)−116 = 15 litres.

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