BANK & INSURANCE (MIXTURE AND ALLIGATION) PART 2

Total Questions: 60

51. A vessel contains milk and water in the ratio of 11:4 respectively. If 30 liters of mixture is taken out and replaced with 33 liters of water, then the quantity of milk in the final mixture becomes 66.66%. Find the initial quantity of the mixture.

Correct Answer: (a) 360 liters 
Solution:

Let the quantity of milk in the initial mixture = 11x
And the quantity of water in the initial mixture = 4x

(11x - 30 × 11/15)/(4x - 30 × 4/15 + 33) = 2/1

(11x - 22) = (4x + 25) × 2
11x - 22 = 8x + 50
x = 24

Required initial quantity = (11 + 4) × 24 = 360 liters

52. 360 liters of mixture contains 75% of milk. If x liters of water are added to the mixture and the quantity of water in the resultant mixture becomes 32.5%, then find the value of x.

Correct Answer: (c) 40
Solution:

(360 × 75/100)/(360 × 25/100 + x) = 2.7/1.3

270 × 1.3 = (90 + x) × 2.7
351 = 243 + 2.7x
2.7x = 108
x = 40

53. Vessel A contains the mixture of milk and water in the ratio of 3:2 and vessel B contains the mixture of oil and water in the ratio of 4:3. If the quantity of vessel A and B is 5:14 and both vessels mixtures are mixed together, then what is the ratio of the milk, oil and water in the final solution?

Correct Answer: (e) None of these
Solution:Required ratio = (5x × 3/5) : (14x × 4/7) : (2/5 × 5x + 3/7 × 14x)
= 3 : 8 : 8

54. A vessel contains the mixture of apple and Orange juice in the ratio of 3:2. When 20 liters of Orange juice is added into the mixture, then the quantity of Orange juice in the resultant mixture is 80% of the total quantity of Apple juice in the final solution. Find the initial quantity of mixture

Correct Answer: (c) 250 liters
Solution:

3x/(2x + 20) = 100/80
10x + 100 = 12x
x = 50

Total quantity of mixture = 50 × 5 = 250 liters

55. A vessel contains 80 liters of oil. 20 liters of oil is taken out and replaced with the same quantity of water. This process is repeated 2 more times, find the final quantity of oil in the vessel.

Correct Answer: (a) 33.75 liters 
Solution:Quantity of oil = 80 × (1 - 20/80)³
= 33.75 liters

56. A vessel contains the mixture of milk and water in the ratio of 3:1 respectively. If 60 liters of water is added to the mixture, the quantity of milk in the mixture becomes 50% more than that of water. Then find the total quantity of milk in the initial mixture.

Correct Answer: (a) 180 liters 
Solution:

Let the quantity of milk in the initial mixture = 3x
And the quantity of water in the initial mixture = 1x

3x/(1x + 60) = 3/2
6x = 3x + 180
x = 60

The quantity of milk in the initial mixture
= 3 × 60 = 180 liters

57. A vessel contains milk and water in the ratio of 2:1. If 15 liters of mixture is taken out and replaced with water, then the ratio of milk and water becomes 7:5, then find the total quantity of mixture initially

Correct Answer: (b) 120 liters 
Solution:

Milk in the initial mixture = 2x
Water in the initial mixture = x

(2x - 15×2/3)/(x - 15×1/3 + 15) = 7/5
(2x - 10)/(x + 10) = 7/5
10x - 50 = 7x + 70
3x = 120
x = 40

Required total = (2 + 1) × 40 = 120 liters

58. A vessel contains milk and water in the ratio of 5:2 respectively. If 21 liters of mixture are taken out and 9 liters of water are added to the mixture, then the ratio of milk to water becomes 5:3, then find the quantity of milk in the final mixture.

Correct Answer: (d) 45 liters 
Solution:

Milk in mixture = 5x
Water in mixture = 2x

(5x - 21×5/7)/(2x - 21×2/7 + 9) = 5/3
(5x - 15)/(2x + 3) = 5/3
15x - 45 = 10x + 15
x = 60/5
x = 12

Required quantity of milk = 5×12 - 15 = 45 liters

59. Vessel A contains 96 liters of a mixture of milk and water in the ratio of 5:3 and the quantity of milk in vessel B is 60% of the total quantity of vessel B. If the quantity of water in vessel A is 24 liters less than that of vessel B, then find the quantity of milk in vessel B.

Correct Answer: (d) 90 liters 
Solution:

Milk in vessel A = 96×5/8 = 60 liters
Water in vessel A = 96 - 60 = 36 liters

Water in vessel B = 36 + 24 = 60 liters
Total quantity of vessel B = 60×100/40 = 150 liters
Milk in vessel B = 150 - 60 = 90 liters

60. A vessel contains the mixture of milk and water, the quantity of water in the vessel is half of the quantity of milk. If 15 liters of water is added to the mixture, then the water becomes 37.5%, then find the initial quantity of mixture.

Correct Answer: (d) 225 liters 
Solution:

Water in mixture = x
Milk in mixture = 2x

2x/(x + 15) = 5/3
6x = 5x + 75
x = 75 liters

Required initial mixture
= 75 + 75×2
= 225 liters