BANK & INSURANCE (MIXTURE AND ALLIGATION) PART 2

Total Questions: 60

41. 580 liter Juice has 75% of water. How much amount of water to be added into the juice, so that the quantity of water in the resultant juice becomes 80%?

Correct Answer: (d) 145 liters 
Solution:Water = 75% of 580 = 435 liters
Quantity of water to be added = x liters
(435 + x) = 80/100 × (580 + x)
=> x = 145 liters

42. Vessel contains 60 liters mixture of milk and water in the ratio of 3:2. If 25 liters of mixture is taken out and replaced by water and then the same quantity of mixture is taken out and replaced by water, then what is the final quantity of milk in the final mixture of the vessel?

Correct Answer: (a) 12.25 liters 
Solution:Milk in 60 liters = 60 × 3/5 = 36 liters
Water in 60 liters = 60 × 2/5 = 24 liters
Final Quantity of the milk = 36 × (1 - 25/60)²
= 12.25 liters

43. A milkman has 65 liters mixture of oil and water in the ratio of 8:5. If he added x liters of water in the mixture, then the ratio of the oil and water becomes 5:6. Find the value of x?

Correct Answer: (b) 23 
Solution:Initial Oil quantity = 8/13 × 65 = 40 liters
Water = 5/13 × 65 = 25 liters
40/(25 + x) = 5/6
125 + 5x = 240
5x = 115
x = 23 liters

44. A vessel contains 180 litres of a mixture of milk and water in the ratio of 3 : 2. 50 litres of mixture is taken out and filled with 18 litres of water. Then find the ratio between the milk and water in the new mixture?

Correct Answer: (d) 39 : 35 
Solution:

The ratio of milk and water in the vessel = 3 : 2
Quantity of milk in the vessel = (180 × 3/5) = 108 liters
Quantity of water in the vessel = (180 × 2/5) = 72 liters

Quantity of milk and water taken out
= (50 × 3/5) and (50 × 2/5)
=> 30 liters and 20 liters

Required ratio
=> (108 - 30) : (72 - 20 + 18)
=> 78 : 70
=> 39 : 35

45. A vessel contains 75 liters of mixture of apple juice and water in the ratio 3 : 2. 40 liters of mixture is taken out and replaced with same quantity of apple juice, and then find the ratio of apple juice to water in the resultant mixture.

Correct Answer: (b) 61 : 14 
Solution:Apple juice in the resultant mixture = 3/5 × (75 - 40) + 40 = 61 liters
Water in the resultant mixture = 2/5 × (75 - 40) = 14 liters
Required ratio = 61 : 14

46. In a vessel, there are two liquids P and Q in the ratio 5:9, 28 liters of the mixture is taken out and 2 liters of type Q liquid is poured into it, then the new ratio of liquids Q and P thus formed is 2:1, find the initial quantity of mixture in the vessel?

Correct Answer: (b) 56 liters 
Solution:

Let the initial quantity of liquids P and Q are 5x, 9x
As per above statement,

5x - 5(28/14)
────────── = 1/2
9x - 9(28/14)×2

5x - 10/9x - 16 = 1/2

x = 4

Total initial quantity of mixture = 5x + 9x = 14 × 4 = 56 litres

47. A vessel contains the mixture of Apple pulp and milk and the milk in the mixture is 40%. How much of the mixture is taken out and replaced with milk and the resulting mixture contains quantity of Apple pulp and milk is reverse of the initial quantity of the apple pulp and Milk?

Correct Answer: (d) 33(1/3)% 
Solution:

Let Total quantity of mixture = 5x
Apple pulp = 60/100 × 5x = 3x
Milk = 40/100 × 5x = 2x

(3x - 3y/5)/(2x - 2y/5 + y) = 2x/3x

20x + 6y = 45x - 9y
25x = 15y
x/y = 3/5

Required percentage = (5x/3)/5x × 100
= 33(1/3)%

48. Alloy A contains the mixture of zinc and copper in the ratio of 5:4. Alloy B contains the mixture of zinc and copper in the ratio of 3:2. If the mixture of alloy B is added to alloy A and the quantity of the zinc in the resultant mixture is 135 gram, then find the initial quantity of alloy A?

Correct Answer: (e) Cannot be determined
Solution:Initial quantity of Alloy A and B is not given
We cannot find the answer.

49. A milkman has 45 liters mixture of milk and water. If he sold seven-tenth of the milk and two-fifth of the water, then the milkman has half of the mixture. Find the initial quantity of milk?

Correct Answer: (b) 15 liters 
Solution:

Quantity of milk = x
Quantity of water = y
x + y = 45 -----(1)
x × 7/10 + y × 2/5 = 45/2
7x + 4y = 45 × 5 -----(2)

From (1) and (2)
3y = 90
y = 30
x = 45 - 30 = 15 liters

50. A 224 liters of mixture contains milk and water in the ratio of 9:7, if mixture B contains milk and water in the ratio of 17:11 is added to the former one, then the ratio of water and milk becomes 3:4, then find the quantity of mixture B?

Correct Answer: (b) 56 liters 
Solution:

Initial quantity of milk in the mixture
= (9/16) × (224) = 126 liters
Therefore remaining (224 - 126) = 98 liters are water.

Let capacity of another mixture is 28x.

Therefore,
(126 + 17x)/(98 + 11x) = 4/3

378 + 51x = 392 + 44x
7x = 14
x = 2

Quantity of the mixture B = 11x + 17x = 28x
= 56 liters