BANK & INSURANCE (MIXTURE AND ALLIGATION) PART 1

Total Questions: 60

51. A mixture of diesel and petrol contains 80% diesel. If 18 liters of petrol is added to the mixture, the quantity of petrol in the mixture becomes half the quantity of diesel in the resultant mixture. Find the initial quantity of mixture

Correct Answer: (b) 90 liters 
Solution:

Let the initial quantity of mixture be ‘x’ liters.
Initial quantity of diesel = 0.8x liters
Initial quantity of petrol = 0.2x liters

According to question,
2(0.2x + 18) = 0.8x
0.4x + 36 = 0.8x
0.4x = 36, x = 90 liters

So, the initial quantity of mixture = 90 liters

52. A mixture of milk and water is mixed in the ratio of 4:3, respectively. If 4 liters of water is added to the mixture, then the ratio of milk to water becomes 6:5, respectively. Find the initial quantity of milk in the mixture.

Correct Answer: (b) 48 liters 
Solution:

Let the initial quantity of milk and water be 4x liters and 3x liters respectively.
According to question,
4x/(3x + 4) = 6/5
20x = 18x + 24
2x = 24, x = 12

So, the initial quantity of milk in the mixture = 4x
= 48 liters

53. The percentage of milk in a mixture of 60 liters containing water and milk is 75%. Find the amount of water to be mixed in the mixture such that the percentage of milk is reduced to 50%.

Correct Answer: (d) 30 liters 
Solution:

Quantity of milk initially = 75% of 60 = 45 liters
Quantity of water initially = 60 − 45 = 15 liters

Let the quantity of water added be ‘x’.
45 = 50% of (60 + x)
90 = 60 + x
x = 30 liters

54. A mixture of milk and water contains ‘x’% of water. If the quantity of milk in the mixture is 16 liters more than the quantity of water and the total mixture is 80 liters, then find the value of ‘x’.

Correct Answer: (a) 40% 
Solution:

According to question,
(100 − x)% of 80 − x% of 80 = 16
(100 − 2x)% of 80 = 16
100 − 2x = 20
2x = 80, x = 40

So, the value of ‘x’ = 40%

55. Water and alcohol are mixed in an empty container in the ratio of 7:2, respectively. If 45 ml of mixture is replaced with 15 ml of water then, the ratio of water to alcohol becomes 4:1, respectively. Find the amount of water mixed initially.

Correct Answer: (a) 140 ml 
Solution:

Water and alcohol mixed initially be ‘7x’ ml and ‘2x’ ml, respectively.
So, (7x − 35 + 15)/(2x − 10) = 4/1
7x − 20 = 8x − 40
x = 20

So, the amount of water mixed initially = 7x
= 140 ml

56. A mixture of milk and water contains 45% water. If the total cost of milk present in the mixture at the rate of Rs. 21/liter is Rs. 2079, then find the additional amount of water to be used in the mixture such that quantity of milk and water becomes same.

Correct Answer: (b) 18 liters 
Solution:

Quantity of milk in the mixture initially = 2079/21
= 99 liters

Quantity of water in the mixture initially
= (99/0.55) × 0.45 = 81 liters

Let the additional amount of water used be ‘x’.
x + 81 = 99
x = 18 liters

57. A container contains 96 liters of mixture of water and milk in the ratio 3:5, respectively. If a person adds 4 liters of water in the mixture, then what will be the ratio of milk to water in the final mixture?

Correct Answer: (a) 3:2 
Solution:

Quantity of water initially = 96 × 3/8 = 36 liters
Quantity of milk initially = 96 × 5/8 = 60 liters

Final ratio = 60 : (36 + 4) = 60 : 40 = 3 : 2

58. A vessel contains mixture of milk and water mixed in the ratio 13:5 respectively. 72 liters of the mixture is taken out of the vessel and replaced with 51 liters of water such that the ratio of the milk to water in the vessel becomes 8:7 respectively, then find the initial quantity of water in the vessel.

Correct Answer: (c) 60 liters 
Solution:

Let the initial quantities of milk and water in the vessel be ‘13x’ liters and ‘5x’ liters, respectively.

Quantity of milk taken out = (13/18) × 72 = 52 liters
Quantity of water taken out = 72 − 52 = 20 liters

According to question,
(13x − 52)/(5x − 20 + 51) = 8/7
91x − 364 = 40x + 248
51x = 612
x = 12

So, the initial quantity of water in the vessel = 12 × 5 = 60 liters

59. In a container, the ratio of milk and water is 4:3. If a milkman adds 7 liters of milk into it then the ratio would change to 5:2. Calculate the amount of water present in the final mixture.

Correct Answer: (a) 6 liters
Solution:

Let the initial quantity of milk and water be 4x and 3x respectively

(4x + 7)/(3x) = 5/2
8x + 14 = 15x
7x = 14
x = 2

Amount of water in the initial and final mixture is same i.e. 3x = 6 liters

60. A mixture of diesel and petrol contains 80% petrol. If 25 liters of diesel is added to the mixture, the quantity of diesel in the resultant mixture becomes 40 liters, find the quantity of petrol initially.

Correct Answer: (b) 60 liters 
Solution:

Let the quantity of mixture initially be ‘x’ liters.
According to question,
0.2x + 25 = 40
0.2x = 15, x = 75

So, the quantity of petrol initially = 80% of 75
= 60 liters