BANK & INSURANCE (MIXTURE AND ALLIGATION) PART 1

Total Questions: 60

1. The vessel has 30 liters of mixture of milk and water in the ratio of 2:1. If 12 liters of mixture is replaced by water, then what is the ratio of the quantity of milk to water in the final mixture?

Correct Answer: (b) 2:3 
Solution:Milk in the vessel = 2/3 × 30 = 20 liters
Water in vessel = 1/3 × 30 = 10 liters
Milk in 12 liters of mixture = 12 × 2/3 = 8 liters
Water in 12 liters of mixture = 12 × 1/3 = 4 liters
Required ratio = (20 – 8):(10 – 4 + 12)
= 12:18
= 2:3

2. A milkman has 40 liters of pure milk and then he added 20 liters of the water in that pure milk. If he sold 18 liters of the mixture and then he replaced with water, then what is the ratio of the milk to water in the final mixture?

Correct Answer: (d) 7:8 
Solution:

Milk = 40 liters
Water = 20 liters
Milk and water = 40:20 = 2:1
Milk in 18 liters of mixture = 2/3 × 18 = 12 liters
Water in the 18 liter mixture = 1/3 × 18 = 6 liters
Milk in the final mixture = 40 – 12 = 28
Water in the final mixture = 20 – 6 + 18 = 32
Required ratio = 28:32
= 7:8

3. In 90 liters of the mixture of milk and water in the ratio of 7: 3. 20 liters of mixture is taken out and replaced with water. What is the ratio of the milk to water in the final mixture?

Correct Answer: (c) 49:41 
Solution:

Milk = 7/10 × 90 = 63
Water = 3/10 × 90 = 27
Milk in 20 liters of the mixture = 20 × 7/10 = 14
Water in 20 liters of the mixture = 20 × 3/10 = 6
Required ratio = (63 – 14)/(27 – 6 + 20)
= 49/41

4. In what ratio must two varieties of rice worth Rs. 30 per kg and Rs. 40 per kg so that selling the rice Rs. 51 per kg he may gain 50%?

Correct Answer: (a) 3:2 
Solution:

CP of the mixture = 51/150 × 100 = 34

(Using alligation)

30     40
..............34
6          4

The required ratio = 3 : 2

5. A milkman has the mixture of milk and water in the ratio 5: 3 and then he added 20 liters of the water, then the ratio of the milk and water becomes 15: 19. What is the initial quantity of water in the mixture?

Correct Answer: (c) 18 liters 
Solution:5x/(3x + 20) = 15/19
45x + 300 = 95x
50x = 300
x = 6 liters
Initial quantity of the water = 3 × 6 = 18 liters

6. A vessel contains 60 liters of the mixture of milk and water in the ratio of 2:1. If 24 liters of the mixture is taken out and replaced by water, then the quantity of the milk in the final mixture approximately what percent of the quantity of the water in the final mixture?

Correct Answer: (c) 66.67% 
Solution:Milk = 2/3 × 60 = 40
Water = 1/3 × 60 = 20
Milk in 24 liter = 2/3 × 24 = 16
Water in 24 liter = 1/3 × 24 = 8 liters
Final quantity of the milk = 40 – 16 = 24
Final quantity of the water = 20 – 8 + 24 = 36
Required percentage = 24/36 × 100 = 66.67%

7. The 80 liters of mixture contains 40% of Petrol and 60% of Kerosene. In how much liters of Petrol added to the mixture, if the percentage of the kerosene in the mixture becomes 40%?

Correct Answer: (b) 40 liters 
Solution:

Petrol = 40/100 × 80 = 32
Kerosene = 60/100 × 80 = 48
(32 + x)/48 = 60/40
2 × (32 + x) = 48 × 3
64 + 2x = 144
x = 40 liters

8. Jar contains 60 liters of milk and water in the ratio of 2:1. x liters of mixture is taken out and then 10 liters of the milk is added to the remaining mixture. Now the ratio of milk to water becomes is 11:4, then find the value of x?

Correct Answer: (b) 20 
Solution:

Milk in Jar A = 60 × 2/3 = 40 liters
Water in Jar A = 60 × 1/3 = 20 liters
Milk in x liter = x × 2/3
Water in x liter = x × 1/3
(40 – 2x/3 + 10) / (20 – x/3) = 11/4
(120 – 2x + 30) / (60 – x) = 11/4
660 – 11x = 600 – 8x
3x = 60
x = 20 liters

9. A jar contains 90 liters of the mixture of milk and water in the ratio of 5: 4 and 45 liters of the mixture is taken out. Then added x liters of the water in the remaining mixture, the ratio of the milk and water becomes 2: 3. Find the value of x?

Correct Answer: (b) 17.5 
Solution:

Milk = 5/9 × 90 = 50 liters
Water = 4/9 × 90 = 40 liters
Milk in 45 liters = 5/9 × 45 = 25 liters
Water in 18 liters = 4/9 × 45 = 20 liters
(50 – 25)/(40 – 20 + x) = 2/3
40 + 2x = 75
2x = 35
x = 17.5 liters

10. A Jar contains 5x liters of the mixture of milk and water in the ratio of 3: 2. 20 liters of the mixture is taken out. Then added 24 liters of the water in the remaining mixture, the ratio of the milk and water becomes 1: 2. Find the value of x?

Correct Answer: (b) 10 
Solution:Milk in 20 liters = 3/5 × 20 = 12 liters
Water in 20 liters = 2/5 × 20 = 8 liters
(3x – 12)/(2x – 8 + 24) = 1/2
2x + 16 = 6x – 24
4x = 40
x = 10 liters