Mixture and Alligation

Mixture and Alligation Problems for Bank Clerk Prelims | Download PDF

Mixture and alligation problems for bank clerk prelims pdf is available here. In the quantitative aptitude section, candidates will skip most of the application sums in exams. Mixture and alligation is one of the topics in the application sums. In the bank clerk prelims exams, you should not take much time for a single question. For that, heavy practice is needed. If you practice well, you can easily solve the question in around a minute. So, practice more using the Mixture and alligation problems for bank clerk prelims pdf. Here we have provided more Mixture and alligation questions of various models. Hence, you can learn a lot of tricks to solve the problem.

In the Mixture and alligation problems, there are various types such as dishonest seller, mixture of qualities, etc. In this Mixture and alligation problems for bank clerk prelims pdf, you can practice all these types of questions.

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Start Quiz

 

1) Vessel A contains 60 liters mixture of milk and water in the ratio of 3:2. If 20 liters of mixture is taken out, then find the ratio of the milk and water in the final mixture?

A.3:2

B.2:1

C.4:3

D.5:4

E.1:1


2) Vessel A contains the mixture of milk and water in the ratio of 3:2. If 20 liters are taken out and added 4 liters of water, then the ratio of the milk and water becomes 6:5. Find the initial quantity of the mixture?

A.50

B.40

C.80

D.60

E.90


3) A vessel contains 60 liters mixture of milk and water in the ratio of 7:5. If certain quantity of mixture is taken out and filled with 13 liters of water, then the ratio of the water and milk becomes 4:3, then find the quantity of water in the final solution?

A.20 liters

B.24 liters

C.28 liters

D.32 liters

E.None of these


4) A mixture of oil and water contains 40% water. If 6 liters of oil is taken out from the mixture, then the quantity of oil and water becomes same, then find the initial quantity of the mixture?

A.30 liters

B.40 liters

C.45 liters

D.50 liters

E.None of these


5) Vessel A contains 60 liters mixture of milk and water in the ratio of 3:2 and vessel B contains x liters mixture of milk and water in the ratio of 5:4. If vessel A and B are mixed, then the ratio of the milk and water in the resultant mixture is 7:5. Find the value of x?

A.45

B.54

C.36

D.90

E.72


6) A Jar contains a 120 liters mixture of oil and water in the ratio of 3:2. If 25% of the mixture is taken out and replaced with water, then find the ratio of oil and water in the final solution?

A.9:11

B.1:2

C.3:4

D.7:11

E.2:1


7) A vessel contains a mixture of milk and water, containing 45% of water. 120 liters of mixture is taken out from the vessel and filled with 4 liters of water and then the quantity of the milk in the final solution is 10% more than that of water. Find the quantity of water in the final solution?

A.30 liters

B.40 liters

C.50 liters

D.60 liters

E.70 liters


8) Vessel A contains 75 liters mixture of milk and water and the quantity of water is 32% of the total quantity of mixture. Vessel B contains 90 liters mixture of milk and water and the quantity of milk is 175% more that of the water. If vessel A and B mixture are mixed together and then added x liters of water and now the ratio of the milk and water in the final mixture becomes 2:1, find the value of x?

A.12.5

B.10.5

C.13.5

D.14.5

E.16.5


9) A vessel contains 180 liters mixture of milk and water is in the ratio of 2: 1. How much quantity of water should be added, so that the percentage of milk in the vessel becomes 60% of the total mixture?

A.10 liters

B.20 liters

C.15 liters

D.25 liters

E.None of these


10) A mixture contains oil and water in the ratio of 5:3. If 120 liters of mixture is taken out and 25 liters of oil and 5 liters of water is added in the remaining mixture, then the ratio of the oil to water becomes 2:1. Find the initial quantity of mixture?

A.160 liters

B.200 liters

C.240 liters

D.280 liters

E.320 liters


Answers :

1) Answer: A

Milk in 60 liters = 3/5 * 60 = 36 liters

Water in 60 liters = 2/5 * 60 = 24 liters

Milk in 20 liters = 3/5 * 20 = 12 liters

Water in 20 liters = 2/5 * 20 = 8 liters

Required ratio = (36 – 12):(24 – 8)

= 24:16

= 3:2


2) Answer: D

Milk in 20 liters = 3/5 * 20 = 12 liters

Water in 20 liters = 2/5 * 20 = 8 liters

(3x – 12)/(2x – 8 + 4) = 6/5

15x – 60 = 12x – 24

x = 12

Quantity of mixture = 12 * 5 = 60 liters


3) Answer: C

Milk in 60 liters = 60 * 7/12 = 35

Water in 60 liters = 60 * 5/12 = 25

(35 – 7x/12)/(25 – 5x/12 + 13) =3/4

114 – 5x/4 = 140 – 7x/3

7x/3 – 5x/4 = 26

x = 24

Final quantity of water = 25 – (5 * 24/12) + 13 = 28 liters


4) Answer: A

Initial quantity of mixture = 100x

Oil = 100x * 60/100 = 60x

Water = 40/100 * 100x = 40x

(60x – 6)/40x = 1/1

60x – 6 = 40x

20x = 6

100x = 6 * 5 = 30


5) Answer: C

Milk vessel A = 60 * 3/5 = 36

Water in vessel A = 60 * 2/5 = 24

(36 + 5x/9)/(24 + 4x/9) = 7/5

168 + 28x/9 = 180 + 25x/9

3x/9 = 12

x = 36


6) Answer: A

Oil = 3/5 * 120 = 72 liters

Water = 2/5 * 120 = 48 liters

25% of mixture = 25/100 * 120 = 30

Oil in 30 liters = 30 * 3/5 = 18

Water in 30 liters = 30 * 2/5 = 12

Required ratio = (72 – 18): (48 – 12 + 30)

= 54:66

= 9:11


7) Answer: B

The initial quantity of milk = 55x

The initial quantity of water = 45x

Milk in 120 liters = 55/100 * 120 = 66 liters

Water in 120 liters = 45/100 * 120 = 54 liters

(55x – 66)/(45x – 54 + 4) = 110/100

495x – 550 = 550x – 660

x = 2

Final quantity of water = 45 * 2 – 50 = 40 liters


8) Answer: B

Milk in Vessel A = 75 * 68/100 = 51

Water in Vessel A = 75 * 32/100 = 24

Ratio of milk and water in B = 275:100 = 11:4

Milk in Vessel B = 90 * 11/15 = 66

Water in Vessel B = 90 * 4/15 = 24

(51 + 66)/(24 + 24 + x) = 2/1

96 + 2x = 117

x = 10.5


9) Answer: B

Milk = 2/3 * 180 = 120Liters

Water = 180 – 120 = 60Liters

120 = (180 + x) * 60%

12000=10800+60x

1200=60x

=> x = 20Liters


10) Answer: C

Initial quantity = 8x

Oil = 5x

Water = 3x

Oil in 120 liters = 120 * 5/8 = 75 liters

Water in 120 liters = 120 * 3/8 = 45 liters

(5x – 75 + 25)/(3x – 45 + 5) = 2/1

6x – 80 = 5x – 50

x = 30

Initial quantity = 8 * 30 = 240 liters

 

Start Quiz

 

11) Vessel A contains 60 liters mixture of milk and water in the ratio of 3:2 and vessel B contains x liters mixture of milk and water in the ratio 6:5. If vessel A and B’s mixture is mixed, then the ratio of the milk and water in the resultant solution is 15:11, then find the value of x?

A.33

B.44

C.55

D.66

E.None of these


12) The vessel contains 45 liters of milk and water in the ratio of 5:4. If x liters of water is added to the mixture and the ratio of the water and milk ratio becomes 5:4, then find the value of x?

A.12.5

B.13.5

C.11.5

D.10.5

E.None of these


13) A vessel has 30 liters mixture of milk and water in the ratio of 3: 2. If x liters of water and 22 liters of milk added to the mixture, then the ratio of the milk to water becomes 4: 5. Find the value of x?

A.28

B.18

C.36

D.45

E.None of these


14) If vessel A contains the mixture of milk and water in the ratio of 4: 3 and vessel B contains 60 litres of mixture of milk and water in the ratio of 7: 5. If the vessel A and B’s mixture is mixed, then the ratio of the milk to water becomes 11: 8, then find the initial quantity of mixture in vessel A?

A.35 litres

B.28 litres

C.56 litres

D.63 litres

E.None of these


15) How many Kg of sugar costing Rs.36/kg must be mixed with 20 kg of sugar costing Rs.50/kg, so that the shopkeeper obtained a profit of 25% by selling the mixture at Rs.50/kg?

A.40 kg

B.30 kg

C.50 kg

D.60 kg

E.None of these


16) A Jar contains 40 liters mixture of milk and water in the ratio of 3: 2 and x liters of mixture is taken out and 20 liters of water added, then the ratio of the milk and water becomes 3: 7. Find the value of x?

A.10

B.15

C.20

D.25

E.None of these


17) A milkman has 45 liters mixture of milk and water in the ratio of 3: 2. If he sold x liters of mixture and replaced by water, then the ratio of milk and water becomes 1: 2, find the value of x?

A.15 liters

B.10 liters

C.30 liters

D.20 liters

E.None of these


18) Vessel A, B and C contains the mixture of milk and water in the ratio of 3:2, 5:4 and 2:1 respectively. If all the vessel mixtures are mixed, then find the ratio of milk and water in the final mixture?

A.82:53

B.82:55

C.80:53

D.81:53

E.None of these


19) A vessel contains the mixture of milk and water in the ratio of 4: 1. If 25 liters of water is added to the vessel, then the ratio of the milk and water becomes 16: 9, what is the initial quantity of the mixture?

A.50 liters

B.75 liters

C.100 liters

D.150 liters

E.None of these


20) A vessel contains 60 liters milk. If x liters of milk is taken out and replaced by water, this process is repeated two more times and then the quantity of the water in the vessel is 29.28 liters, find the value of x?

A.10

B.12

C.15

D.18

E.20


Answers :

11) Answer: B

Milk in vessel A = 3/5 * 60 = 36 liters

Water in vessel A = 2/5 * 60 = 24 liters

(36 + 6x/11)/(24 + 5x/11) = 15/11

(396 + 6x) * 11 = 15 * (264 + 5x)

396 = 9x

x = 44 liters


12) Answer: E

Milk = 5/9 * 45 = 25 liters

Water = 4/9 * 45 = 20 liters

25/(20 + x) = 4/5

80 + 4x = 25 * 5

4x = 45

x = 11.25 liters


13) Answer: E

Milk = 3/5 * 30 = 18 liters

Water = 2/5 * 30 = 12 liters

(18 + 22)/(12 + x) = 4/5

40/(12 + x) = 4/5

x = 38 liters


14) Answer: A

Milk in vessel B = 7/12 * 60 = 35 liters

Water in vessel B = 5/12 * 60 = 25 liters

Let us take the quantity of mixture in vessel A be x

(4x/7 + 35)/(3x/7 + 25) = 11/8

33x/7 + 275 = 32x/7 + 280

x/7 = 5

x = 35 litres


15) Answer:  C

CP of the mixture = 50/125 * 100 = 40

= (50 – 40): (40 – 36) = 10: 4 = 5: 2

5: 2 = x: 20

x = 50 kg


16) Answer: C

Milk in 40 liters = 3/5 * 40 = 24 liters

Water in 40 liters = 2/5 * 40 = 16 liters

(24 – (3x/5))/(16 – (2x/5) + 20) = 3/7

(120 – 3x)/(180 – 2x) = 3/7

540 – 6x = 840 – 21x

15x = 300

x = 20 liters


17) Answer: D

Milk in 45 liters = 3/5 * 45 = 27 liters

Water in 45 liters = 2/5 * 45 = 18 liters

(27 – 3x/5)/(18 – 2x/5 + x) = ½

90 – 2x + 5x = 270 – 6x

9x = 180

x = 20 liters


18) Answer: A

Required ratio = (3/5 + 5/9 + 2/3):(2/5 + 4/9 + 1/3)

= (27 + 25 + 30):(18 + 20 + 15)

= 82:53


19) Answer: C

4x/(x + 25) = 16/9

16x + 25 * 16 = 36x

20x = 400

x = 20

Total quantity = 20 * 5 = 100 liters


20) Answer: B

60 * (1 – (x/60))3 = 60 – 29.28

60 * (1 – (x/60))3 = 30.72

(1 – x/60)3 = 512/1000

1 – x/60 = 8/10

x = 12 liters

 

Start Quiz

 

21) Ratio of the mixture of milk and water in Jar A is 3:2 and the ratio of the mixture of milk and water in Jar B is 4:3. If both mixtures are mixed in Jar C, then what is the ratio of the milk and water in Jar C?

A.44:29

B.41:27

C.41:29

D.43:29

E.None of these


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

A.40

B.50

C.60

D.30

E.None of these


23) Vessel A contains 70 liters mixture of milk and water in the ratio of 4:1 and vessel B contains 90 liters mixture of milk and water in the ratio of 5:4. If both mixtures are mixed, then what is the percentage of the milk in the final mixture?

A.72.67%

B.66.25%

C.59.50%

D.48.72%

E.None of these


24) How many litres of water should be added to 80 litres of mixture containing milk and water in the ratio of 3: 2, such that the resultant mixture has 50 % milk in it?

A.24 litres

B.20 litres

C.28 litres

D.16 litres

E.None of these


25) A milkman has the mixture of milk and water in the ratio of 5:3. If he sold 16 liters of the mixture and added 16 liters of the water to the mixture, so the ratio becomes 15:17. What is the initial quantity of the mixture?

A.48 liters

B.56 liters

C.64 liters

D.80 liters

E.None of these


26) A Vessel contains 60 liters of milk and water in the ratio of 4: 1. If 20 liters of mixture is taken out, then x liters of the milk are added to the remaining mixture, now the ratio of milk to water becomes is 5: 1. Find the value of x?

A.12

B.8

C.6

D.10

E.None of these


27) A milkman has 64 liters mixture of milk and water in the ratio of 5: 3. X liters of mixture taken out and replaced with water, now the resultant ratio of the milk to water is 25: 39. Find the value of x?

A.8

B.16

C.32

D.24

E.None of these


28) How many kg of variety 1 rice costing Rs. 52/kg should mixed with 25 kg of variety 2 rice costing Rs. 58 per kg, so that he makes a profit of 25% on selling the mixture at Rs. 67.5/kg?

A.40 kg

B.60 kg

C.50 kg

D.70 kg

E.None of these


29) A milkman has 80 litres mixture of milk and water in the ratio of 11: 9. If he sold 40 litres of mixture and then he filled with 8 liters of milk and x litres of water, now the ratio of the milk and water is 1: 1. Find the value of x?

A.10 litres

B.12 litres

C.14 litres

D.16 litres

E.None of these


30) A vessel contains the mixture of milk and water in the ratio of 5: 4. If 36 liters of mixture is taken out and then 10 liters of water added to the remaining mixture, now the ratio of the milk and water becomes 5: 6. Find the initial quantity of the mixture?

A.36 liters

B.45 liters

C.63 liters

D.81 liters

E.None of these


Answers :

21) Answer: C

Milk in Jar A = 3/5

Water in Jar A = 2/5

Milk in Jar B = 4/7

Water in Jar B = 3/7

Milk and water in Jar C = (3/5 + 4/7):(2/5 + 3/7)

=(21 + 20):(14 + 15)

= 41:29


22) Answer: B

Milk in 20 litres = 3/5 * 20 = 12 litres

Water in 20 litres = 2/5 * 20 = 8 litres

(3x – 12)/(2x – 8 + 24) = 1/2

2x + 16 = 6x – 24

4x = 40

x = 10 litres

Total mixture = 5 * 10 = 50 litres


23) Answer: B

Milk in vessel A = 70 * 4/5 = 56 liters

Milk in vessel B = 90 * 5/9 = 50 liters

Required percentage = [(56 + 50)/(70 + 90)] *100

= 66.25%


24) Answer: D

Total mixture = 80 litres

The milk and water in the ratio = 3: 2

Milk = (80/5) * 3 = 48 litres, Water = (80/5) * 2 = 32 litres

Given,

48/(32 + x) = 1/1

48 = 32 + x

x = 48 – 32 = 16 litres


25) Answer: C

Milk in 16 liters = 5/8 * 16 = 10 liters

Water in 16 liters = 3/8 * 16 = 6 liters

(5x – 10) / (3x – 6 + 16) = 15/17

45x + 150 = 85x – 170

40x = 320

x = 8 liters

Total quantity of the mixture = 8 * 8 = 64 liters


26) Answer: B

Milk = 60 * 4/5 = 48 liters

Water = 60 * 1/5 = 12 liters

Milk in 20 liters = 20 * 4/5 = 16 liters

Water in 20 liters = 20 * 1/5 = 4 liters

(48 – 16 + x)/(12 – 4) = 5/1

40 = 32 + x

x = 8 liters


27) Answer: D

Milk = 5/8 * 64 = 40 liters

Water – 3/8 * 64 = 24 liters

(40 – 5x/8) / (24 – 3x/8 + x) = 25/39

(320 – 5x) * 39 = 25 * (192 + 5x)

12480 – 195x = 4800 + 125x

320x = 7680

x = 24 liters


28) Answer: C

CP of mixture = (67.5 *100)/125 = Rs. 54

= > 2 : 1

Total kg of variety 1 rice = 25 * 2 = 50 kg


29) Answer: B

Milk in 80 litres = 11/20 * 80 = 44 litres

Water in 80 litres = 9/20 * 80 = 36 litres

Milk in 40 litres = 11/20 * 40 = 22 litres

Water in 40 litres = 9/20 * 40 = 18 litres

(44 – 22 + 8)/(36 – 18 + x) = 1/1

30 = 18 + x

x = 12 litres


30) Answer: D

Milk in 36 liters = 36 * 5/9 = 20 liters

Water in 36 liters = 36 * 4/9 = 16 liters

(5x – 20)/(4x – 16 + 10) = 5/6

20x – 30 = 30x – 120

10x = 90

x = 9 liters

Total quantity = 9 * 9 = 81 liters

 

Start Quiz

 

31) 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?

A.1:2

B.2:3

C.3:4

D.4:5

E.1:1


32) 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?

A.1:2

B.3:4

C.5:6

D.7:8

E.None of these


33) 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?

A.35:31

B.28:21

C.49:41

D.77:71

E.None of these


34) 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%?

A.3: 2

B.1: 2

C.3: 4

D.4: 7

E.3: 5


35) 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?

A.12 liters

B.15 liters

C.18 liters

D.21 liters

E.None of these


36) 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?

A.33.33%

B.44.44%

C.66.66%

D.77.77%

E.22.22%


37) 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%?

A.30 liters

B.40 liters

C.20 liters

D.50 liters

E.None of these


38) 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?

A.15

B.20

C.30

D.25

E.None of these


39) A Jar contains 90 litres of the mixture of milk and water in the ratio of 5: 4 and 45 litres 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?

A.18

B.17.5

C.16

D.15.5

E.14.5


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

A.15

B.10

C.20

D.30

E.None of these


Answers :

31) Answer: B

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


32) Answer: D

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


33) Answer: C

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


34) Answer: A     

CP of the mixture = 51/150 * 100 = 34

The required ratio = 3: 2


35) Answer: C

5x/(3x + 20) = 15/19

45x + 300 = 95x

50x = 300

x = 6 liters

Initial quantity of the water = 3 * 6 = 18 liters


36) Answer: C

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%


37) Answer: B

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


38) Answer: B

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


39) Answer: B

Milk = 5/9 * 90 = 50 litres

Water = 4/9 * 36 = 40 litres

Milk in 45 litres = 5/9 * 45 = 25 litres

Water in 18 litres = 4/9 * 45 = 20 litres

(50 – 25)/(40 – 20 + x) = 2/3

40 + 2x = 75

2x = 35

x = 17.5 litres


40) Answer: B

Milk in 20 litres = 3/5 * 20 = 12 litres

Water in 20 litres = 2/5 * 20 = 8 litres

(3x – 12)/(2x – 8 + 24) = 1/2

2x + 16 = 6x – 24

4x = 40

x = 10 litres

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This post was last modified on September 21, 2023 5:47 pm