Mixture and Allegation Questions For Bank Clerk Prelims

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1) 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 becomes 5:4, then find the value of x?

A.12.5 liters

B.13.5 liters

C.11.5 liters

D.10.5 liters

E.None of these

2) Vessel A contains 28 liters of milk and x liters of water. If 24 liters of mixture is taken out which is contains 8 liters of water, then find the value of x?

A.12

B.14

C.16

D.18

E.20

3) Vessel A contains the mixture of milk and water in the ratio of x:y. If 30 liters of milk is added to vessel A, then the ratio of the milk and water becomes 3:1. if 20 liters of water added to vessel A, then the ratio of the milk and water becomes 3:4. Find the ratio of x and y?

A.1:2

B.3:2

C.5:4

D.4:3

E.5:3

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

A.20 liters

B.24 liters

C.28 liters

D.32 liters

E.None of these

5) A vessel has 90 liters mixture of milk and water and quantity of milk is 40% more than water. 36 liters of the mixture is replaced by same quantity of the water and repeated one more time. Find the quantity of the milk in the resultant solution?

A.18.9 liters

B.20.6 liters

C.16.9 liters

D.21.8 liters

E.None of these

6) A vessel contains 180 liters mixture of milk and water. The ratio of the milk to water is 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

7) 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

8) The price of A1 quality rice is Rs.70 per kg and the price of A2 quality rice is Rs.45 per kg. If both quality of rice are mixed in the ratio of 9:11, then what is the price per kg of the mixture?

A.Rs.58.75

B.Rs.56.80

C.Rs.54.75

D.Rs.52.90

E.Rs.50.45

9) A Jar contains 40 liters of pure milk. If 4 liters of milk is taken out and replaced by water and this process is repeated two more times, then find the quantity of milk in the final mixture?

A.28.17 liters

B.29.16 liters

C.30.19 liters

D.32.46 liters

E.None of these

10) A mixture contains 60 liters of oil and rest is water and the oil which contains 75% of the mixture. If x liters of water and 10 liters of oil is added to the mixture, then the quantity of oil in the resultant mixture is double of water. Find the value of x?

A.10

B.15

C.20

D.18

E.8

Answers :

1) 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

2) Answer: B

Quantity of mixture = 24 liters

Water in mixture = 8 liters

Milk in mixture = 24 – 8 = 16 liters

Ratio of milk and water = 16:8 = 2:1

x = 1/2 * 28 = 14 liters

3) Answer: B

(x + 30)/y = 3/1

3y = x + 30

x/(y + 20) = 3/4

3y + 60 = 4x

x + 30 + 60 = 4x

x = 30

y = 60/3 = 20

Ratio of x and y = 30:20 = 3:2

4) 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

5) Answer: A

Ratio of milk and water = 140:100 = 7:5

Milk in 90 liters = 7/12 * 90 = 52.5 liters

Water in 90 liters = 5/12 * 90 = 37.5 liters

Milk in final solution = 52.5 * (1 – 36/90)²

= 18.9 liters

6) Answer: B

Milk = 2/3 * 180 = 120Liters

Water = 180 – 120 = 60Liters

120 = (180 + x) * 60%

12000=10800+60x

1200=60x

=> x = 20 Liters

7) 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

8) Answer: A

(70 – x)/(x – 45) = 9/11

9x – 405 = 770 – 11x

20x = 1175

x = 58.75

9) Answer: B

Milk in the final quantity = 40 * (1 – 4/40)³

= 29.16 liters

10) Answer: B

Water = 60 * 25/75 = 20

(60 + 10)/(20 + x) = 2/1

40 + 2x = 70

x = 15

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