Hello Aspirants. Welcome to Online Quantitative Aptitude section in AffairsCloud.com. Here we are given some** Mixture and Alligations** problems that is important for competitive exams. We have included Some questions that are repeatedly asked in exams !!

**Two vessels A and B contain a mixture of Milk and Water. In the first vessel (i.e) Vessel A has the ratio of Milk to water is 8 : 3 and in the second vessel, Vessel B has the ratio of 5 : 1. A 35 litre capacity vessel is filled from these two vessels so as to contain a mixture of Milk and water in ratio of 4 : 1. Then how many litres should be taken from the first vessel, Vessel “A”.**

A. 12 L

B. 17 L

C. 14 L

D. 11 L

E. None of the AboveAnswer –**D. 11 L**

**Explanation :**

[8/11(x) + 5/6(35-x)]/[3/11(x) + 1/6(35-x)] = 4/1

x = 11**When one litre of water is added to a mixture of milk and water, the new mixture contains 25% of milk. When one litre of milk is added to the new mixture, then the resulting mixture contains 40% milk. What is the percentage of milk in the original mixture?**

A. 100/6 %

B. 50/6 %

C. 100/3 %

D. 50/3 %

E. None of the AboveAnswer –**C. 100/3 %**

**Explanation :**

Original Mixture = x L

In (x + 1) Mixture, quantity of milk = (x + 1)* (25/100) = (x + 1)/4

one litre of milk is added to the new mixture

[((x + 1)/4 )+ 1 ]/ x + 2 = 40%

x = 3 ; quantity of milk = (3 + 1)/4 = 1L

percentage of milk in the original mixture = 1/3 * 100 = 100/3 %**The price of a box and a pen is Rs.60. The box was sold at a 40% profit and the pen at a loss of 10%. If the Shop keeper gains Rs.4 in the whole transaction, then how much is the cost price of Box?**

A. Rs.10

B. Rs.30

C. Rs.20

D. Rs.40

E. None of the AboveAnswer –**C. Rs.20**

**Explanation :**

40x/100 – 10(60-x)/100 = 4

40x + 10x = 400 + 600

x = 20**A vessel contains a mixture of diesel and petrol in which there is 20% diesel. Five litres are drawn off and then the vessel is filled with petrol. If the diesel present in the mixture is now 15% then how much does the vessel hold?**

A. 10 L

B. 20 L

C. 30 L

D. 40 L

E. None of the AboveAnswer –**B. 20 L**

**Explanation :**

20/15 = x/x-5

x = 20**In a lab, two chemical solutions Acid “A” with 90% purity and Acid “B” with 96% purity are mixed resulting in 24 litres of mixture of 92% purity. How much is the quantity of the first solution, Acid “A” in the resulting mixture?**

A. 12 L

B. 20 L

C. 16 L

D. 14 L

E. None of the AboveAnswer –**C. 16 L**

**Explanation :**

90x + (24 – x)* 96 = 24 * 92

x = 16**60 kg of a certain variety of Sugar at Rs.32 per kg is mixed with 48 kg of another variety of sugar and the mixture is sold at the average price of Rs.28 per kg. If there be no profit or no loss due to the new selling price, then what is the price of second variety of Sugar?**

A. Rs.25

B. Rs.23

C. Rs.29

D. Rs.27

E. None of the AboveAnswer –**B. Rs.23**

**Explanation :**

Total CP of first variety = 60 * 32 = 1920

Total CP of second variety = 48 * x = 48x

SP of Mixture = 1920 + (108 * 28) = 3024

1920 + 48x = 3024 => x = 23**Six litre of milk was taken out from a vessel and is then filled with water. This operation is performed two more times. The ratio of the quantity of milk now left in vessel to that of the water is 8 : 27. How much is the quantity of the milk contained by the vessel originally?**

A. 18 litre

B. 16 litre

C. 14 litre

D. 12 litre

E. None of the AboveAnswer –**A. 18 litre**

**Explanation :**

[x(1-6/x)/x]³ = (8/27)

[x(1-6/x)/x]³ = (2/3)³

(x-6)/x = 2/3

x = 18**A vessel is filled with 120 litres of Chemical solution, Acid “A”. Some quantity of Acid “A” was taken out and replaced with 23 litres of Acid “B” in such a way that the resultant ratio of the quantity of Acid “A” to Acid “B” is 4:1. Again 23 litres of the mixture was taken out and replaced with 28 litre of Acid “B”. What is the ratio of the Acid “A” to Acid “B” in the resultant mixture?**

A. 43 : 29

B. 46 : 23

C. 47 : 21

D. 46 : 29

E. None of the AboveAnswer –**D. 46 : 29**

**Explanation :**

In 23 litre mixture, Quantity of Acid “B” = 23 * 1/5 = 4.6 litre

Acid “A” in the mixture = 23 – 4.6 = 18.4 litre

120 – x / 23 = 4 / 1

x = 28

Ratio = 92-18.4 : 18.4 + 28

Ratio = 46 : 29**18 litres of Petrol was added to a vessel containing 80 litres of Kerosene. 49 litres of the resultant mixture was taken out and some more quantity of petrol and kerosene was added to the vessel in the ratio 2:1. If the respective ratio of kerosene and petrol in the vessel was 4:1, what was the quantity of kerosene added in the vessel?**

A. 1 litre

B. 2 litre

C. 5 litre

D. 3 litre

E. None of the AboveAnswer –**E. None of the Above**

**Explanation :**

Total quantity of the mixture = 18+80 = 98 litre

quantity of petrol remaining = 18/2 = 9

quantity of kerosene remaining = 80/2 = 40

(40 + 2x) / (9 + x) = 4 / 1

x = 2

Quantity of kerosene added in the vessel = 2x = 4 litre**A vessel which contains a mixture of acid and water in ratio 13:4. 25.5 litres of mixture is taken out from the vessel and 2.5 litres of pure water and 5 litres of acid is added to the mixture. If resultant mixture contains 25% water, what was the initial quantity of mixture in the vessel before the replacement in litres?**

A. 58 litre

B. 68 litre

C. 78 litre

D. 48 litre

E. None of the AboveAnswer –**B. 68 litre**

**Explanation :**

Quantity of Acid = 13x

Quantity of water = 4x

Total = 17x

Resultant Mixture = 17x – 25.5 + 2.5 + 5 = 17x – 18

Resultant water = 4x – 25.5 * (4/17) + 2.5 = 4x – 3.5

Resultant mixture contains 25% water

(17x – 18)*25/100 = 4x – 3.5

x = 4

Initial quantity = 17*4 = 68

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