## Mixture and Alligation - Quantitative Aptitude Questions and Answers

This section focuses on "Mixture and Alligation" of Quantitative Aptitude. These Multiple Choice Questions (mcq) should be practiced to improve the Quantitative Aptitude skills required for various interviews (campus interviews, walk-in interviews, company interviews), placements, entrance exams and other competitive examinations.

1. In what ratio should a shopkeeper mix two types of rice, one costing 40 rupees/kg and another costing 20
rupees/kg to get a rice variety costing 28 rupees/kg .

A. 3:2

B. 2:3

C. 4:3

D. 2:7

View Answer

Ans : B

Explanation: we can use Alligation as follows

X = 40-28 = 4 ; y = 28-20 = 8

The ratio between the type 1 and type 2 rice is 4:6 or 2: 3

2. In what ratio must water be mixed with milk costing Rs.30 per litre in order to get a mixture worth of Rs.18
per litre?

A. 1:3

B. 2:3

C. 4:3

D. 3:2

View Answer

Ans : B

Explanation: C.P. of 1 lt of water = 0

C.P. of 1 lt of milk = 30

Mean price = 30

So, 30-18 : 18-0

=> 12:18 => 2:3

3. In 1 kg mixture of iron and carbon, 40% is carbon. How much iron should be added so that the proportion
of carbon becomes 20%.

A. 1KG

B. 2KG

C. 3KG

D. 4KG

View Answer

Ans : A

Explanation: By the rule of allegation ,we have

% of carbon in mixture = 40

% of carbon in pure iron = 0

Mean=20

Quantity of the mixture : Quantity of iron = 20 : 20 = 1 : 1

Given that quantity of the mixture = 1 kg

Hence quantity of iron to be added = 1 kg

4. 5 litre of coconut oil is added to 15 litre of a solution containing 40% of groundnut oil. The percentage of
groundnut in the new mixture is:

A. 20%

B. 30%

C. 40%

D. 50%

View Answer

Ans : B

Explanation: We have a 15 litre solution containing 40% of groundnut in the coconut oil.

=> Quantity of groundnut in the solution =(15* 40)/100= 6

Now 5 litre of coconut oil is added to the solution.

=> Total quantity of the new solution = 15 + 5= 20

Percentage of groundnut in the new solution = 6*100/20 = 600/20

= 30%

5. In what ratio must coffee powder worth Rs. 40 per kg be mixed with coffee powder worth Rs. 45 a kg such
that by selling the mixture at Rs. 48.40 a kg ,there can be a gain 10%?

A. 1:2

B. 2:3

C. 1:4

D. 4:1

View Answer

Ans : C

Explanation: Cost Price(CP) of 1 kg mixture = Rs. 68.20

Profit = 10%

Cost Price(CP) of 1 kg mixture = 48.40×100/110

= 4840 /110

= 44

45-44 : 44-40 => 1:4

6. How many litres of a 36 litre mixture containing milk and water in the ratio of 4 : 6 be replaced with pure
milk so that the resultant mixture contains milk and water in equal proportion?

A. 4

B. 6

C. 8

D. 10

View Answer

Ans : B

Explanation: The mixture contains 40% milk and 60% water in it.

That is 14.4 litres of milk and 21.6 litres of water.

Now we are replacing the mixture with pure milk so that the amount of milk and water in the mixture
is 50% and 50%.

That is we will end up with 18 litres of milk and 18 litres of water.

Water gets reduced by 3.6 litres.

To remove 3.6 litres of water from the original mixture containing 60% water,

we need to remove ={3.6}/{0.6} litres of the mix

7. 12 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the water is 81 : 256. How much wine did the cask originally hold?

A. 40

B. 44

C. 48

D. 52

View Answer

Ans : C

Explanation: Let initial quantity of wine = x litre

After a total of 4 operations, quantity of wine

x(1-(y/x))^n = x(1-12/x})^4

Given that after a total of 4 operations, the ratio of the quantity of wine left in cask to that of water = 81 : 256

x (1-12 / x)4

/ x = 81/ 256

(1-12/x)^4 = (3 /4)^4

X – 12 / x = 3 / 4

4x – 48 = 3x

X = 48

8. Vessel A contains milk and water in the ratio 3:2. Vessel B contains milk and water in the proportion 4:5. In
what proportion should quantities be taken from A & B to form a mixture in which milk and water are in the
ratio 7:2?

A. 8:15

B. 15:8

C. 7:15

D. 15:7

View Answer

Ans : A

Explanation: For this question, we will consider the proportion of milk in each mixture.

In Vessel A, the proportion of milk in 3/((3+2) )=3/5.

vessel B, the proportion of milk is 4/(4+5) = 4/9

The ratio is (3/9) : (8/45) = 8:15

9. In what ratio must a person mix three kinds of musted seeds costing Rs.65/kg, Rs.70/kg and Rs.105 /kg
so that the resultant mixture when sold at Rs.96/kg yields a profit of 20%?

A. 40:8:25

B. 8:25:40

C. 25:8:40

D. 25:40:8

View Answer

Ans : A

Explanation: The resultant mixture is sold at a profit of 20% at Rs.96/kg

i.e. 1.2 (cost) = Rs.96 => Cost = = Rs.80 / kg.

Let the three varities be A, B, and C costing Rs.65, Rs.70 and Rs.105 respectively.

The mean price falls between B and C.

Hence the following method should be used to find the ratio in which they should be mixed.

Mean : 80

A:C=4:5 B:C=2:5

The resultant ratio A : B : C :: 40 : 8 : 25.

10. A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?

A. 10

B. 20

C. 21

D. 14

View Answer

Ans : C

Explanation: Quantity of A in mixture left = (7x - ((7/12)*9)) => (7x-(21/4)) lt

Quantity of B in mixture left = (5x - ((5/12)*9)) => (5x-(15/4)) lt

Quantity of A/Quantity of B = 7/9

252x - 189 = 140x + 147

112x = 336

x = 3.

So, the can contained 21 litres of A.

Discussion