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 should wheat at Rs12.60 per kg be mixed with wheat at Rs. 14.60 per kg so that the mixture
be worth Rs.13 per kg ?
A. 6:7
B. 8:7
C. 4:3
D. 4:1
View Answer
Ans : D
Explanation: So the ratio will be :
1460 - 1300 : 1300-1260
=> 160 : 40 => 4:1
3. 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
4. How many kg of dal at Rs.8.40 per kg be mixed with32 kg of dall at Rs10.20 per kg to get a mixture worth
Rs.9.60 per kg?
A. 8
B. 12
C. 16
D. 20
View Answer
Ans : C
Explanation: By the rule of allegation ,we have
C.P. of 1 kg of 1st kind dal = 840
C.P. of 1 kg of 2nd kind dal = 1020
Price of 1kg of mixture = 960
So, 1020-960 : 960-840 => 60:120 => 1:2
=> Quantity of 1st kind dall:32 = 1:2
Quantity of 1st kind dall =32 *1/2 = 16
5. 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
6. How many litres of water should be added to a 30 litre mixture of milk and water containing milk and
water in the ratio of 3:7 such that the resultant mixture has 40% water in it?
A. 3
B. 4
C. 5
D. 6
View Answer
Ans : C
Explanation: 60 litres of the mixture has milk and water in the ratio 3:7.
i.e. the solution has 21 litres of milk and 9 litres of water.
When you add more water, the amount of milk in the mixture remains constant at 21 litres.
In the first case, before addition of further water, 21 litres of milk accounts for 70% by volume.
After water is
added, the new mixture contains 60% milk and 40% water.
Therefore, the 21 litres of milk accounts for 60% by volume.
Hence, 100%
7. 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%
8. Suprith bought 40 kg of rava at the rate of Rs.8.50 per kg and 55 kg at the rate of Rs.8.75 per kg. He
mixed the two. Approximately at what price per kg should he sell the mixture to make 40% profit at the cost
price?
A. 10
B. 12
C. 14
D. 16
View Answer
Ans : B
Explanation: CP = 40 × 8.50 + 55 ×8.75
= 340 + 481.25
= 821.25
Profit = 40%
SP= (100 +40) /100 × c.p
= 1.4 × 821.25
Total quantity = 40 + 55 = 95 kg
SP per kg =(1.4 x821.25) / 95} = 12
9. 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
10. How many kgs of Ponni rice costing Rs.21/kg should a shopkeeper mix with 12.5 kgs of ordinary rice
costing Rs.12 per kg so that he makes a profit of 25% on selling the mixture at Rs.20/kg?
A. 10
B. 11
C. 12
D. 13
View Answer
Ans : A
Explanation: As the trader makes 25% profit by selling the mixture at Rs.20/kg, his cost per kg of the mixture = Rs.16/kg.
C.P of 1 kg of rice of 1st kind = Rs. 21
C.P of 1 kg of rice of 2nd kind = Rs. 12
Mean price = Rs. 16
By the rule of alligation
Let the amount of ponni rice being mixed be x kgs
4:5 = x : 12.5
X = 10 kg
11. 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
12. A container contains 55 litres of milk. From this container 5.5 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
A. 38.06 liters
B. 39.08 liters
C. 40.09 liters
D. 41.09 liters
View Answer
Ans : C
Explanation: Where x is the initial quantity of milk in the cask y is the quantity of milk withdrawn in each process and n is the number of processes.
Initial quantity:55
Withdrawn quantity=5.5
number of times repeated=3
Hence from the above rule it can be say that, Formula,=[a(1-b/a)n ]
Quantity of milk left after the 3rd operation =55*((55-5.5)/55) ^3 =40.09litres
13. 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
14. Two vessels A and B contain sugar and rava in the ratio 4 : 3 and 2 : 3 respectively. Find the ratio in
which these mixtures be mixed to obtain a new mixture in vessel C containing sugar and rava in the ratio 1 :
2?
A. 2:7
B. 7:4
C. 3:7
D. 7:3
View Answer
Ans : B
Explanation: Let Cost Price(CP) of 1 kg sugar be Rs.1
Quantity of sugar in 1kg mixture from vessel A=4/7
Cost Price(CP) of 1kg mixture from vessel A = Rs. =4/7
Quantity of sugar in 1 kg mixture from vessel B =2/5
Cost Price(CP) of 1 kg mixture from vessel B = Rs. =2/5
Quantity of sugar to be obtained in 1 kg mixture from vessel C=1/2
Cost Price(CP) of 1 kg mixture from vessel C(Mean Price) = Rs.=1/2
Mixture from Vessel A : Mixture from Vessel B
1/10 :
15. 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
16. The cost of Type 1 material is Rs. 50per kg and Type 2 material is Rs.75 per kg. If both Type 1 and Type
2 are mixed in the ratio of 3:2 then what is the price per kg of the mixed variety of material?
A. 40
B. 50
C. 60
D. 70
View Answer
Ans : C
Explanation: Cost Price (CP) of Type 1 material is Rs. 50 per kg
Cost Price (CP) of Type 2 material is Rs. 75 per kg
Let Cost Price(CP) of resultant mixture be Rs.x per kg
Type 1 material : Type 2 material = 3/2
75-x : x-50 =3/2
X = 60
17. 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.
18. In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
A. 3:7
B. 7:3
C. 2:7
D. 4:7
View Answer
Ans : B
Explanation: By the rule of alligation:
Cost of 1 kg pulses of 1st kind = Rs 15
Cost of 1 kg pulses of 2nd kind Rs. 20
Mean Price = Rs. 16.50
Required rate = 3.50 : 1.50 = 7 : 3.
19. 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.
20. A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
A. 26.34 lt
B. 27.36 lt
C. 28 lt
D. 29.16 lt
View Answer
Ans : D
Explanation: Amount of milk left after 3 operations = ( 40 (1 - ((4/10)^3)) => 29.16 litres.
Discussion