Alligation and Mixture

29 April 2020


Alligation and Mixture is an important part of various entrance tests as well as competitive exams. Mostly students ignore the topic but looking at the fact, There are a lot of questions asked every year from this topic and thus, having proper understanding of the concepts is important. So, here are some basic concepts and formulas of the Mixture and Alligation along with variety of questions to help the students learn the concept.


Formulas For Alligation and Mixture 

1. Alligation:  It is the rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of desired price. 

2. Mean Price:  The cost of a unit quantity of the mixture is called the mean price. 

3. Rule of Alligation: If two ingredients are mixed, then 

We present as under: 

4. Suppose a container contains x of liquid from which y units are taken out and replaced by water. 

After n operations, the quantity of pure liquid = 


Practice Questions For Alligation and Mixture 

Q1) 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) 29.16 litres

B) 28 litres

C) 28.2 litres

D) 26 litres

Solution :


Q2) Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety of tea in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, what is the price of the third variety per kg ?

A) Rs.175.50

B) Rs.180

C) Rs.182.50

D) Rs.170.5

Solution :


Q3) A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?

A) 5litres, 7 litres

B) 4litres, 8 litres

C) 6litres, 6 litres

D) 7litres, 4 litres

Solution :


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Q4)The cost of Type 1 material is Rs. 15 per kg and Type 2 material is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then what is the price per kg of the mixed variety of material?

A) Rs. 17

B) Rs. 18

C) Rs. 19

D) Rs. 16

Solution :


Q5) A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removals and replacement, what is the ratio of milk and water  in the resultant mixture?

A) 17 : 3 

B) 9 : 1

C) 3 : 17

D) 5 : 3

Solution :

The 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture. Step 1. When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the 
container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water. Step 2. When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step. 
Therefore, the ratio of milk and water is 18 : 2 or 9 : 1. 

Q6) In what ratio, water must be mixed with fruit juice costing Rs.24 per litre so that the juice would be worth of Rs.20 per litre? 

A) 1:4 

B) 1:5 

C) 1:6

D) 2:5

Solution :

Cost of 1 litre of water = Rs.0 = cheaper quantity. 
Cost of 1 litre of juice = Rs.24 = dearer quantity. 
And, the mean price = m = Rs.20 Therefore, (Cheaper quantity) : (Dearer quantity) = (d - m) : (m - c) = 4:20 = 1:5 
Hence, the required answer is 1:5. 

Q7) A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup? 

A) 1/3 
B) 1/4 
C) 1/5 
D) 1/7 

Solution:

Suppose the vessel initially contains 8 litres of liquid. 
Let x litres of this liquid be replaced with water. 
Quantity of water in new mixture =3 -3x/8+ xlitres 
Quantity of syrup in new mixture =5 -5x/8litres 
3 -3x/8+ x=5 -5x/8 
5x + 24 = 40 - 5x 
10x = 16 
x =8/5. 
So, part of the mixture replaced = 8/5x1/8=1/5. 

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Q8) 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 litres 
B) 29.16 liters 
C) 28 liters 
D) 28.2 liters 

Solution: 

Milk contained by the container now 
= 40(1-4/40)^3 
= 4(1- 1/10)^3 
Practice Questions for Aptitude Preparation 
= 40×9/10×9/10×9/10 
= 29.16 

9) One type of liquid contains 25 % of benzene, the other contains 30% of benzene. A can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of benzene in the new mixture. 

A) 28 % 
B) 25 % 
C) 30 % 
D) 27% 

Solution: 

Let the percentage of benzene =X 
(30 - X)/(X- 25) = 6/4 = 3/2 
=> 5X = 135 or 
X = 27 so, 
required percentage of benzene = 27 % 

Q10)How many kgs of Basmati rice costing Rs.42/kg should a shopkeeper mix with 25 kgs of ordinary rice costing Rs.24 per kg so that he makes a profit of 25% on selling the mixture at Rs.40/kg? 

A) 20.0 kgs 
B) 12.5 kgs 
C) 16.0 kgs 
D) 200.0 kgs 

Solution: 

Let the amount of Basmati rice being mixed be x kgs. 
As the trader makes 25% profit by selling the mixture at Rs.40/kg, his cost per kg of the mixture 
= Rs.32/kg. 
i.e. (x×42)+(25×24)=32(x+25) 
42x+600=32x+800 
10x=200 
x=20kgs.

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