7. Mixture and Alligation, Quantitative Aptitude, Civil Service Examination, RPSC | RAS RPSC Prelims Preparation - Notes, Study Material & Tests - RPSC RAS (Rajasthan) PDF Download

1. Alligation

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

2. Mean Price

Mean price is the cost price of a unit quantity of the mixture

3. 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 = [x(1−y/x)n] units.

4. Rule of Alligation

If two ingredients are mixed, then

(Quantity of cheaper/Quantity of dearer)=(C.P. of dearer - Mean Price)/(Mean price - C.P. of cheaper)

5. => (Cheaper quantity) : (Dearer quantity) = (d - m) : (m - c)

Solved Examples
 

Answer : Option B

Explanation :

Assume that a container contains x of liquid from which y units are taken out and replaced 

=[x(1−y/x)n] 

Hence milk now contained by the container = 40(1−4/40)3=40(1−1/10)3

40×9/10×9/10×9/10=(4×9×9×9)/100=29.16

Answer : Option D

Explanation :

Concentration of alcohol in 1st Jar = 40%

Concentration of alcohol in 2nd Jar = 19%

After the mixing, Concentration of alcohol in the mixture = 26%

By the rule of alligation

Hence ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2

Answer : Option B

Explanation :

By the rule of alligation, we have

Required ratio = .8 : .7 = 8 : 7.

Answer: Option C

Explanation:

By the rule of alligation, we have

Required Ratio = 4 : 8 = 1 : 2

Answer : Option D

Explanation :

By the rule of alligation, we have

=> Quantity of the mixture : Quantity of iron = 10 : 10 = 1 : 1

Given that Quantity of the mixture = 1 Kg

Hence Quantity of iron to be added = 1 Kg

Answer : Option A

Explanation :

By the rule of alligation, we have

=>Quantity of part1 : Quantity of part2 = 1 : 3 

Given that total quantity = 1600 Kg

Hence quantity of part2 (quantity sold at 12%) = 1600×3/4=1200

Answer : Option B

Explanation :

By the rule of alligation, we have

=> Quantity of water : Quantity of the mixture = 10 : 80 = 1 : 8

Here Quantity of the mixture = 16 litres

=> Quantity of water : 16 = 1 : 8

Quantity of water = 16×1/8=2 litre

Answer : Option C

Explanation :

By the rule of alligation,we have

=> Quantity of part1 : Quantity of part2 = 4 : 6 = 2 : 3

Total quantity is given as 1000Kg

So Quantity of part2 (Quantity sold at 18% profit) = 1000×3/5=600Kg

Answer : Option C

Explanation :

Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed in the ratio 1 : 1

So their average price = (126+135)2=130.5 

Hence let's consider that the mixture is formed by mixing two varieties of tea. 

one at Rs. 130.50 per kg and the other at Rs. x per kg in the ratio 2 : 2, i.e., 

1 : 1. Now let's find out x.

By the rule of alligation, we can write as

(x - 153) : 22.5 = 1 : 1

=>x - 153 = 22.50

=> x = 153 + 22.5 = 175.5

Answer : Option C

Explanation :

Let cost of 1 litre milk be Rs.1

Milk in 1 litre mix in 1st can = 3/4 litre

Cost Price(CP) of 1 litre mix in 1st can = Rs.3/4

Milk in 1 litre mix in 2nd can = 1/2 litre

Cost Price(CP) of 1 litre mix in 2nd can = Rs.1/2

Milk in 1 litre of the final mix=5/8

Cost Price(CP) of 1 litre final mix = Rs.5/8

=> Mean price = 5/8

By the rule of alligation, we can write as

=> mix in 2nd can :mix in 1st can = 1/8 : 1/8 = 1:1

ie, from each can, 12×12=6 litre should be taken