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

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

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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)

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

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

Solved Examples
 

1. 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 litres

C. 28 litres

D. 28.2 litres

 

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

2. A jar full of whiskey contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohols and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is

A. 43

B. 34

C. 32

D. 23

 

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

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

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

3. In what ratio should rice at Rs.9.30 per Kg be mixed with rice at Rs. 10.80 per Kg so that the mixture be worth Rs.10 per Kg ?

A. 7 : 8

B. 8 : 7

C. 6 : 7

D. 7 ; 6

 

Answer : Option B

Explanation :

By the rule of alligation, we have

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

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

4. In what ratio must water be mixed with milk costing Rs.12 per litre in order to get a mixture worth of Rs.8 per litre?

A. 1 : 3

B. 2 : 2

C. 1 : 2

D. 3 : 1

 

Answer: Option C

Explanation:

By the rule of alligation, we have

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

Required Ratio = 4 : 8 = 1 : 2

5. In 1 kg mixture of iron and manganese 20% of manganese. How much iron should be added so that the proportion of manganese becomes 10%

A. 1.5 Kg

B. 2 Kg

C. .5 Kg

D. 1 Kg

 

Answer : Option D

Explanation :

By the rule of alligation, we have

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

=> 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

6. A trader has 1600Kg of sugar. He sells a part at 8% profit and the rest at 12% profit. If he gains 11% on the whole , find the quantity sold at 12%.

A. 1200 Kg

B. 1400 Kg

C. 1600 Kg

D. 800 Kg

 

Answer : Option A

Explanation :

By the rule of alligation, we have

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

=>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

7. How many litres of water must be added to 16 liters of milk and water contains 10% water to make it 20% water in it

A. 4 litre

B. 2 litre

C. 1 litre

D. 3 litre

 

Answer : Option B

Explanation :

By the rule of alligation, we have

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

=> 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

8. A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is

A. 300

B. 400

C. 600

D. 500

 

Answer : Option C

Explanation :

By the rule of alligation,we have

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

=> 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

9. 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.182.50

B. Rs.170.5

C. Rs.175.50

D. Rs.180

 

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

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

(x - 153) : 22.5 = 1 : 1

=>x - 153 = 22.50

=> x = 153 + 22.5 = 175.5

10. 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. 7litres, 4 litres

C. 6litres, 6 litres

D. 4litres, 8 litres

 

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

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

=> 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

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

1. What is the concept of mixture and alligation in quantitative aptitude?
Ans. Mixture and alligation is a concept in quantitative aptitude that deals with the calculation of the proportion in which two or more ingredients of varying costs are mixed to obtain a desired average cost. It helps in solving problems related to combining different elements or quantities with different prices or values.
2. How is mixture and alligation related to the Civil Service Examination?
Ans. Mixture and alligation is a topic that is frequently asked in the quantitative aptitude section of the Civil Service Examination. Questions related to this concept assess the candidate's ability to solve problems involving the mixture of different elements or quantities, which is a crucial skill required for various administrative roles.
3. What are some common applications of mixture and alligation in real life?
Ans. Mixture and alligation is a concept that finds applications in various real-life scenarios. It can be used to calculate the average price of a mixture of different grades of oil, determine the ratio of ingredients in a food recipe, or even calculate the average speed of a vehicle during a journey with varying speeds.
4. How can one approach solving mixture and alligation problems in the quantitative aptitude section?
Ans. To solve mixture and alligation problems, one can follow a step-by-step approach. First, identify the different elements or quantities involved and assign variables to them. Then, set up equations based on the given information and use the concept of alligation to calculate the desired ratio or average. Finally, verify the solution by checking if it satisfies all the given conditions.
5. Are there any shortcuts or tricks to solve mixture and alligation problems quickly?
Ans. Yes, there are certain shortcuts and tricks that can be used to solve mixture and alligation problems more efficiently. These include direct formulae for finding the mean value, shortcuts for calculating the proportion of mixtures, and tricks to quickly solve problems involving multiple mixtures. Practicing these techniques can help candidates save time during the examination.

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