The document 7. Mixture and Alligation, Quantitative Aptitude, Civil Service Examination, RPSC UPSC Notes | EduRev is a part of the UPSC Course RAS RPSC Prelims Preparation - Notes, Study Material & Tests.

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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(1âˆ’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__

| |

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(1âˆ’y/x)n]

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

40Ã—9/10Ã—9/10Ã—9/10=(4Ã—9Ã—9Ã—9)/100=29.16

| |

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

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

| |

A. 7 : 8 | B. 8 : 7 |

C. 6 : 7 | D. 7 ; 6 |

**Answer :** Option B

**Explanation :**

By the rule of alligation, we have

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

| |

A. 1 : 3 | B. 2 : 2 |

C. 1 : 2 | D. 3 : 1 |

**Answer:** Option C

**Explanation:**

By the rule of alligation, we have

Required Ratio = 4 : 8 = 1 : 2

| |

A. 1.5 Kg | B. 2 Kg |

C. .5 Kg | D. 1 Kg |

**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

| |

A. 1200 Kg | B. 1400 Kg |

C. 1600 Kg | D. 800 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%) = 1600Ã—3/4=1200

| |

A. 4 litre | B. 2 litre |

C. 1 litre | D. 3 litre |

**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 = 16Ã—1/8=2 litre

| |

A. 300 | B. 400 |

C. 600 | D. 500 |

**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) = 1000Ã—3/5=600Kg

| |

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

(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

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

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

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