Table of Contents

## Mixture and Alligation

**Mixture and Alligation: **Quantitative Aptitude is a very important section for government recruitment exams like SSC, railway, and banking. In this article, we are going to discuss one of the most important topic of the quantitative aptitude section i.e. rule of mixtures and alligations. Mixture and alligation is a mathematical technique used to solve problems related to mixing different ingredients or components at different ratios to obtain a desired mixture with a specified property (e.g., concentration, price, etc.). The rule of alligation enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of the desired price.

**Mixture:** An aggregate of two or more two types of quantities gives us a mixture.

**Alligation:** It is a method of solving arithmetic problems related to mixtures of ingredients. This rule enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of the desired price.

## Formula Of Mixture and Alligation

- It is a modified form of finding the weighted average. If 2 ingredients are mixed in a ratio and the cost price of the unit quantity of the mixture, called the Mean Price is given then,

The above formula can be represented with the help of a diagram which is easier to understand. Here ‘d’ is the cost of a dearer ingredient, ‘m’ is the mean price, and ‘c’ is the cost of a cheaper ingredient.

Quantity of Cheaper element /Quantity of Dearer element = CP of 1 unit of dearer element – Mean Price /Mean Price CP of 1 unit of cheaper element

Thus, (Cheaper quantity) : (Dearer quantity) = (d – m) : (m – c).

## Questions On Mixture and Alligation

**Ques 1.** A container contains 40 liters of milk. From this container, 4 liters of milk were taken out and replaced by water. This process was repeated further two times. How much milk is now contained in the container?

Solution: ( B)

**Explanation**

Assume that 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

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

**Ques 2.**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?

Solution: (C)

**Explanation**

Suppose the vessel initially contains 8 liters of liquid.

Let x liters of this liquid be replaced with water.

Quantity of water in new mixture = (3 – 3x/8 + x) litre

Quantity of syrup in new mixture = (5 – 5x/8) litres

So (3 – 3x/8 + x) = (5 – 5x/8) litres

=> 5x + 24 = 40 – 5x

=>10x = 16

=> x = 8/5 .

So, part of the mixture replaced = (8/5 x 1/8) = 1/5

**Ques 3.**A can contain a mixture of two liquids A and B is a ratio of 7: 5. When 9 liters of the mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7: 9. How many liters of liquid A were contained in the can initially?

**Explanation:**

Suppose the can initially contain 7x and 5x of mixtures A and B respectively.

Quantity of A in mixture left = (7x – 7/12 x 9)litres

= (7x – 21/4) litres.

Quantity of B in mixture left = (5x – 5/12 x 9) litres

= (5x – 15/4) litres.

So (7x – 21/4)/((5x – 15/4) +9) = 7/9

=> (28x – 21)/(20x + 21) = 7/9

=> 252x – 189 = 140x + 147

=> 112x = 336

=> x = 3.

So, they can contain 21 liters

**Ques 4**. 8 liters are drawn from a cask full of wine and are then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in the cask to that of the water is 16: 65. How much wine did the cask originally hold?

**Explanation :**

Let the initial quantity of wine = x litre

After a total of 4 operations, quantity of wine = x(1-y/x)^n=x(1-8/x)^4

Given that after a total of 4 operations, the ratio of the quantity of wine left in cask to that of water = 16 : 65

Hence we can write as (x(1-8/x)^4)/x =16/81

(1-8/x)^4 = (2/3)^4

(1-8/x) = 2/3

(x-8/x) = 2/3

3x-24=2x

x=24

@Mosaic

_/_ 🙂

Thank u sir,,very useful

1.B

..

Gladi maths k post pe aa jaya kro discuss krne

solve krne mei baht problem h abhi bhi 🙁

I hate dis chapter,bt will try

..

Aap yaha bhi:))

2.B ?

jaha mam bulaenge waha ham jaenge 😛

Hihi :)) mega kuch tips de so sbi or Po k liye is baar clear ho jaye

1=b

3=c

ye jo gladiator ji dikh rhe haina.. ye abhi medical clear karwake aye hai.. direct inhi se tips lelo.. hm bhi inse he lete hain 😀

Gladi kaha ho. Its me Sam

Hanji jaroor 🙂

1-b ,2-c ,3-c

:O mixture n alligation _/_

lunch k baad try krta hoon..:P

Mt kro lunch

😛 ammmma bhuk lag gyi

Shayar yar ye chapter samajh me aata kabhi bhi plz help.after Lunch

ok.. lunch k baad aata hoon..

tab tak try krte rhiyo

1-B, 2-C, 3-C, 4-C, 5-D6-C, 7-C, 8-C, 9-D, 10-B

Hmm..

B.B.C.C.?.C.C.C.D.B

explain ???

????..

explain..?

which one

4-10 pls explain??

B,?,C,C,D,C,C,C,D,B

Let 100 ml was there and it contained 40 alcohol

No 40(1-x)+19*x= 26

X= 2/3

saare..

wait answers explanations ke sth ajaenge

any problem.. i hav problem dis chapter

Without explanation :((

Explain to mam krengi naaa

Han…

Aajkal quiz ne hoti kya yaha @mosaic ki??

dikha nhi..mujhe kal se vo……

Han mai bhi usey hi search kar rahi hu kal se.. 🙁

Bhai log SSC cgl me challan banvane ke bad kya krna hoga.pic and sign phle hi upload ho gya hai

1-10

BCCCD

CCCDB

D most easiest one

D most easiest one

Hi, after the payment step of SSC CGL application I didnt get any email or msg confirmation from SSC. Is this happening with everyone?????

ur from which region?

Uff…..sam…

Pehchan hi nahi saka…

Hi sam …hw r u??

Hello,,gladi yr mujhe sbi po and ibps po k liye tips do,,I wanna clear exam this year abhi tk 1single paper clear ne hua hai almost 1 1/2 yr ho gaye hai

Why in questions no. 2 it is multipled with 1/8. Please explain

Dear admin please suggest me in question no 7 the value is 16/81 or 16/65 you mention here 16/65 please explain

Same doubt…what happened in que no 7

Plz explain 2 & 4 questions. …

Bcz of in qustion mention, ratio(16:65) is obtain after drawn liquid so when we equate this then we take total quantity of liqued(16/16+65)=16:81..

Thanks a lot priyanshu ji for clear my doubt

Yaar ye Slov kase kaiya h samja hi nhi aa rha

Post office. Ka exam h