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# Mixture and Alligation, Notes, Methods and Questions

## 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?

A. 26 liters
B. 29.16 liters
C. 28 liters
D. 28.2 litres

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?
A. 1/3
B. 1/4
C. 1/5
D. 1/7

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?
A. 10
B. 20
C. 21
D. 25
Solution: (C)
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?
A. 30 liters
B. 26 liters
C. 24 litres
D. 32 litres
Solution: (C)
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
 Check Other Links: Percentage Study Notes Profit and Loss Formula Partnership Formula Speed, Time, and Distance

## FAQs

### What is the formula of mixture and alligation?

The cost of a unit quantity of the mixture is called the mean price. (Cheaper quantity) : (Dearer quantity) = (d - m) : (m - c).

### Where can I get some sample questions on mixture and alligation?

The article above provides you with some sample questions on mixture and alligation.

Join the Conversation

1. BÃRBÎÊ GÎRL says:

@Mosaic

2. Pallavi Shekar_DREAM BIG :D says:

_/_ 🙂

3. kumar says:

Thank u sir,,very useful

4. Prabhas says:

1.B

5. Gladiator:: The Bibliophile :) says:

..

6. BÃRBÎÊ GÎRL says:

Gladi maths k post pe aa jaya kro discuss krne

7. L@mbkin_SBI clerk says:

solve krne mei baht problem h abhi bhi 🙁

8. BÃRBÎÊ GÎRL says:

I hate dis chapter,bt will try

9. Säuräbh~ {ʍ€gąʍɨɲď} says:

..

10. BÃRBÎÊ GÎRL says:

Aap yaha bhi:))

11. Prabhas says:

2.B ?

12. Säuräbh~ {ʍ€gąʍɨɲď} says:

jaha mam bulaenge waha ham jaenge 😛

13. BÃRBÎÊ GÎRL says:

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

14. L@mbkin_SBI clerk says:

1=b
3=c

15. Säuräbh~ {ʍ€gąʍɨɲď} says:

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 😀

16. BÃRBÎÊ GÎRL says:

Gladi kaha ho. Its me Sam

17. BÃRBÎÊ GÎRL says:

Hanji jaroor 🙂

18. Mjjoshi says:

1-b ,2-c ,3-c

19. Benaam Shayar says:

:O mixture n alligation _/_
lunch k baad try krta hoon..:P

20. BÃRBÎÊ GÎRL says:

Mt kro lunch

21. Benaam Shayar says:

😛 ammmma bhuk lag gyi

22. BÃRBÎÊ GÎRL says:

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

23. Benaam Shayar says:

ok.. lunch k baad aata hoon..
tab tak try krte rhiyo

24. Säuräbh~ {ʍ€gąʍɨɲď} says:
25. BÃRBÎÊ GÎRL says:

Hmm..

26. gusto says:

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

27. Mjjoshi says:

explain ???

28. angela says:

????..

29. angela says:

explain..?

30. Säuräbh~ {ʍ€gąʍɨɲď} says:

which one

31. Mjjoshi says:

4-10 pls explain??

32. Ethan hunt says:

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

33. gusto says:

Let 100 ml was there and it contained 40 alcohol
No 40(1-x)+19*x= 26
X= 2/3

34. Säuräbh~ {ʍ€gąʍɨɲď} says:

saare..
wait answers explanations ke sth ajaenge

35. angela says:

any problem.. i hav problem dis chapter

36. BÃRBÎÊ GÎRL says:

Without explanation :((

37. Ethan hunt says:

Explain to mam krengi naaa

38. BÃRBÎÊ GÎRL says:

Han…

39. BÃRBÎÊ GÎRL says:

Aajkal quiz ne hoti kya yaha @mosaic ki??

40. Ethan hunt says:

dikha nhi..mujhe kal se vo……

41. BÃRBÎÊ GÎRL says:

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

42. ratnab. says:

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

43. @wari!!* says:
44. Rohit chauhan says:

D most easiest one

45. Rohit chauhan says:

D most easiest one

46. Satish says:

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

47. freedomfighter says:

ur from which region?

48. Gladiator:: The Bibliophile :) says:

Uff…..sam…
Pehchan hi nahi saka…
Hi sam …hw r u??

49. BÃRBÎÊ GÎRL says:

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

50. Dhruba Jyoti Thakuria says:

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

51. Viveksingh Chauhan says:

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

52. Gaurav says:

Same doubt…what happened in que no 7

53. Divik Shah says:

Plz explain 2 & 4 questions. …

54. priyanshu says:

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..

55. Viveksingh Chauhan says:

Thanks a lot priyanshu ji for clear my doubt

56. Mahi Walia says:

Yaar ye Slov kase kaiya h samja hi nhi aa rha

57. Mahi Walia says:

Post office. Ka exam h