IntroductionIntroduction

Mixer is combination of two matters or materials in some proportions. Objective is to

quantify these materials based on certain relationships. In this image, water and milk is

shown to produce mixture of thick and thin milk. The cost of milk will depending upon

quality of mixture.

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Mixer and Allegations9

Fig 1 Milk mixture preparation by adding certain amount of water

Fig 2 Air in atmosphere is mixture

Air Composition (% by Volume)

78.1%

20.9%

Oxygen

Nitrogen

Argon

Other

Fig 3 Coffee in a cup is mixture

Fig 4 Green Chatni is a mixture

MixtureMixture

A Mixture is basically combination of two or more substance i.e. is mixing of two or more

substance.

For example:-

1) 30% acid solutions is mixed 70 % acid solutions.

2) 20% water is mixed with 80% pure milk.

Pure Milk(100% conc.)

Pure Orange Juice(100% Milk conc.)

UnPure Orange Shake(50% Milk, 50% Orange)

1 Ltr

1 Ltr2 Ltr

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AlligationAlligation

It is the rule that 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 desired price. A process or rule for the

solution of problems concerning the compounding or mixing of ingredients differing in

price or quality.

Mean PriceMean Price

The cost price of a unit quantity of the mixture is called the mean price.

Basic FormulaBasic Formula

If two ingredients A and B of price x and y respectively are mixed and the price of resultant

mixture is M (mean price) then the ratio (R) in which ingredients are mixed is given by, the

rule of allegation

Thus the required ratio is

D - MR

M C=

-

Mixture of More Than Two ElementsMixture of More Than Two Elements

In order to calculate final ratio of ingredients when mixture contains more than two

ingredients,

1. Take two ingredients such that 1st ingredient is LOWER than the mean value and

CP of Cheaper(C)

CP of Costlier(D)

Mean Price(M)

D – M M – C

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the other one is HIGHER than the mean value.

2. Calculate the ratio of ingredients

3. Repeat for all possible pairs

4. Final ratio is the ratio obtained from step 2 (if an ingredient is common in the ratios,

add values for this particular ingredient)

Solved QuestionsSolved Questions

Q (ps-1) If 20 ltr of milk and 10 ltr of water are mixed in a container, what is the volume

of total solution.

Ans: 20 ltr + 10 ltr = 30 Ltr

Q (ps-2) Calculate percentage of water in the total solution of above mixture?

Ans: (10/30) × 100 = 33.3 %

Q (ps-3) If impurity in solution is 10%, what is purity of solution?

Ans: 90%

Q (ps-4)How many liters of 20% milk should be added to 160 liters of a 70% milk to

obtain a mixture that is a 30% milk solution?

Ans Let x be the amount of 20% milk

20% of x 70% of 160 30% of (x 160)

20 70 30x 160 (x 160)

100 100 1000.20x 0.70 (160) 0.30(x 160)

0.30x 0.20x 112 48

0.10x 64

10x 64

10064 100

x 64010

Hence, add 6

+ = +

+́́ =+

+ =+

-=-

Þ=

Þ=

´Þ= =

40 liter of 20% milk solutions

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Q(ps-5) How many liters of 10% milk should be added to 80 liters of a 35% milk solution

to obtain a mixture that is a 30% milk solution?

Ans Let x be the amount of 10% milk solution

10% of x 35% of 80 30% of (x 80)

10 35 30x 80 (x 80)

100 100 1000.10x 0.35 (80) 0.30(x 80)

0.30x 0.10x 28 24

0.20x 4

20 x 4

1004 100

x 2020

Hence, add

+ = +

+́́ = +

+ =+

-=-

Þ=

Þ=

´Þ= =

20 liter of 10 % milk solutions

Unsolved QuestionsUnsolved Questions

Q (pq9.1) A person stole milk from a shop which contained 40% of milk and he

replaced what he had stolen by milk containing only 16% milk The shop has then the

milk having strength of 24% only. How much did the person teal?

Q (pq9.2) A flask contain 160 mL of solution that is 25% milk by volume. How much

milk must be added to the flask so that the resulting solution is 60% milk by volume?

Q ( pq-3) 85 litre mixture contain milk andwater in the ratio 27 :7. How much more water

is to be added to get a new mixture containing milk & water in the ratio 3: 1

ANSWERS

(1) Shopkeeper has 1/3 part and thief has 2/3 part

(2) 140ml

(3) 5 litre

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Some more solved questionsSome more solved questions

Q (1) In what proportion must rice at Rs. 3.00 per kg be hexed with rice at Rs, 4.00 per kg

so that the mixture be worth Rs. 3. 80 a kg?

Ans By the allegation rule

(Quanity of cheper rice) 20 1

(Quantity of dearer rice) 80 4

They must be mixed in ratio 1 : 4

==

\

Q (2) the average age of Boys is 20 and the average age of girl is 25 years. Find the ratio of

Boy and girl if the average age of class is 22 years

Ans Let Boys x

Girls y

20x 25y22

x y

20x 25y 22x 22y

25y 22y 22x 20x

3y 2x

x 2

y 3

The ratio of Boy girl is 2 : 3

=

=

+=

+

+=+

-=-

=

Þ=

+

Q (3) Two varieties of sugar I Rs. 5 per kg & 2nd Rs. 7 per kg mixed together. The average

cost is Rs. 6.5 per kg. In what ratio he mixed both varieties?

Ans Let 1 var iety be x

2 var iety be y

5x 7y6.5

x y

5x 7y 6.5x 6.5y

7y 6.5y 6.5x 5x

0.5y 1.5x

x 0.5

y 1.5

x 1

y 3

the two var ieties mixed in 1 : 3

+=

+

+=+

-=-

=

Þ=

Þ=

1

Q (4) the average height of girls is 156 cm and that of boys is 174 cm, if the average height

of all the class is 160 cm. calculate the ratio of girls & boys in the class

Ans By allegation rule

14Ratio of girl & boy = =7:2

4

Q (5) Raju bought a wheat for 30 per pound & other type at so per pound. If he mixed the

wheat in a certain ratio and the mixture cost 33 per pound calculate the ratio in which the

quantities are mixed

Unsolved QuestionsUnsolved Questions

C

C

F

F

Ans By allegation rule

the ratio of 1 & 2 17 : 3 type of wheat

(1) what is the Freezing point of water (in o )

Ans O o

(2) what is the Freezing point of water (in o )

Ans 32o

(3) what is boiling po

=

C

C

F

F

C F

C F

int of water (in o )

Ans 100o

(4) what is the boiling point of water (in o )

Ans 212 o

(5) what is the room temperature (in o & in o )

Ans 25o 77 o

Q (1) two varieties of pulses I Rs. 20per kg & Rs. 25kg are mixed together. The average

cost is Rs. 22per kg. Is Rs. 22per kg. In what ratio both varieties are mixed?

Q (2) A gold smith has two Quantities of Gold one of 12 carat and other of 20 carat. In

what proportion should he mix both to make and armament of 18 carat?

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Q (3) Suman bought a rice for 20 per kg and other type at so per kg. If he mixed the rice in

a certain ratio and the mixture cost Rs. 38 per kg calculate the ratio in which the

quantifies are mixed?

Q (4) the average weight of boy in a school is 58 kg and that of girl is 48 kg. If the average

weight of world is 55 kg. Calculate the ratio of boy & girls?

Q (5) two varieties of salt are I type Rs. 4 per kg & 2n Rs. 8 per kg. The average cost is Rs. 5

per kg. In what ratio both varieties of salt are mixed?

ANSWERS

(1) 3 : 2 (2) 1 : 3 (3) 2:3 (4) 7 : 3 (5) 3: 1

WorksheetWorksheet

Q. (1) a mixture contains milk and water in the ratio 4:3. If 5 liters of water is added to the

mixture, the ratio becomes 4:5. Find the ratio quantity of milk in the given mixture?

(a) 10 liters

(b) 5 liters

(c) 6 liters

(d) 8 liters

Q. (2) an alloy to contain topper and Zinc in the ratio 9:4. How much Zinc required to be

melted with 24 Kg of topper?

2(a) 10 Kg

31

(b) 10 Kg3

2(c) 9 Kg

3(d) 9 Kg

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Q. (3) 60 Kg of an alloy A is mixed with 100 Kg of alloy B. If alloy A has lead & tin in the

ratio 3:2 and alloy B has tin & copper in the ratio 1:4 find the amount of tin in the new

alloy?

(a) 36 Kg

(b) 44 Kg

(c) 53 Kg

(4) 80 Kg

Q. (4) 15 liters of mixture contain 20% alcohol and the rest water. If 3 liters of water be

mixed with it. Find the percentage of alcohol in the new mixture?

(a) 15%

2(b) 16 %

3(c) 17%

1(d) 18 %

2

Q. (5) 20 liters of mixture contain milk and water in the ratio 5:3. If 4 liters of this

mixtures be replaced by 4 liters of milk. What would be the ratio of milk to water in the

new mixture?

(a) 2:1

(b) 8:3

(c) 7: 3

(d) 4:3

Q. (6) 85 Kg of mixture contain milk and water in the ratio 27:7 how much more water is

to be added to get a new mixture containing milk and water in ratio 3:1?

(a) 2 Kg

(b) 1 Kg

(c) 3 Kg

(d) 5 Kg

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Q. (7) in what ratio must a grocer mix two verities of rice costing Rs. 15 & 20 per Kg

respectively 501 as to get a mixture worth Rs. 16.50 per Kg?

(a) 3:7

(b) 7:3

(c) 5:7

(d) 7:5

Q. (8) in what ratio must sugar at Rs. 62 per kg be mixed with sugar at Rs. 72 per kg so

that the mixture must be worth Rs. 64.50 per Kg?

(a) 3:1

(b) 4:3

(c) 3:2

(d) 5:3

Q. (8) in what ratio must sugar at Rs. 62 per kg be mixed with sugar at Rs. 72 per kg so

that the mixture must be worth Rs. 64.50 per Kg?

(a) 3:1

(b) 4:3

(c) 3:2

(d) 5:3

Q. (9) one quantity of wheat at Rs. 9.30 per Kg is mixed with another quality at a certain

rate in the ratio 8:7. If the mixture so formed be worth Rs. 10 per Kg. what is the rate per

Kg of the second quality of wheat?

(a) 10.30

(b) 10.60

(c) 11

(d) 10.80

Q. (10) Silver is 19 times as heavy as water & copper is a times as heavy a water. In what

ratio should these be mixed to get an alloy 15 times as heavy as water?

(a) 1:1

(b) 2:3

(c) 1:2

(d) 3:2 1

Q. (11) tin & copper are matted together in the ratio 9:11 what is the weight of melted

mixture. If 28.8Kg of him has been consumed in it?

(a) 58Kg

(b) 60Kg

(c) 64 Kg

(d) 70 Kg

Q. (12) in what ratio must close at Rs. 9.30 per kg be mixed with coffee at Rs. 10.80 per kg

so that the mixture be worth Rs. 10 per Kg.?

(a) 8:7

(b) 7:9

(c) 7:15

(d) 8:15

ANSWERS

1. A 2. A 3. B 4. B 5. C

6. D 7. B 8. A 9. D 10. D

11. C 12. A

Q.1 Take one glass of water having 300ml + add 500ml milk what is ratio of mixture?

Q.2 Tea have ratio of water : milk as 2:3 calculate amount of water and milk in 500 ml

tea

Q.3 Coffee has mixture of coffee beans, milk, sugar as 1:3:1 in 200ml, calculate

quantity of each.

Q .4 A gold smith has two Quantities of Gold one of 12 carat and other of 20 carat. In

what proportion should he mix both to make and armament of 18 carat?

Q.5 Suman bought a rice for 20 per kg and other type at 3o per kg. If he mixed the rice

in a certain ratio and the mixture cost Rs. 38 per kg calculate the ratio in which the

quantifies are mixed?

Q.6 The average weight of boy in a school is 58 kg and that of girl is 48 kg. If the

average weight of world is 55 kg. Calculate the ratio of boy & girls?

Q .7 Two varieties of salt are I type Rs. 4 per kg and Rs. 8 per kg. The average cost is

Rs. 5 per kg. In what ratio both varieties of salt are mixed?

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ProjectsProjects

Take one glass of water add one spoon salt into it and taste it. It is salty. Now add two

spoons of salt and taste it. Now is more salty and having more salty. Now add one more

spoon salt it will become more salty due to three spoon salts. Taste independently water

and salt.

1. Tea and coffee is also mixture of milk , sugar and tea or coffee. Qty of each item can be

placed in table form

2. Getting chatni made from mixy or grinder is mixture. Hence, chatni green or red we

eat with dosa or roti is mixture.

3. Air is mixture of nitrogen 78%, oxygen 21% and gases 1%. Test these contents.

4. Birthday cake is mixture of maida , sugar , milk , egg ,baking soda , chocolate etc.

Tabulate contents qty.

5. Mix two water colors in transparent tube with water and see changes in the color, now

mix one more color and see changes. This is mixture.

6. Take one basket and place few mangoes, apples , potatoes , capsicum and lady fingers.

Roll basket so that these items have been mixed. Now make a table of these with items

name and quantity . We can place them in percentage, item wise.

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