Alligation or Mixture Aptitude Questions, Problems, Tricks, Formulas and Shortcuts

Alligation or Mixture Formulas

Alligation literally means “linking”.

A: It is a rule to find respective prices should be mixed to give a mixture at a given price.

B: The means or average price of a mixture when the price of two or more ingredients which may be mixed together and the proportion in which they are mixed are given,

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

Or in easy term Alligation is a rule which is used to solve the problems related to mixture and its ingredient.

Alligation Rule: Suppose, Rs. D per unit be the price of first ingredient (superior quality) mixed with another ingredient (cheaper quality) of price Rs.C per unit to form a mixture whose mean price is Rs.M per unit, then the two ingredients must be mixed in the ratio:

i.e. the two ingredients are to be mixed in the inverse ration of the two different are to be mixed and the mean price. The above rule may be represented schematically as under:

Explanation: Suppose x kg of cheaper quality is mixed with y kg of superior quality.

Price of the cheaper ingredient – Rs.cx Price of superior ingredient = Rs.dy

Price of mixture = Rs.(cx + dy)

And quantity of mixture = (x + Y) kg.

Price of mixture/kg = Rs. (cx + dy)

and quantity of mixture = (x + y) kg.

Price of mixture/kg = Rs.

= m

cx = dy = mx = my

dy - my = mx - cx

y(d - m) = x(m - c)

Important Examples and Questions of Alligation or Mixture

Example 1: In what ration two varieties of tea one costing Rs.27 per kg and the other costing Rs.32 per kg should be blended to produce a blended variety of tea worth Rs.30 per kg. how much should be the quantity of second variety of tea, if the first variety is 60 kg.

Solution:

The required ration of the two varieties of tea is 2 : 3, i.e.

Quantity of superior tea =

Example 2: Sugar at Rs.15 per kg is mixed with suger at Rs.20 per kg in the ration 2 : 3. Find the price per kg of the mixture.

Solution: Let the mean of the mixture be Rs.x.

Thus the price per kg of the mixture is Rs. 18

Previous Year Questions on Alligation or Mixture

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Question 1 of 15

1. Question

1 points

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?(S.B.I 2002)

Correct

Suppose the vessel initially contains 8 litres of liquid.

Let x litres of this liquid be replaced with water.

Quantity of water in new mixture = litres

Quantity of syrup in new mixture = litres

5x + 24 = 40 - 5x

10x = 16

So, part of the mixture replaced =

Incorrect

Suppose the vessel initially contains 8 litres of liquid.

Let x litres of this liquid be replaced with water.

Quantity of water in new mixture = litres

Quantity of syrup in new mixture = litres

5x + 24 = 40 - 5x

10x = 16

So, part of the mixture replaced =

Question 2 of 15

2. Question

1 points

Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:(bank p.o 2002)

Correct

Since first and second varieties are mixed in equal proportions.

So, their average price = Rs.

So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.

By the rule of alligation, we have:

x = 175.50

Incorrect

Since first and second varieties are mixed in equal proportions.

So, their average price = Rs.

So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.

By the rule of alligation, we have:

x = 175.50

Question 3 of 15

3. Question

1 points

A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?

Correct

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

Quantity of A in mixture left = litres

Quantity of B in mixture left = litres

252x - 189 = 140x + 147

112x = 336

x = 3.
So, the can contained 21 litres of A.

Incorrect

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

Quantity of A in mixture left = litres

Quantity of B in mixture left = litres

252x - 189 = 140x + 147

112x = 336

x = 3.
So, the can contained 21 litres of A.

Question 4 of 15

4. Question

1 points

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?(bank p.o 2000)

Correct

Let the cost of 1 litre milk be Re. 1

Milk in 1 litre mix. in 1st can = litre, C.P. of 1 litre mix. in 1st can Re

Milk in 1 litre mix. in 2nd can = itre, C.P. of 1 litre mix. in 2nd can Re.

Milk in 1 litre of final mix. = litre, Mean price Re

By the rule of alligation, we have:

= 6 litres
So, quantity of mixture taken from each can = = 6 litres

Incorrect

Let the cost of 1 litre milk be Re. 1

Milk in 1 litre mix. in 1st can = litre, C.P. of 1 litre mix. in 1st can Re

Milk in 1 litre mix. in 2nd can = itre, C.P. of 1 litre mix. in 2nd can Re.

Milk in 1 litre of final mix. = litre, Mean price Re

By the rule of alligation, we have:

= 6 litres
So, quantity of mixture taken from each can = = 6 litres

Question 5 of 15

5. Question

1 points

In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?

Correct

By the rule of alligation:

Required rate = 3.50 : 1.50 = 7 : 3.

Incorrect

By the rule of alligation:

Required rate = 3.50 : 1.50 = 7 : 3.

Question 6 of 15

6. Question

1 points

A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:

Correct

Let C.P. of 1 litre milk be Re. 1

Then, S.P. of 1 litre of mixture = Re. 1, Gain = 25%.

Ratio of milk to water = 4 : 1.

Hence, percentage of water in the mixture = = 20%

Incorrect

Let C.P. of 1 litre milk be Re. 1

Then, S.P. of 1 litre of mixture = Re. 1, Gain = 25%.

Ratio of milk to water = 4 : 1.

Hence, percentage of water in the mixture = = 20%

Question 7 of 15

7. Question

1 points

How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg?

Correct

S.P. of 1 kg of mixture = Rs. 9.24, Gain 10%.

C.P. of 1 kg of mixture = Rs = 8.50

By the rule of allilation, we have:

Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.

Let x kg of sugar of 1st be mixed with 27 kg of 2nd kind.

Then, 7 : 3 = x : 27

= 63 kg.

Incorrect

S.P. of 1 kg of mixture = Rs. 9.24, Gain 10%.

C.P. of 1 kg of mixture = Rs = 8.50

By the rule of allilation, we have:

Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.

Let x kg of sugar of 1st be mixed with 27 kg of 2nd kind.

Then, 7 : 3 = x : 27

= 63 kg.

Question 8 of 15

8. Question

1 points

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?

Correct

Amount of milk left after 3 operations = = 29.16 litres.

Incorrect

Amount of milk left after 3 operations = = 29.16 litres.

Question 9 of 15

9. Question

1 points

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

Correct

By the rule of alligation, we have:

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

Required quantity replaced =

Incorrect

By the rule of alligation, we have:

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

Required quantity replaced =

Question 10 of 15

10. Question

1 points

In what ratio must water be mixed with milk to gain 16% on selling the mixture at cost price?

Correct

Let C.P. of 1 litre milk be Re. 1.

S.P. of 1 litre of mixture = Re.1, Gain = %

C.P. of 1 litre of mixture =

By the rule of alligation, we have:

Ratio of water and milk = = 1 : 6

Incorrect

Let C.P. of 1 litre milk be Re. 1.

S.P. of 1 litre of mixture = Re.1, Gain = %

C.P. of 1 litre of mixture =

By the rule of alligation, we have:

Ratio of water and milk = = 1 : 6

Question 11 of 15

11. Question

1 points

Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.

Correct

By the rule of alligation:

Required ratio = 60 : 90 = 2 : 3.

Incorrect

By the rule of alligation:

Required ratio = 60 : 90 = 2 : 3.

Question 12 of 15

12. Question

1 points

In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10%?

Correct

S.P. of 1 kg of the mixture = Rs. 68.20, Gain = 10%.

C.P. of 1 kg of the mixture = Rs.

By the rule of alligation, we have:

Required ratio = 3 : 2.

Incorrect

Question 13 of 15

13. Question

1 points

The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is:

Correct

Let the price of the mixed variety be Rs. x per kg.

By rule of alligation, we have:

60 - 3x = 2x - 30

5x = 90

x = 18.

Incorrect

Let the price of the mixed variety be Rs. x per kg.

By rule of alligation, we have:

60 - 3x = 2x - 30

5x = 90

x = 18.

Question 14 of 15

14. Question

1 points

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:

Correct

By the rule of alligation, we have:

Ration of 1st and 2nd parts = 4 : 6 = 2 : 3

Quantity of 2nd kind = kg = 600 kg

Incorrect

By the rule of alligation, we have:

Ration of 1st and 2nd parts = 4 : 6 = 2 : 3

Quantity of 2nd kind = kg = 600 kg

Question 15 of 15

15. Question

1 points

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

Correct

Let the quantity of the wine in the cask originally be x litres.

Then, quantity of wine left in cask after 4 operations =

3x - 24 = 2x , x = 24.

Incorrect

Let the quantity of the wine in the cask originally be x litres.

Then, quantity of wine left in cask after 4 operations =

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