# Alligations and Mixtures Questions and Answers

## Allegations and Mixtures Questions

Allegation is the process which allows us to identify the proportion in which the numerous ingredients must be mixed at the specified price in order to create a mixture at a given price. Allegation includes two different types of methods namely, allegation medial which is used to calculate the quantity of a mixture and allegation alternate which is used to calculate the quantity of each ingredient required to produce a mixture.

### Rule

• If two different ingredients are assorted in a proportion, then
• $\frac{( \text{ Quantity of cheaper})}{ (\text{ Quantity of dearer})}= \frac{(C.P. of dearer)-(Mean Price)}{ (Mean Price)-(C.P.of Cheaper)}$
• Furthermore, it can be presented as:

• (Cheaper quantity): (dearer quantity) = (d – m): (m – c)
• Repeated Dilution: If a barrel contains ‘a’ units of liquid out of which ‘b’ units are removed and substituted by water. Then, after ‘n’ processes, the amount of liquid,
$= [x (1 – y/x)^{n}] units$
• Furthermore, it is used to analyze the quantity of pure liquid left after ‘n’ number of procedures of constant substitution is prepared on the pure quantity.

Question 1

Time: 00:00:00
A cheater shopkeeper confesses to sell his pulses at cost price but he mixes it with pebbles and thereby gains 25%. The percentage of pebbles in the mixture is:

14%

14%

16%

16%

20%

20%

25%

25%

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Question 2

Time: 00:00:00
A vessel comprises 100 litres of fresh juice. Out of this vessel 12 litres of juice was pulled out and changed by water. This whole process was done two more times. Now calculate the quantity of fresh juice contained by the vessel?

64.12

64.12

65.87

65.87

68.14

68.14

69.54

69.54

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Question 3

Time: 00:00:00
Sugar cost INR 130 per kilogram and INR 139 per kilogram are combined along a new type in the ratio 1 : 1 : 2. If the combination is cost Rs. 163 kilogram, then find out the price of the new type per kilogram ?

170.50

170.50

179.50

179.50

185.50

185.50

191.50

191.50

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Question 4

Time: 00:00:00
A deals in two types of black-eyed peas. Each costing INR 14 and INR 21 per kg. What ratio should the both types be mixed to get a combination worth INR18.50 per kg.

5:9

5:9

5:7

5:7

7:5

7:5

5:3

5:3

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Question 5

Time: 00:00:00
A jug has 5 parts of tomato soup and 3 parts of water. Now if we want a new combination with 1/2 water and 1/2 tomato soup, how much of the mixture must be swapped with water?

19

19

17

17

16

16

20

20

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Question 6

Time: 00:00:00
Two jugs X and Y having coca cola and water mixed in the proportion 5: 2 and 7: 6 respectively. Now if we want a new mixture in jug Z having coca cola and water in the proportion of 8:5 then what will be the ratio?

5:6

5:6

3: 4

3: 4

6: 7

6: 7

7: 9

7: 9

None of the above

None of the above

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Question 7

Time: 00:00:00
In what proportion must kerosene be mixed with petrol to earn 16(2/3)% if we sell the combination at cost price?

2: 7

2: 7

6: 1

6: 1

2: 3

2: 3

1: 6

1: 6

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Question 8

Time: 00:00:00
A fixed amount of water is mixed with Sangria costing Rs 12 per litre. The rate of mixture is Rs 8 per litre. Find out the proportion of water and Sangria in the new combination.

3:2

3:2

4:3

4:3

1:2

1:2

None of the above

None of the above

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Question 9

Time: 00:00:00
A pot contains 40 litres of Mint juice. 4 litres of Mint juice is replaced with Honey. This is done two times more. Find out the quantity of Mint juice which is in the pot now?

29.16

29.16

30.15

30.15

32.43

32.43

33.19

33.19

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Question 10

Time: 00:00:00
A sells 3 types of mustard seeds at the price of INR 126 per kg and INR 135 per kg and 3rd variety in the ratio of 3 : 2 : 5. If the cost of the final mix is INR 155 per kg, find the rate of third type of mustard seeds.

170.54

170.54

195.43

195.43

180.40

180.40

190.76

190.76

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Question 11

Time: 00:00:00
A lemon water hawker has two pots of lemon water. The first pot has 75% of lemon water. The second has 50% lemon water. How much lemon water should he mix from each of the pots so as to get 12 litres of lemon water such that the proportion of lemon water to soda is 5 : 3?

12litres

12litres

10litres

10litres

8litres

8litres

6litres

6litres

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Question 12

Time: 00:00:00
A shopkeeper has two tins of ghee first having 25% of oil and another covers 50% oil. Remaining part is of pure ghee in both of tins. Now if he wants a new tin of 12 litre with a ghee to oil ratio as 5:2 then how much ghee he should mix from each of the tin?

9.50

9.50

10

10

10.28

10.28

14.35

14.35

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