Mixture And Alligation Test-1

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Mixture And Alligation Test-1

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Question 1
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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?

A
26 litres

B
29.16 litres

C
28 litres

D
28.2 litres

Solution

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

Hence milk now contained by the container = 40
Question 2
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Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety of tea in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, what is the price of the third variety per kg ?

A
Rs.182.50

B
Rs.170.5

C
Rs.175.50

D
Rs.180

Solution

► Since first and second varieties are mixed in equal proportions.So, their average price = Rs.
= Rs. 130.50
► 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:
Question 3
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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?

A
5 litres, 7 litres

B
7litres, 4 litres

C
6litres, 6 litres

D
4litres, 8 litres

Solution

► Let x and (12-x) litres of milk be mixed from the first and second container respectively
► Amount of milk in x litres of the the first container = .75x
► Amount of water in x litres of the the first container = .25x
► Amount of milk in (12-x) litres of the the second container = .5(12-x)
► Amount of water in (12-x) litres of the the second container = .5(12-x)
► Ratio of water to milk = [.25x + .5(12-x)] : [.75x + .5(12-x)] = 3 : 5
⇒(.25x+6-5x)/(.75x+6-.5x) =3/5
⇒(6 −.25x)/(.25x+6) =3/5
⇒30 −1.25x=.75x+18
⇒2x=12
⇒x=6
► Since x = 6, 12-x = 12-6 = 6
Hence 6 and 6 litres of milk should mixed from the first and second container respectively
Question 4
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Two vessels A and B contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixture be mixed to obtain a new mixture in vessel C containing spirit and water in the ration 8 : 5 ?

A
3: 4

B
4 : 3

C
9 : 7

D
7 : 9

Solution

► Spirit in 1 litre mix of A = 5/7 litre.
► Spirit in 1 litre mix of B = 7/13 litre.
► Spirit in 1 litre mix of C = 8/13 litre.
By rule of alligation we have required ratio X:Y
Therefore required ratio = 1/13 : 9/91
= 7:9
Question 5
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The cost of Type 1 material is Rs. 15 per kg and Type 2 material is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then what is the price per kg of the mixed variety of material?

A
Rs. 19

B
Rs. 16

C
Rs. 18

D
Rs. 17

Solution

► Cost Price(CP) of Type 1 material is Rs. 15 per kg
► Cost Price(CP) of Type 2 material is Rs. 20 per kg
Type 1 and Type 2 are mixed in the ratio of 2 : 3
Therefore, rice per kg of the mixed variety of material = Rs.18
Question 6
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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.

A
4 : 3

B
3 : 4

C
2 : 3

D
3 : 2

Solution
Question 7
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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 the water is 16:65. How much wine did the cask originally hold?

A
30 litres

B
26 litres

C
24 litres

D
32 litres

Solution

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 the water is 16 ∶65
Calculations:
Let the quantity of the wine in the cask originally be x litres.
After first operation, wine left in the cask = (x - 8) litres So, the ratio of the quantity of wine now left in cask to that of filled cask =
This operation is performed three more times. Then, Wine : Water = 16 : 65 or wine : water = 16 : (16 + 65) = 81
Correct answer is 24.
Question 8
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A jar is full of whiskey contains 40% alcohol. A part of this whiskey is replaced by another containing 19% alcohols and now the percentage of alcohol was found to be 26%. The quantity of whiskey replaced is:

A
4/3

B
3/4

C
3/2

D
2/3

Solution

By the rule of alligation we have
► So ratio of 1st and 2nd quantities = 7:14
= 1:2
∴ Required quantity replaced = 2/3
Question 9
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How many kilograms 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 ?

A
60 Kg

B
63 kg

C
58 Kg

D
56 Kg

Solution

► S.P. of 1 kg of mixture = Rs. 9.24, Gain 10%.
By the rule of allilation, we have:
Ratio of quantities of 1^st and 2^nd kind = 14 : 6 = 7 : 3.
► Let x kg of sugar of 1^st be mixed with 27 kg of 2^nd kind.
Then, 7 : 3 = x : 27
Question 10
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A mixture of 100 litres of spirit and alcohol contains 25% alcohol. How much more alcohol should be added to the mixture to increase the percentage of alcohol to 30% in the new mixture?

A
3.33 litres

B
7.14 litres

C
5 litres

D
4 litres

Solution

Alcohol content in the alcohol to be added = 100%
Therefore, the allegation diagram for this problem can be drawn as:
Therefore, ratio of the mixture to alcohol = 70/5 = 14/1
So, alcohol to be added = 100/14
Hence, the answer is "7.14 litres ".
Choice B is the correct answer.