Aptitude - Alligation or Mixture

Why Aptitude Alligation or Mixture?

In this section you can learn and practice Aptitude Questions based on "Alligation or Mixture" and improve your skills in order to face the interview, competitive examination and various entrance test (CAT, GATE, GRE, MAT, Bank Exam, Railway Exam etc.) with full confidence.

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You can easily solve all kind of Aptitude questions based on Alligation or Mixture by practicing the objective type exercises given below, also get shortcut methods to solve Aptitude Alligation or Mixture problems.

Exercise :: Alligation or Mixture - General Questions

1. 

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

Answer: Option C

Explanation:

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 = 3 - 3x + x litres
8

Quantity of syrup in new mixture = 5 - 5x litres
8

3 - 3x + x = 5 - 5x
8 8

5x + 24 = 40 - 5x

10x = 16

x = 8 .
5

So, part of the mixture replaced = 8 x 1 = 1 .
5 8 5


2. 

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:

A. Rs. 169.50
B. Rs. 170
C. Rs. 175.50
D. Rs. 180

Answer: Option C

Explanation:

Since first and second varieties are mixed in equal proportions.

So, their average price = Rs. 126 + 135 = Rs. 130.50
2

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:

Cost of 1 kg of 1st kind Cost of 1 kg tea of 2nd kind
Rs. 130.50 Mean Price
Rs. 153
Rs. x
(x - 153) 22.50

x - 153 = 1
22.50

x - 153 = 22.50

x = 175.50


3. 

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?

A. 10
B. 20
C. 21
D. 25

Answer: Option C

Explanation:

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

Quantity of A in mixture left = 7x - 7 x 9 litres = 7x - 21  litres.
12 4

Quantity of B in mixture left = 5x - 5 x 9 litres = 5x - 15  litres.
12 4

7x - 21
4
= 7
5x - 15  + 9
4
9

28x - 21 = 7
20x + 21 9

252x - 189 = 140x + 147

112x = 336

x = 3.

So, the can contained 21 litres of A.


4. 

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. 4 litres, 8 litres
B. 6 litres, 6 litres
C. 5 litres, 7 litres
D. 7 litres, 5 litres

Answer: Option B

Explanation:

Let the cost of 1 litre milk be Re. 1

Milk in 1 litre mix. in 1st can = 3 litre, C.P. of 1 litre mix. in 1st can Re. 3
4 4

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

Milk in 1 litre of final mix. = 5 litre, Mean price = Re. 5
8 8

By the rule of alligation, we have:

C.P. of 1 litre mixture in 1st can    C.P. of 1 litre mixture in 2nd can
3
4
Mean Price
5
8
1
2
1
8
1
8

Ratio of two mixtures = 1 : 1 = 1 : 1.
8 8

So, quantity of mixture taken from each can = 1 x 12 = 6 litres.
2


5. 

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?

A. 3 : 7
B. 5 : 7
C. 7 : 3
D. 7 : 5

Answer: Option C

Explanation:

By the rule of alligation:

Cost of 1 kg pulses of 1st kind Cost of 1 kg pulses of 2nd kind
Rs. 15 Mean Price
Rs. 16.50
Rs. 20
3.50 1.50

Required rate = 3.50 : 1.50 = 7 : 3.




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