alligation or mixture aptitude questions

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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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