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Aptitude :: Alligation or Mixture
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?
1
A.
3
1
B.
4
1
C.
5
1
D.
7
Answer: Option C
Explanation:
Suppose the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water.
3x
Quantity of water in new mixture = 3 - +x litres
8
5x
Quantity of syrup in new mixture = 5 - litres
8
3x 5x
3- +x = 5-
8 8
5x + 24 = 40 - 5x
10x = 16
8
x= .
5
8 1 1
So, part of the mixture replaced = x = .
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
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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.
7 21
Quantity of A in mixture left = 7x - x 9 litres = 7x -
12 4 litres.
5 15
Quantity of B in mixture left = 5x - x 9 litres = 5x -
12 4 litres.
21
7x -
4 7
=
15 9
5x -
4 +9
28x - 21 7
=
20x + 21 9
252x - 189 = 140x + 147
112x = 336
x = 3.
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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
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
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C. 7 : 3
D. 7 : 5
Answer: Option C
6. 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:
A. 4%
B.
6 %
C. 20%
D. 25%
Answer: Option C
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7. 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?
A. 36 kg
B. 42 kg
C. 54 kg
D. 63 kg
Answer: Option D
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8. 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. 26.34 litres
B. 27.36 litres
C. 28 litres
D. 29.16 litres
Answer: Option D
Explanation:
4 3
Amount of milk left after 3 operations = 40 1 -
40 litres
9 9 9
= 40 x x x = 29.16 litres.
9. 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:
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1
A.
3
2
B.
3
2
C.
5
3
D.
5
Answer: Option B
10.
In what ratio must water be mixed with milk to gain 16 % on selling the mixture at cost price?
A. 1:6
B. 6 : 1
C. 2 : 3
D. 4 : 3
Answer: Option A
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11. 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. 1:3
B. 2 : 3
C. 3 : 4
D. 4 : 5
Answer: Option B
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12. 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%?
A. 3:2
B. 3 : 4
C. 3 : 5
D. 4 : 5
Answer: Option A
13. 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:
A. Rs. 18
B. Rs. 18.50
C. Rs. 19
D. Rs. 19.50
Answer: Option A
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14. 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?
A. 18 litres
B. 24 litres
C. 32 litres
D. 42 litres
Answer: Option B
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15. 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:
A. 400 kg
B. 560 kg
C. 600 kg
D. 640 kg
Answer: Option C
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