This set of Aptitude Questions and Answers (MCQs) focuses on “Alligation or Mixture”. These questions are beneficial for various competitive exams, placement interviews, and entrance tests.
1. 5 liters of water is mixed in x liters of milk. If the water is 20% of the mixture, find the value of x.
a) 5 liters
b) 25 liters
c) 10 liters
d) 20 liters
View Answer
Explanation: The quantity of milk is x liters.
The quantity of water is 5 liters
Water is 20% of the final solution
20% of the solution is 5 liters
100% of the solution = 100 / 20 * 5 = 25
The quantity of milk = 25 – 5 = 20 liters.
2. A solution contains 20% of mixture p and 50% of mixture q. If the quantity of r is 18 liters, find the quantity of the entire mixture.
a) 30 liters
b) 45 liters
c) 60 liters
d) 90 liters
View Answer
Explanation: The percentage of mixture r = 100 – (20 + 50) = 100 – 70 = 30%
30% of the solution is 18 liters.
100 % of the mixture = 18 / 30 * 100 = 60 liters.
3. A solution containing 50% of milk is mixed with another mixture containing x% of milk in equal proportions. The mixture so formed contains 45% of milk. Find the value of x.
a) 10
b) 20
c) 30
d) 40
View Answer
Explanation: The mixtures are mixed in equal proportions.
Let the quantity of both the mixtures be 100 liters initially.
The volume of milk from the first mixture = 50% of 100 = 50 liters
The volume of milk from the second mixture = x% of 100 = x liters
The volume of milk in the newly formed mixture = 45% of 200 = x + 50
X + 50 = 45% of 200 = 90
X + 50 = 90, x = 90 – 50 = 40
X = 40
4. A solution containing 55% of milk is mixed with another mixture containing x% of milk in equal proportions. The mixture so formed contains 75% of milk. Find the value of x.
a) 55
b) 65
c) 85
d) 95
View Answer
Explanation: The mixtures are mixed in equal proportions.
Let the quantity of both the mixtures be 100 liters initially.
The volume of milk from the first mixture = 55% of 100 = 55 liters
The volume of milk from the second mixture = x% of 100 = x liters
The volume of milk in the newly formed mixture = 75% of 200 = x + 55
75% of 200 = x + 55 = 150 = x + 55, x = 150 – 55 = 95
X = 95
5. A solution containing 35% of oil is mixed with another mixture containing x% of oil in a ratio 2 : 3. If the mixture so formed contains 20% of oil, find the value of x.
a) 10
b) 15
c) 20
d) 25
View Answer
Explanation: The mixtures are mixed in a ratio 2 : 3.
Let the quantities of mixture mixed be 200 liters and 300 liters, respectively.
The amount of oil in first mixture = 35% = 35% of 200 = 70 liters
The amount of oil in the second mixture = x% = x% of 300 = 3x
The mixture formed by mixing the two given mixtures contains 20% of oil = 20% of 500 = 100 liters
100 liters = 70 liters + 3x
3x = 30, x = 10
6. A mixture containing 50% of water is mixed with another mixture x% of water in the ratio 4 : 5. If the percentage of water in the new mixture is 40%, find the value of x.
a) 30
b) 32
c) 34
d) 40
View Answer
Explanation: The mixtures are mixed in a ratio 4 : 5.
Let the quantities of the mixture mixed be 400 liters and 500 liters, respectively.
The percentage of water in first mixture = 50% = 50% of 400 = 200 liters
The quantity of water in the second mixture = x% of 500 = 5x
The quantity of water in the final mixture = 40% of 900 = 360 liters
5x + 200 liters = 360 liters
5x = 360 – 200 = 160 liters
X = 160 / 5 = 32
X = 32
7. A mixture containing 35% acid is mixed in another liquid containing x% acid in a ratio 3 : 2. If the percentage of acid in the final solution is 30%, find the value of x.
a) 17.5
b) 22.5
c) 25.5
d) 27.5
View Answer
Explanation: The mixtures are mixed in a ratio 3 : 2.
Let the quantity of the mixtures mixed be 300 liters and 200 liters, respectively.
The quantity of acid in the first mixture = 35% of 300 = 105 liters
The quantity of acid in the second mixture = x% of 200 = 2x
The quantity of acid in the final mixture = 30% of 500 = 150 liters
2x + 105 liters = 150 liters, 2x = 45 liters, x = 45 / 2 = 22.5
8. A mixture containing 70% of water is mixed in another mixture containing x% of water in the ratio 1 : 10. If the percentage of water in the mixture so formed is 20%, find the value of x.
a) 15
b) 20
c) 25
d) 30
View Answer
Explanation: The mixtures are mixed in a ratio 1 : 10.
Let the mixtures mixed be 100 liters and 1000 liters.
The quantity of water in the first mixture = 70% of 100 = 70 liters
The quantity of water in the second mixture = x% of 1000 = 10x
The quantity of water in the final mixture = 20% of 1100 = 220
70 + 10x = 220, 10x = 150, x = 15
9. A mixture containing 65% of ethanol is mixed with another mixture containing x% of ethanol in the ratio 8 : 13. If the percentage of ethanol in the final mixture is 50%, find the value of x.
a) 40.76
b) 42.67
c) 44.76
d) 46.67
View Answer
Explanation: The mixtures are mixed in a ratio 8 : 13.
Let the quantities of mixture mixed be 800 liters and 1300 liters, respectively.
The quantity of ethanol in the first mixture = 65% of 800 = 520 liters
The quantity of ethanol in the second mixture = x% of 1300 = 13x
The quantity of ethanol in the final mixture = 50% of 2100 = 1050
13x + 520 = 1050, 13x = 530, x = 530 / 13 = 40.76
10. A mixture containing 45% of oil is mixed with another mixture containing x% of oil in a ratio 3 : 5. If the quantity of oil in the final mixture is 50% of the mixture, find the value of x.
a) 51
b) 52
c) 53
d) 55
View Answer
Explanation: The mixtures are mixed in a ratio 3 : 5.
Let the quantities of the mixture mixed be 300 liters and 500 liters, respectively.
The amount of oil in the first mixture = 45% of 300 = 135 liters
The quantity of oil in the second mixture = x% of 500 = 5x
The quantity of oil in the final mixture = 50% of 800 = 400 liters
5x + 135 = 400, 5 = 400 – 135 = 265, x = 265 / 5 = 53
X = 53
11. A solution containing 95% of oil is mixed with another mixture containing x% of oil in a ratio 3 : 2. If the mixture so formed contains 60% of oil, find the value of x.
a) 7.5
b) 10
c) 12.5
d) 15
View Answer
Explanation: The mixtures are mixed in a ratio 3 : 2.
Let the quantities of mixture mixed be 300 liters and 200 liters, respectively.
The amount of oil in first mixture = 95% = 95% of 300 = 285 liters
The amount of oil in the second mixture = x% = x% of 200 = 2x
The mixture formed by mixing the two given mixtures contains 60% of oil = 60% of 500 = 300 liters
300 liters = 285 liters + 2x
2x = 15, x = 7.5
12. A mixture containing 30% of water is mixed with another mixture x% of water in the ratio 5 : 2. If the percentage of water in the new mixture is 30%, find the value of x.
a) 20
b) 30
c) 40
d) 50
View Answer
Explanation: The mixtures are mixed in a ratio 5 : 2.
Let the quantities of the mixture mixed be 500 liters and 200 liters, respectively.
The percentage of water in first mixture = 30% = 30% of 500 = 150 liters
The quantity of water in the second mixture = x% of 200 = 2x
The quantity of water in the final mixture = 30% of 700 = 210 liters
2x + 150 liters = 210 liters
2x = 210 – 150 = 60 liters
X = 60 / 2 = 30
X = 30
13. A mixture containing 75% acid is mixed in another liquid containing x% acid in a ratio 1 : 3. If the percentage of acid in the final solution is 37.5%, find the value of x.
a) 17
b) 22
c) 25
d) 27
View Answer
Explanation: The mixtures are mixed in a ratio 1 : 3.
Let the quantity of the mixtures mixed be 100 liters and 300 liters, respectively.
The quantity of acid in the first mixture = 75% of 100 = 75 liters
The quantity of acid in the second mixture = x% of 300 = 3x
The quantity of acid in the final mixture = 37.5% of 400 = 150 liters
3x + 75 liters = 150 liters, 3x = 75 liters, x = 75 / 3 = 25
14. A mixture containing 10% of water is mixed in another mixture containing x% of water in the ratio 2 : 3. If the percentage of water in the mixture so formed is 22%, find the value of x.
a) 15
b) 20
c) 25
d) 30
View Answer
Explanation: The mixtures are mixed in a ratio 2 : 3.
Let the mixtures mixed be 200 liters and 300 liters.
The quantity of water in the first mixture = 10% of 200 = 20 liters
The quantity of water in the second mixture = x% of 300 = 3x
The quantity of water in the final mixture = 22% of 500 = 110
20 + 3x = 110, 3x = 90, x = 30
15. A mixture containing 25% of ethanol is mixed with another mixture containing x% of ethanol in the ratio 7 : 8. If the percentage of ethanol in the final mixture is 17%, find the value of x.
a) 5
b) 7
c) 10
d) 13
View Answer
Explanation: The mixtures are mixed in a ratio 7 : 8.
Let the quantities of mixture mixed be 700 liters and 800 liters, respectively.
The quantity of ethanol in the first mixture = 25% of 700 = 175 liters
The quantity of ethanol in the second mixture = x% of 800 = 8x
The quantity of ethanol in the final mixture = 17% of 1500 = 255 liters
8x + 175 = 255, 8x = 80, x = 80 / 8 = 10
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