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Mixture and Alligation Questions: Solved 187 Mixture and Alligation Questions and answers section with explanation for various online exam preparation, various interviews, Aptitude Category online test. Category Questions section with detailed description, explanation will help you to master the topic.
Mixture and Alligation Questions
81. How many liters of water should be added to a 30 liter mixture, containing milk and water in the ratio 7:3 such that the resultant mixture has 40 % water in it.
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Correct Ans:5
Explanation:
Given: 30 Liters of mixture, Milk and water in the ratio 7 : 3 Which means, we have 21 liters of milk and 9 liters of water.
We add water the resulting solution is 21 liters of milk and 9 + x liters of water.
Total quantity = 30 +x.
Water percentage is 40 % = > 40 x (30+x)/100 = 9 + x
=>4(30+x) = 10(9+x)
=> 120 + 4x = 90 + 10x
=> 10x - 4x = 120-90
=>6x = 30
=> x = 5
Thus the quantity of water added = 5 liters
We add water the resulting solution is 21 liters of milk and 9 + x liters of water.
Total quantity = 30 +x.
Water percentage is 40 % = > 40 x (30+x)/100 = 9 + x
=>4(30+x) = 10(9+x)
=> 120 + 4x = 90 + 10x
=> 10x - 4x = 120-90
=>6x = 30
=> x = 5
Thus the quantity of water added = 5 liters
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82. 50 liters of mixture has 60% milk. How much milk should be added to the mixture to make it 80% pure?
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Correct Ans:135 liters
Explanation:
Original mixture comprises 50 liters of milk and water.
Out of the 50 liters, 60% is pure milk.
=> ( 60 / 100 ) x 50 = pure milk
=>30 liters = pure milk
In 50 liters mixture, remaining 20 liters = water
When "x" liters of pure milk is added to 50 liters of mixture
New mixture = ( 50 + x ) liters
Milk in new mixture = (30 + x) liters
Given milk in new mixture = 80% of (50 + x)
=> 30 + x = (80 / 100) * (50+ x)
=> 30 + x = (8 / 10) * (50+ x)
=> 10 (30 + x) = 8 (50+ x)
=> 130 + 10x = 400 + 8x
=> 10 x - 8 x = 400 - 130
=> 2x = 270
=> x = 135 liters
Hence we need to add 135 liters of pure milk to the 50 liters of mixtureto make it 80% pure.
Out of the 50 liters, 60% is pure milk.
=> ( 60 / 100 ) x 50 = pure milk
=>30 liters = pure milk
In 50 liters mixture, remaining 20 liters = water
When "x" liters of pure milk is added to 50 liters of mixture
New mixture = ( 50 + x ) liters
Milk in new mixture = (30 + x) liters
Given milk in new mixture = 80% of (50 + x)
=> 30 + x = (80 / 100) * (50+ x)
=> 30 + x = (8 / 10) * (50+ x)
=> 10 (30 + x) = 8 (50+ x)
=> 130 + 10x = 400 + 8x
=> 10 x - 8 x = 400 - 130
=> 2x = 270
=> x = 135 liters
Hence we need to add 135 liters of pure milk to the 50 liters of mixtureto make it 80% pure.
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83. How many liters of a 12 litre mixture containing milk and water in the ratio of 2 : 3 be replaced with pure milk so that the resultant mixture contains milk and water in equal proportion?
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Correct Ans:2 liters
Explanation:
The mixture contains 40% milk and 60% water in it.
That is 4.8 liters of milk and 7.2 liters of water.
Now we are replacing the mixture with pure milk so that the amount of milk and water in the mixture is 50% and 50%.
That is we will end up with 6 liters of milk and 6 liters of water. Water gets reduced by 1.2 liters.
To remove 1.2 liters of water from the original mixture containing 60% water, we need to remove 1.2 / 0.6 liters of the mixture = 2 liters.
That is 4.8 liters of milk and 7.2 liters of water.
Now we are replacing the mixture with pure milk so that the amount of milk and water in the mixture is 50% and 50%.
That is we will end up with 6 liters of milk and 6 liters of water. Water gets reduced by 1.2 liters.
To remove 1.2 liters of water from the original mixture containing 60% water, we need to remove 1.2 / 0.6 liters of the mixture = 2 liters.
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84. 20 liters of mixture has 70% milk. How much milk should be added to the mixture to make it 90% pure?
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Correct Ans:40 liters
Explanation:
Original mixture comprises 20 liters of milk and water.
Out of the 20 liters, 70 % is pure milk.
=> ( 70 / 100 ) x 20 = pure milk
=>14 liters = pure milk
In 20 liters mixture, remaining 6 liters = water
When "x" liters of pure milk is added to 20 liters of mixture
New mixture = ( 20 + x ) liters
Milk in new mixture = (14 + x) liters
Given milk in new mixture = 90% of (20+ x)
=> 14 + x = (90 / 100) * (20 + x)
=> 14 + x = (9 / 10) * (20+ x)
=> 10 (14 + x) = 9 (20 + x)
=> 140 + 10x = 180 + 9x
=> 10 x - 9 x = 180 - 140
=> x = 40 liters
Hence we need to add 40 liters of pure milk to the 20 liters of mixtureto make it 90% pure.
Out of the 20 liters, 70 % is pure milk.
=> ( 70 / 100 ) x 20 = pure milk
=>14 liters = pure milk
In 20 liters mixture, remaining 6 liters = water
When "x" liters of pure milk is added to 20 liters of mixture
New mixture = ( 20 + x ) liters
Milk in new mixture = (14 + x) liters
Given milk in new mixture = 90% of (20+ x)
=> 14 + x = (90 / 100) * (20 + x)
=> 14 + x = (9 / 10) * (20+ x)
=> 10 (14 + x) = 9 (20 + x)
=> 140 + 10x = 180 + 9x
=> 10 x - 9 x = 180 - 140
=> x = 40 liters
Hence we need to add 40 liters of pure milk to the 20 liters of mixtureto make it 90% pure.
Workspace
85. Two liquids A and B are mixed together in the ratio 2 : 3. The average cost of liquid B is Rs 35 per liter and the average cost of the mixture is Rs. 30 per liter, then find the average cost of liquid A per liter.
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Correct Ans:22.5
Explanation:
Given, Ratio of liquids A and B =2 : 3
Average cost of liquid B per liter = Rs. 35
Average cost of mixture per liter = Rs. 30
Let theAverage cost of liquid A per liter = Rs. x
According to alligation equation,
(35-30)/(30-x) = 2/3
=> 5 /(30-x) =2/3
=> 5 * 3 = 2 *(30-x)
=> 15 = 60 - 2x
=> 2x = 60 - 15
=> 2x = 45
=> x = 22.5
Therefore,Average cost of liquid A per liter = Rs. x = Rs. 22.5
Average cost of liquid B per liter = Rs. 35
Average cost of mixture per liter = Rs. 30
Let theAverage cost of liquid A per liter = Rs. x
According to alligation equation,
(35-30)/(30-x) = 2/3
=> 5 /(30-x) =2/3
=> 5 * 3 = 2 *(30-x)
=> 15 = 60 - 2x
=> 2x = 60 - 15
=> 2x = 45
=> x = 22.5
Therefore,Average cost of liquid A per liter = Rs. x = Rs. 22.5
Workspace
86. How many liters of water should be added to a 30 liter mixture of milk and water containing milk and water in the ratio 7:3 such that the resultant mixture has 40 % water in it.
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Correct Ans:5
Explanation:
Given, Total quantity of mixture = 30 liter
=> Milk + water = 30 liter
Given,Ratio of Milk and water = 7 : 3
=> Milk quantity = 7x liter
and waterquantity = 3x liter
Thus, 7x + 3x = 30
=> 10x = 30
=> x = 3
Hence, Milk =7x= 7 * 3 = 21 liter
Water = 3x = 3 * 3 = 9 liter
If we add "x" liters of water to the 30 liter mixture, to obtain 40% water in it,
the total quantity of resultant mixture = 30 + x liter
water quantity will become = 9 + x liter
thus, 40% of new mixture = water
=> 40% of (30 + x) =9 + x
=> (40/100) * (30 + x) = 9 +x
=> (4/10) * (30 + x) = 9 +x
=> 4 * (30 + x) = 10 * (9 +x)
=> 120 + 4x = 90 + 10x
=> 10x - 4x = 120 - 90
=> 6x = 30
=> x = 5
Thus,to obtain 40% water in new mixture, the quantity of water to be added = 5 liter.
=> Milk + water = 30 liter
Given,Ratio of Milk and water = 7 : 3
=> Milk quantity = 7x liter
and waterquantity = 3x liter
Thus, 7x + 3x = 30
=> 10x = 30
=> x = 3
Hence, Milk =7x= 7 * 3 = 21 liter
Water = 3x = 3 * 3 = 9 liter
If we add "x" liters of water to the 30 liter mixture, to obtain 40% water in it,
the total quantity of resultant mixture = 30 + x liter
water quantity will become = 9 + x liter
thus, 40% of new mixture = water
=> 40% of (30 + x) =9 + x
=> (40/100) * (30 + x) = 9 +x
=> (4/10) * (30 + x) = 9 +x
=> 4 * (30 + x) = 10 * (9 +x)
=> 120 + 4x = 90 + 10x
=> 10x - 4x = 120 - 90
=> 6x = 30
=> x = 5
Thus,to obtain 40% water in new mixture, the quantity of water to be added = 5 liter.
Workspace
87. How many liters of water should be added to a 30 liter mixture of milk and water containing milk and water in the ratio 7:3 such that the resultant mixture has 40 % water in it.
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Correct Ans:5
Explanation:
Given, In 30 Liters of mixture, Milk and water in the ratio 7 : 3.
=> milk = 7x liters
water = 3x liters
Now, Milk + water = 30 liters
=> 7x + 3x = 30
=> 10 x = 30
=> x = 3
Milk = 7x liters = 7 * 3 = 21 liters
Water = 3x liters = 3 * 3 = 9 liters
When we add x liters of water, the resulting solution is 21 liters of milk and 9 + x liters of water.
Then,Total quantity = 30+x
Water percentage is 40 %
= > 40 x (30+x)/100 = 9 + x
=>4(30+x) = 10(9+x)
=> 120 + 4x = 90 + 10x
=> 10x – 4x = 120-90
=>6x = 30
=> x = 5
=> Water added = 5 liters
Workspace
88. Two liquids A and B are mixed together in the ratio 5 : 6. The average cost of liquid B is Rs 15 per litre and the average cost of the mixture is Rs. 10 per liter, then find the average cost of liquid A per litre.
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Correct Ans:Rs. 4
Explanation:
Given, Ratio of liquids A and B = 5 : 6
Average cost of liquid B per liter = Rs. 15
Average cost of mixture per liter = Rs. 10
Let theAverage cost of liquid A per liter = Rs. x
According to alligation equation,
(15 - 10)/(10 - x) = 5/6
=> 5 /(10 - x) = 5/6
=> 5 * 6 = 5 *(10 - x)
=> 30 = 50 - 5x
=> 5x = 50 - 30
=> 5x = 20
=> x = 4
Therefore,Average cost of liquid A per liter = Rs. x = Rs. 4
Average cost of liquid B per liter = Rs. 15
Average cost of mixture per liter = Rs. 10
Let theAverage cost of liquid A per liter = Rs. x
According to alligation equation,
(15 - 10)/(10 - x) = 5/6
=> 5 /(10 - x) = 5/6
=> 5 * 6 = 5 *(10 - x)
=> 30 = 50 - 5x
=> 5x = 50 - 30
=> 5x = 20
=> x = 4
Therefore,Average cost of liquid A per liter = Rs. x = Rs. 4
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89. Petrol & Kerosene are mixed in the ratio of 15:18. Total Volume of the mixture is 100 litres. Find the composition of Petrol in the overall mixture?
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Correct Ans:45.45
Explanation:
Given Petrol & Kerosene are in the ratio of 15:18
Given volume of mixture = 100 litres
Quantity of Petrol = 15/(15+18) x 100
= 45.45
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90. Petrol & Kerosene are mixed in the ratio of 15:16. Total Volume of the mixture is 100 litres. Find the composition of Petrol in the overall mixture?
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Correct Ans:48.39
Explanation:
Given Petrol & Kerosene are in the ratio of 15:16
Given volume of mixture = 100 litres
Quantity of Petrol = 15/(15+16) x 100
= 48.39
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91. Petrol & Kerosene are mixed in the ratio of 15:12. Total Volume of the mixture is 100 litres. Find the composition of Petrol in the overall mixture?
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Correct Ans:55.56
Explanation:
Given Petrol & Kerosene are in the ratio of 15:12
Given volume of mixture = 100 litres
Quantity of Petrol = 15/(15+12) x 100
= 55.56
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92. Petrol & Kerosene are mixed in the ratio of 15:10. Total Volume of the mixture is 100 litres. Find the composition of Petrol in the overall mixture?
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Correct Ans:60
Explanation:
Given Petrol & Kerosene are in the ratio of 15:10
Given volume of mixture = 100 litres
Quantity of Petrol = 15/(15+10) x 100
= 60
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93. Petrol & Kerosene are mixed in the ratio of 15:8. Total Volume of the mixture is 100 litres. Find the composition of Petrol in the overall mixture?
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Correct Ans:65.22
Explanation:
Given Petrol & Kerosene are in the ratio of 15:8
Given volume of mixture = 100 litres
Quantity of Petrol = 15/(15+8) x 100
= 65.22
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94. Petrol & Kerosene are mixed in the ratio of 15:6. Total Volume of the mixture is 100 litres. Find the composition of Petrol in the overall mixture?
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Correct Ans:71.43
Explanation:
Given Petrol & Kerosene are in the ratio of 15:6
Given volume of mixture = 100 litres
Quantity of Petrol = 15/(15+6) x 100 = 71.43
Given volume of mixture = 100 litres
Quantity of Petrol = 15/(15+6) x 100 = 71.43
Workspace
95. Petrol & Kerosene are mixed in the ratio of 15:4. Total Volume of the mixture is 100 litres. Find the composition of Petrol in the overall mixture?
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Correct Ans:78.95
Explanation:
Given Petrol & Kerosene are in the ratio of 15:4
Given volume of mixture = 100 litres
Quantity of Petrol = 15/(15+4) x 100
= 78.95
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96. Petrol & Kerosene are mixed in the ratio of 15:2. Total Volume of the mixture is 100 litres. Find the composition of Petrol in the overall mixture?
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Correct Ans:88.24
Explanation:
Given Petrol & Kerosene are in the ratio of 15:2
Given volume of mixture = 100 litres
Quantity of Petrol = 15/(15+2) x 100
= 88.24
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97. Milk & Water are mixed in the ratio of 13:18. Total Volume of the mixture is 450 litres. Find the composition of Milk in the overall mixture?
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Correct Ans:188.71
Explanation:
Given Milk & Water are in the ratio of 13:18
Given volume of mixture = 450 litres
Quantity of Milk = 13/(13+18) x 450 = 188.71
Given volume of mixture = 450 litres
Quantity of Milk = 13/(13+18) x 450 = 188.71
Workspace
98. Milk & Water are mixed in the ratio of 13:16. Total Volume of the mixture is 450 litres. Find the composition of Milk in the overall mixture?
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Correct Ans:201.72
Explanation:
Given Milk & Water are in the ratio of 13:16
Given volume of mixture = 450 litres
Quantity of Milk = 13/(13+16) x 450
= 201.72
Workspace
99. Milk & Water are mixed in the ratio of 13:14. Total Volume of the mixture is 450 litres. Find the composition of Milk in the overall mixture?
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Correct Ans:216.67
Explanation:
Given Milk & Water are in the ratio of 13:14
Given volume of mixture = 450 litres
Quantity of Milk = 13/(13+14) x 450
= 216.67
Workspace
100. Milk & Water are mixed in the ratio of 13:12. Total Volume of the mixture is 450 litres. Find the composition of Milk in the overall mixture?
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Correct Ans:234
Explanation:
Given Milk & Water are in the ratio of 13:12
Given volume of mixture = 450 litres
Quantity of Milk = 13/(13+12) x 450 = 234
Given volume of mixture = 450 litres
Quantity of Milk = 13/(13+12) x 450 = 234
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