There is yet another important concept in the quantitative aptitude section that is mixture and alligations. Here in this article we will be discussing about 10 Mixture & Alligation Preparation Tips, Practice Questions, Answer Key & Detailed Solutions.
When two or more substance/elements are mixed in a certain ratio, the resultant compound is known as a mixture.
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Properties of a mixture:
Suppose a ‘L’ litre mixture consists of two elements ‘a’ and ‘b’ in the ratio p:q, respectively. If ‘M’ litres of the mixture is taken out, then in those ‘M’ litres, the ratio of quantities of elements ‘a’ and ‘b’ is in the same ratio i.e. p:q, respectively. Essentially, all mixtures are assumed to be homogenous unless stated otherwise.
I:
If a 100 litre mixture consists of two elements ‘a’ and ‘b’ in the ratio p:q, respectively and 40 litres of the mixture is taken out from it, then,
Quantity of element ‘a’ taken out = 40 × {p/(p + q)} litres
Quantity of element ‘b’ taken out = 40 × {q/(p + q)} litres
Mixture replacement:
Suppose a 100 litre mixture consists of two elements ‘a’ and ‘b’ in the ratio p:q, respectively.
Then, quantity of element ‘a’ in the mixture =
Quantity of element ‘b’ in the mixture =
If ‘x%’ of the mixture is replaced with an equal quantity of element ‘a’,
Then, quantity of element ‘a’ in the resultant mixture =
Quantity of element ‘b’ in the resultant mixture =
Replacing ‘x%’ of a pure element with element ‘b’ and repeating the process ‘n’ times:
Suppose a container contains 100 units of pure element ‘a’.
If ‘x%’ of the pure element is removed and is replaced with an equal quantity of element ‘b’ and this process is repeated ‘n’ times, then quantity of element ‘a’ remaining in the mixture is given by
100 × {1 – (x/100)}n units
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Alligation is a method which gives us the ratio in which two different mixtures must be mixed to obtain a third mixture in the desired proportion. Alligation can also be used to find the ratio in which elements with two different prices must be mixed to obtain a mixture in the desired price.
I:
Let mixture ‘A’ consist of two elements ‘a’ and ‘b’ where the proportion of element ‘a’ in the mixture is (m/100)
Let mixture ‘B’ consist of the same two elements ‘a’ and ‘b’ where the proportion of element ‘b’ in the mixture is (n/100)
Then, ratio of quantities in which mixtures ‘A’ and ‘B’ must be respectively mixed to obtain a proportion of (p/100) [where m > p > n] is given by:
Question 1: A mixture contains milk and water in the ratio of 13:11 respectively. If 288 ml of mixture is taken out, and the 68 ml of milk and 120 ml of water is added in the remaining mixture, such that the ratio of milk to water in the resulting mixture becomes 8:9. Find the quantity of mixture initially.
A) 648 ml
B) 504 ml
C) 432 ml
D) 576 ml
E) None of these
Question 2: 240 litres of a mixture (milk and water) contains milk and water in the ratio 7:5, respectively. 60 litres of mixture is withdrawn and is replaced with 60 litres of another mixture (milk and water) which contain 25% water. Find the ratio of milk to water in resultant mixture.
A) 5:3
B) 7:5
C) 9:7
D) 3:2
E) 4:3
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Question 3: A 512 ml mixture contains milk and water in the ratio of 9:7, respectively. If 25% of mixture is taken out and 116 ml of another mixture containing milk and water in the ratio of 21:8, respectively is added into the remaining mixture then find the ratio of milk to water in the resultant mixture.
A) 3:2
B) 3:4
C) 4:3
D) 5:4
E) None of these
Question 4: A mixture contains milk and water in the ratio of 9:7 respectively. If 288 ml of mixture is taken out, and 38 ml of milk and 34 ml of water is added in the remaining mixture such that the ratio of milk to water in the resultant mixture becomes 5:4. Find the original quantity of mixture.
A) 576 ml
B) 720 ml
C) 640 ml
D) 800 ml
E) None of these
Question 5: In a mixture of milk and water, quantity of milk is 20% more than that of water. If 33 litres of water is added to the mixture, then the quantity of water becomes 20% more than that of milk. Find the initial quantity of water.
A) 45 litres
B) 90 litres
C) 60 litres
D) 75 litres
E) None of these
Question 6: A mixture contains milk and water mixed in the ratio of 5:7 respectively. If 324 ml of mixture is taken out and replaced with 64 ml of milk then quantity of milk in the final mixture becomes 46 ml more than that of water. Find the original quantity of mixture.
A) 648 ml
B) 432 ml
C) 456 ml
D) 480 ml
E) None of these
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Question 7: A mixture contains milk and water in the ratio of 5:4 respectively. If 270 ml of mixture is taken out and 30 ml of milk and 108 ml of water is added into it then the quantity of milk in the final mixture will be 40% of the total quantity of mixture. Find the original quantity of mixture.
A) 432 ml
B) 324 ml
C) 414 ml
D) 450 ml
E) None of these
Question 8: 432 ml of mixture A containing milk and water in the ratio of 13:11, respectively is mixed with 234 ml of mixture B (containing milk and water). If ratio of milk to water in the resultant mixture is 19:18, then find the ratio of milk to water in mixture B.
A) 6:7
B) 5:7
C) 7:5
D) 7:6
E) 3:2
Question 9: Mixture ‘A’ of lime juice and water contains 45% lime juice and rest water. ‘x’ ml of lime juice and 2x ml of water is added to mixture ‘A’ such that ratio of lime juice to water in the resultant mixture becomes 15:23. Find the ratio of the initial quantity of mixture ‘A’ to ‘x’.
A) 5:4
B) 10:3
C) 8:3
D) 5:2
E) None of these
Question 10: Can ‘A’ contains mixture of oil and water in the ratio 5:2, respectively. When 80% of this mixture is replaced with 30 litres of water, the ratio of oil to water in can ‘A’ becomes 5:3. Find quantity of oil in can ‘A’ initially.
A) 750 litres
B) 450 litres
C) 340 litres
D) 850 litres
E) 600 litres
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प्रश्न 1: एक मिश्रण में दूध और पानी का अनुपात क्रमशः 13:11 है।यदि 288ml मिश्रण बाहर निकाला जाता है और शेष मिश्रण में 68 ml दूध और 120 ml पानी डाला जाता है, तो परिणामी मिश्रण में दूध और पानी का अनुपात 8: 9 हो जाता है।प्रारंभ में मिश्रण की मात्रा ज्ञात करें?
A) 648 ml
B) 504 ml
C) 432 ml
D) 576 ml
E) इनमें से कोई नहीं
प्रश्न 2: एक मिश्रण (दूध और पानी) के 240 litres में दूध और पानी का अनुपात क्रमशः 7: 5 है।60 litres मिश्रण को निकाल लिया जाता है और इसे एक अन्य मिश्रण (दूध और पानी) के 60 litres से प्रतिस्थापित किया जाता है, जिसमें 25% पानी होता है।परिणामी मिश्रण में दूध और पानी का अनुपात ज्ञात करें?
A) 5:3
B) 7:5
C) 9:7
D) 3:2
E) 4:3
प्रश्न 3: एक 512 ml मिश्रण में दूध और पानी का अनुपात क्रमशः 9: 7 है।यदि मिश्रण का 25% बाहर निकाल दिया जाता है और शेष मिश्रण में एक अन्य 116ml मिश्रण मिलाया जाता है जिसमे दूध और पानी का अनुपात क्रमशः 21: 8 है, तो परिणामी मिश्रण में दूध और पानी का अनुपात ज्ञात करें?
A) 3:2
B) 3:4
C) 4:3
D) 5:4
E) इनमें से कोई नहीं
प्रश्न 4: एक मिश्रण में दूध और पानी का अनुपात क्रमशः 9: 7 है।यदि 288ml मिश्रण बाहर निकाला जाता है, और शेष मिश्रण में 38 ml दूध और 34 ml पानी मिलाया जाता है तो परिणामी मिश्रण में दूध और पानी का अनुपात 5: 4 हो जाता है।मिश्रण की वास्तविक मात्रा ज्ञात करें?
A) 576 ml
B) 720 ml
C) 640 ml
D) 800 ml
E) इनमें से कोई नहीं
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प्रश्न 5: दूध और पानी के मिश्रण में, दूध की मात्रा पानी की मात्रा से 20% अधिक होती है।यदि मिश्रण में 33 litres पानी डाला जाता है, तो पानी की मात्रा दूध की मात्रा से 20% अधिक हो जाती है।पानी की प्रारंभिक मात्रा ज्ञात करें?
A) 45 litres
B) 90 litres
C) 60 litres
D) 75 litres
E) इनमें से कोई नहीं
प्रश्न 6: एक मिश्रण में क्रमशः 5: 7 के अनुपात में दूध और पानी मिलाया जाता है। यदि 324 ml मिश्रण को बाहर निकाल दिया जाता है और 64 ml दूध के साथ बदल दिया जाता है, तो अंतिम मिश्रण में दूध की मात्रा पानी की मात्रा से 46 ml अधिक हो जाती है। मिश्रण की वास्तविक मात्रा ज्ञात करें?
A) 648 ml
B) 432 ml
C) 456 ml
D) 480 ml
E) इनमें से कोई नहीं
प्रश्न 7: एक मिश्रण में दूध और पानी का अनुपात क्रमशः 5: 4 है। यदि 270 ml मिश्रण निकाला जाता है और 30 ml दूध और 108 ml पानी इसमें मिलाया जाता है, तो अंतिम मिश्रण में दूध की मात्रा मिश्रण की कुल मात्रा का 40% होगी। मिश्रण की वास्तविक मात्रा कितनी है?
A) 432 ml
B) 324 ml
C) 414 ml
D) 450 ml
E) इनमें से कोई नहीं
प्रश्न 8: 432 ml मिश्रण A, जिसमे दूध और पानी का अनुपात क्रमशः 13:11 है, को 234 ml मिश्रण B (दूध और पानी युक्त) के साथ मिलाया जाता है। यदि परिणामी मिश्रण में दूध और पानी का अनुपात 19:18 है, तो मिश्रण B में दूध और पानी का अनुपात ज्ञात करें?
A) 6:7
B) 5:7
C) 7:5
D) 7:6
E) 3:2
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प्रश्न 9: Lime juice और water के एक मिश्रण ‘A’ में 45% lime juice है और शेष water है|मिश्रण ‘A’ में ‘x’ ml lime juice और 2x ml water मिलाया जाता है जिससे कि परिणामी मिश्रण में lime juice और water का अनुपात 15:23 हो जाता है|मिश्रण ‘A’ की प्रारंभिक मात्रा और ‘x’ का अनुपात ज्ञात करें|
A) 5:4
B) 10:3
C) 8:3
D) 5:2
E) इनमे से कोई नहीं
प्रश्न 10: Can ‘A’ के एक मिश्रण में तेल और पानी का अनुपात क्रमशः 5:2 है| जब इस मिश्रण के 80% को 30 litres पानी से प्रतिस्थापित किया जाता है तो can ‘A’ में तेल और पानी का अनुपात 5:3 हो जाता है|प्रारंभ में can ‘A’ में तेल की मात्रा ज्ञात करें|
A) 750 litres
B) 450 litres
C) 340 litres
D) 850 litres
E) 600 litres
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| 1) – D) | 2) – A) | 3) – A) | 4) – A) | 5) – D) | 6) – B) |
| 7) – A) | 8) – A) | 9) – B) | 10) – A) |
Solution 1: D)
Let quantity of milk and water in the original mixture is 13x ml and 11x ml respectively.
Quantity of milk in 288 ml of mixture = 13/24 × 288 = 156 ml
Quantity of water in 288 ml of mixture = 11/24 × 288 = 132 ml
According to question;
[13x – 156 + 68]/[11x – 132 + 120] = 8/9
117x – 792 = 88x – 96
29x = 696
So, x = 24
So, original quantity of mixture = 24 × 24 = 576 ml
Hence, option d.
Solution 2: A)
Quantity of milk left in the mixture = (240 – 60) × (7/12) = 105 litres
Quantity of water left in the mixture = (240 – 60) × (5/12) = 75 litres
Required ratio = (105 + 0.75 × 60)/(75 + 0.25 × 60) = 5:3
Hence, option a.
Solution 3: A)
Quantity of milk in 512 ml of mixture = 9/16 × 512 = 288 ml
Quantity of water in 512 ml of mixture = 7/16 × 512 = 224 ml
Quantity of milk in 116 ml of mixture = 21/29 × 116 = 84 ml
Quantity of water in 116 ml of mixture = 8/29 × 116 = 32 ml
Desired ratio = (0.75 × 288 + 84):(0.75 × 224 + 32) = 300:200 = 3:2
Hence, option a.
Solution 4: A)
Let quantity of milk and water in the original mixture be 9x ml and 7x ml respectively.
Quantity of milk in 288 ml of mixture = 9/16 × 288 = 162 ml
Quantity of water in 288 ml of mixture = 7/16 × 288 = 126 ml
According to question;
(9x – 162 + 38)/(7x – 126 + 34) = 5/4
36x – 496 = 35x – 460
So, x = 36
Desired Answer = 36 × 16 = 576 ml
Hence, option a.
Solution 5: D)
Let the initial quantity of water be 5x litres
Therefore, initial quantity of milk = 1.2 × 5x = 6x litres
According to the question,
5x + 33 = 1.2 × 6x
Or, x = 33/2.2 = 15
Therefore, initial quantity of water = 5x = 75 litres
Hence, option d.
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Solution 6: B)
Let quantity of milk and water in the original mixture be 5x ml and 7x ml respectively.
Quantity of milk in 324 ml of mixture = 5/12 × 324 = 135 ml
Quantity of water in 324 ml of mixture = 7/12 × 324 = 189 ml
According to question;
5x – 135 + 64 = 7x – 189 + 46
2x = 72
Or, x = 36
Desired Answer = 36 × 12 = 432 ml
Hence, option b.
Solution 7: A)
Let amount of milk and water in the mixture initially is 5x ml and 4x ml respectively.
Quantity of milk in 270 ml of mixture = 5/9 × 270 = 150 ml
Quantity of water in 270 ml of mixture = 270 – 150 = 120 ml
According to question;
(5x – 150 + 30)/(4x – 120 + 108) = 2/3
Or, 15x – 360 = 8x – 24
Or, 7x = 336
Or, x = 48
Original quantity of mixture = 48 × 9 = 432 ml
Hence, option a.
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Solution 8: A)
Quantity of milk in mixture A = 13/24 × 432 = 234 ml
Quantity of water in mixture A = 432 – 234 = 198 ml
Let quantity of milk in mixture B is ‘x’ ml
Quantity of water in mixture B = ‘234 – x’ ml
According to question;
(234 + x)/(198 + 234 – x) = 19/18
Or, 4212 + 18x = 8208 – 19x
Or, 37x = 3996
Or, x = 108
Quantity of milk in mixture B = 108 ml
Quantity of water in mixture B = 234 – 108 = 126 ml
Desired ratio = 108:126 = 6:7
Hence, option a.
Solution 9: B)
Let the initial quantity of mixture ‘A’ be ‘y’ litres
Therefore, initial quantity of lime juice in mixture ‘A’ = 0.45y ml
Initial quantity of water in mixture ‘A’ = 0.55y ml
According to the question,
(0.45y + x)/(0.55y + 2x) = 15:23
Or, 10.35y + 23x = 8.25y + 30x
Or, 2.1y = 7x
Or, y:x = 10:3
Hence, option b.
Solution 10: A)
Let the quantity of oil and water in the mixture be 5x litres and 2x litres, respectively
Final quantity of oil in can ‘A’ = 0.2 × 5x = x litres
Final quantity of water in can ‘A’ = 0.2 × 2x + 30 = (0.4x + 30) litres
According to the question,
{x/(0.4x + 30)} = 5/3
Or, 3x = 2x + 150
Or, x = 150
Therefore, quantity of oil in can ‘A’ initially = 5x = 750 litres
Hence, option a.
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