Mixture and Allegation is one important concept for which candidates must practice questions in order to ace the reasoning section. In this blog we are going to provide aspirants with Practice Mixture & Alligation Questions for Mains Exams. Since RBI Assistant mains exam is just around the corner these questions will surely help in building a strong conceptual foundation. Mentioned below are the basics and few properties of Mixture and Allegations along with practice questions and answers.
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Basics:
When two or more substance/elements are mixed in a certain ratio, the resultant compound is known as a mixture.
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:
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:
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Question 1: Total population of a town was 3000 in 2011. In 2012, male population was increased by 12% while female population was increased by 18% and total population in 2012 becomes 3435. Find the number of females in the town in 2012.
A) 1960
B) 1750
C) 1250
D) 1475
E) None of these
Question 2: A mixture contains 120 litres acetone and rest water. 35% of mixture is taken out and 7 litres of water is added to it such that the ratio of acetone to water in 35% of the mixture becomes 2:1. Find the quantity of water in the initial mixture.
A) 40 litres
B) 25 litres
C) 60 litres
D) 30 litres
E) Cannot be determined
Question 3: 480 litres of a mixture contains milk to water in the ratio of 5:x. If after addition of 20 litres of water to it, the ratio of milk to water in resultant mixture becomes 3:2, then find the quantity water in the initial mixture.
A) 300 litres
B) 180 litres
C) 210 litres
D) 240 litres
E) None of these
Question 4: A mixture contains milk and water in the ratio of 13:12 respectively. If 40% of mixture is taken out and 47 ml of milk and 40 ml of water is added then the ratio of milk and water in the resulting solution becomes 11:10. Find the quantity of mixture taken out.
A) 200 ml
B) 250 ml
C) 350 ml
D) 300 ml
E) None of these
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Question 5: 144 kg of mixture ‘A’ contains only sugar and salt in the ratio of 7:5, respectively. 87 kg of mixture ‘B’ (salt + pepper) contains 65% as much salt as in mixture ‘A’. If mixtures ‘A’ and ‘B’ are mixed entirely along with 21 kg of salt, then what will be the ratio of quantity of salt to that of pepper in the resultant mixture?
A) 5:3
B) 5:2
C) 6:5
D) 7:4
E) 7:5
Question 6: Mixture ‘A’ contains alcohol and water only in the ratio 9:7 respectively while mixture ‘B’ contains water and alcohol in the ratio of 3:5, respectively. Total quantity of mixture ‘A’ is 240 litres while the quantity of alcohol in mixture ‘B’ is 25 litres more than that in mixture ‘A’. Find quantity of water in mixture ‘B’.
A) 96 litres
B) 72 litres
C) 108 litres
D) 112 litres
E) 124 litres
Question 7: Mixture of milk and water in vessel A is in the ratio of 3:2 and milk and water in vessel B is in the ratio of 5:4, respectively. If 25 litres of mixture taken out from vessel A and poured into vessel B so that ratio of milk to water in vessel B changes to 23:18, then find initial quantity of water (in litres) in vessel A, if new quantity of mixture in vessel B is 85 litres more than initial quantity of mixture in vessel A.
A) 36 litres
B) 48 litres
C) 54 litres
D) 64 litres
E) 72 litres
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Question 8: A vessel contains only water. x% of the water is taken out of the vessel and replaced with milk. Now x% of the mixture is taken out of the vessel and replaced with milk. This process is further repeated one more time. Find the value of ‘x’ if the percentage of the milk in the resultant mixture is 48.8%.
A) 10%
B) 20%
C) 30%
D) 40%
E) None of these
Question 9: A piece of alloy contains brass and bronze mixed in the ratio of 7:6 respectively. The alloy is melted in the furnace and 91 g of the alloy is taken out of it and replaced with 60 g bronze so that the ratio of the brass to bronze in the alloy thus formed becomes 3:4. Find the initial quantity of the alloy.
A) 299 g
B) 312 g
C) 325 g
D) 338 g
E) None of these
Question 10: 360 litres of mixture of milk and water is poured into a vessel of sufficiently large quantity in the ratio of 5:3, respectively. If (x + 25) litres of additional water is added to the vessel, then the ratio of milk and water in the final mixture becomes 9:8, respectively. Find the value of ‘x’.
A) 20
B) 25
C) 30
D) 40
E) 50
प्रश्न 1: 2011 में एक town की कुल जनसंख्या 3000 थी। 2012 में पुरुष जनसंख्या में 12% की वृद्धि हुई, जबकि महिला जनसंख्या में 18% की वृद्धि हुई और 2012 में कुल जनसंख्या 3435 हो गई। 2012 में town में महिलाओं की संख्या ज्ञात करें?
A) 1960
B) 1750
C) 1250
D) 1475
E) इनमें से कोई नहीं
प्रश्न 2: एक मिश्रण में 120 litres acetone और शेष water है|35% मिश्रण को बाहर निकाला जाता है और इसमें 7 litres water मिलाया जाता है जिससे कि 35% मिश्रण में acetone और water का अनुपात क्रमशः 2:1 है|प्रारंभिक मिश्रण में water की मात्रा ज्ञात करें|
A) 40 litres
B) 25 litres
C) 60 litres
D) 30 litres
E) निर्धारित नहीं किया जा सकता
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प्रश्न 3: 480 litres मिश्रण में दूध और पानी का अनुपात 5:x है|इसमें 20 litres पानी मिलाने के बाद परिणामी मिश्रण में दूध और पानी का अनुपात 3:2 हो जाता है, तो प्रारंभिक मिश्रण में पानी की मात्रा ज्ञात करें|
A) 300 litres
B) 180 litres
C) 210 litres
D) 240 litres
E) इनमे से कोई नहीं
प्रश्न 4: एक मिश्रण में दूध और पानी का अनुपात क्रमशः 13:12 है|यदि 40% मिश्रण को निकाला जाता है और 47ml दूध और 40ml पानी जोड़ा जाता है तो परिणामी मिश्रण में दूध और पानी का अनुपात 11:10 हो जाता है|निकाले गए मिश्रण की मात्रा ज्ञात करें|
A) 200 ml
B) 250 ml
C) 350 ml
D) 300 ml
E) इनमे से कोई नहीं
प्रश्न 5: 144 kg मिश्रण ‘A’ में केवल चीनी और नमक का अनुपात क्रमशः 7:5 है। 87 kg मिश्रण ‘B’ (नमक + काली मिर्च) में नमक की मात्रा मिश्रण ‘A’ में नमक की मात्रा का 65% है। यदि मिश्रण ‘A’ और ‘B’ को पूरी तरह से 21kg नमक के साथ मिलाया जाता है, तो परिणामी मिश्रण में नमक की मात्रा और काली मिर्च की मात्रा का अनुपात कितना होगा?
A) 5:3
B) 5:2
C) 6:5
D) 7:4
E) 7:5
प्रश्न 6: मिश्रण ‘A’ में केवल अल्कोहल और पानी का अनुपात क्रमशः 9:7 है जबकि मिश्रण ‘B’ में पानी और अल्कोहल का अनुपात क्रमशः 3:5 है। मिश्रण ‘A’ की कुल मात्रा 240 litres है जबकि मिश्रण ‘B’ में अल्कोहल की मात्रा मिश्रण ‘A’ की तुलना में 25 litresअधिक है। मिश्रण ‘B’ में पानी की मात्रा ज्ञात करें।
A) 96 litres
B) 72 litres
C) 108 litres
D) 112 litres
E) 124 litres
प्रश्न 7: vessel A में दूध और पानी का मिश्रण 3: 2 के अनुपात में है और vessel B में दूध और पानी क्रमशः 5: 4 के अनुपात में है। यदि vessel A से 25 litres मिश्रण निकाला जाए और vessel B में डाल दिया जाए ताकि vessel B में पानी और दूध का अनुपात 23:18 हो जाएगा, तो vessel A में पानी की प्रारंभिक मात्रा (litres में) ज्ञात करें, यदि vessel B के मिश्रण की नयी मात्रा, vessel A में मिश्रण की प्रारंभिक मात्रा से 85 litres अधिक है।
A) 36 litres
B) 48 litres
C) 54 litres
D) 64 litres
E) 72 litres
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प्रश्न 8: एक vessel में केवल water है|x% water को vessel से निकाला जाता है और milk से प्रतिस्थापित किया जाता है|अब x% मिश्रण को vessel से निकाला जाता है और milk से प्रतिस्थापित किया जाता है| इस प्रक्रिया को एक बार और दोहराया जाता है|’x’ का मान ज्ञात करें यदि परिणामी मिश्रण में milk का प्रतिशत 48.8% है|
A) 10%
B) 20%
C) 30%
D) 40%
E) None of these
प्रश्न 9: एक alloy में brass और bronze का अनुपात क्रमशः 7:6 है|Alloy को एक furnace में पिघलाया जाता है और इसमें से 91kg alloy को निकाला जाता है और 60kg bronze से प्रतिस्थापित किया जाता है और इस तरह alloy में brass और bronze का अनुपात क्रमशः 3:4 हो जाता है|Alloy की प्रारंभिक मात्रा ज्ञात करें|
A) 299 g
B) 312 g
C) 325 g
D) 338 g
E) None of these
प्रश्न 10: Milk और water के 360 litres मिश्रण को एक बड़ी मात्रा वाले vessel में डाला जाता है, और मिश्रण में milk और water की मात्रा का अनुपात क्रमशः 5:3 है|यदि vessel में (x + 25) litres water मिलाया जाता है तो अंतिम मिश्रण में milk और water का अनुपात क्रमशः 9:8 हो जाएगा|’x’ का मान ज्ञात करें|
A) 20
B) 25
C) 30
D) 40
E) 50
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| 1) – D) | 2) – A) | 3) – B) | 4) – B) | 5) – B) | 6) – A) |
| 7) – B) | 8) – B) | 9) – C) | 10) – D) |
Solution 1: D)
Overall increase in population of the town in 2012 = [(3435 – 3000)/3000] × 100 = 14.5%
So, number of females in the town in 2011 = 5/12 × 3000 = 1250
Number of females in 2012 = 1.18 × 1250 = 1475
Hence, option d.
Solution 2: A)
Let the quantity of water in the initial mixture be ‘x’ litres
According to the question,
(0.35 × 120)/(0.35x + 7) = 2/1
Or, 42/(0.35x + 7) = 2/1
Or, 0.35x + 7 = 21
Or, x = 14/0.35 = 40 litres
Therefore, quantity of water in the initial mixture = 40 litres
Hence, option a.
Solution 3: B)
The quantity of milk in mixture = [5/(5 + x)] × 480 = 2400/(5 + x)
So, quantity of water in mixture = [x/(5 + x)] × 480 = 480x/(5 + x)
According to question,
2400/(5 + x): [480x/(5 + x) + 20] = 3:2
4800/(5 + x) = (480x × 3)/(5 + x) + 60
4800 = 1440x + 300 + 60x
1500x = 4800 – 300 = 4500
x = 4500/1500
x = 3
Quantity of water in the original mixture = 3/8 × 480 = 180 litres
Hence, option b.
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Solution 4: B)
Let the quantity of milk and water in the mixture be 13x ml and 12x ml, respectively.
When 40% of mixture is taken out,
Quantity of milk in the mixture = 0.6 × 13x = 7.8x ml
Quantity of water in the mixture = 0.6 × 12x = 7.2x ml
Quantity of mixture taken out = 0.4 × (13x +12x) = 10x ml
According to question,
(7.8x + 47)/(7.2x + 40) = 11/10
78x + 470 = 79.2x + 440
1.2x = 30
x = 25
Quantity of mixture taken out = 25 × 10 = 250 ml
Hence, option b.
Solution 5: B)
Quantity of sugar in mixture ‘A’ = 144 × (7/12) = 84 kg
Quantity of salt in mixture ‘A’ = 144 × (5/12) = 60 kg
Quantity of salt in mixture ‘B’ = 60 × (65/100) = 39 kg
So, quantity of pepper in mixture ‘B’ = 87 – 39 = 48 kg
After mixing mixtures ‘A’ and ‘B’ entirely along with 21 kg of salt, ratio of quantity of salt to that of pepper = (60 + 39 + 21):48 = 120:48 = 5:2
Hence, option b.
Solution 6: A)
Let the quantity of alcohol in mixture ‘A’ = 9x kg
Then, quantity of water in mixture ‘A’ = 7x kg
According to the question,
9x + 7x = 240
Or, x = 240/16 = 15
Total quantity of alcohol in mixture ‘B’ = 9x + 25 = 135 + 25 = 160 litres
Quantity of water in mixture ‘B’ = 160 × (3/5) = 96 litres
Hence, option a.
Solution 7: B)
Let, Initial quantity (in litres) of milk and water in vessel B be 5x and 4x, respectively.
According to question,
[5x + (3/5) × 25]/[4x + (2/5) × 25] = 23/18
[5x + 15]/[4x + 10] = 23/18
90x + 270 = 92x + 230
2x = 40, x = 20
Therefore, total initial quantity of mixture in vessel B = 20(5 + 4) = 180 litres
So, initial quantity of mixture in vessel A = (180 + 25) – 85 = 120 litres
Therefore, initial quantity of water in vessel A = (2/5) × 120 = 48 litres
Hence, option b.
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Solution 8: B)
Let the initial quantity of water in the vessel = 100 litres
Quantity of milk in the resultant mixture = 100 × 48.8 = 48.8 litres
So the quantity of water in the resultant mixture = 100 – 48.8 = 51.2 litres
According to question: 100 × (1 – x/100)3 = 51.2
(100 – x)3 = 512000
100 – x = 80, x = 20
So the value of ‘x’ = 20%
Hence, option b.
Solution 9: C)
Let the initial quantities of brass and bronze in the alloy are 7x g and 6x g respectively.
91 g alloy contains 49 g brass and 42 g bronze
According to the question: (7x – 49)/ (6x – 42 + 60) = 3/4
28x – 196 = 18x + 54
10x = 250, x = 25
So the initial quantity of alloy = 25 × 13 = 325 g
Hence, option c.
Solution 10: D)
Quantity of milk initially in vessel = (5/8) × 360 = 225 litres
So, quantity of water initially in vessel = (3/8) × 360 = 135 litres
According to question,
225/ (135 + x + 25) = 9/8
25 × 8 = 160 + x
x = 200 – 160
x = 40
Hence, option d.
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This brings us to the end of the mixture and allegation questions and answers blog. Stay tuned for more such practice questions based on different concepts.
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