<\/p>\n\n\n\n
If we take a look at the RBI Grade B Phase 1 Quantitative Aptitude section of past years, questions on Mixture & Alligation usually appear 1 to 3 times (out of 30 questions). This makes up around 3% to 10% of the section. While the number seems small, the scoring potential is high because these questions are straightforward once you know the method. You just need to recall the right formula and set it up correctly. In this post, you\u2019ll get the important concepts, the main alligation formula, and some fast tricks to solve such questions in seconds. By the end, you will be ready to tackle any Mixture & Alligation question with confidence.<\/p>\n\n\n\n
<\/p>\n\n\n\n
<\/p>\n\n\n\n
ALSO READ: How to Score Maximum Marks in Cloze Test<\/a><\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n Mixture & Alligation is a method to quickly solve problems involving the mixing of two or more items with different prices, quantities, or concentrations to achieve a desired average.<\/p>\n\n\n\n You will mostly see two kinds of questions in RBI Grade B:<\/p>\n\n\n\n When two items with values C1 and C2 are mixed to get a mean value M:<\/p>\n\n\n\n Quantity ratio = (C2 \u2013 M) : (M \u2013 C1)<\/strong><\/p>\n\n\n\n Here:<\/p>\n\n\n\n <\/p>\n\n\n\n ALSO READ: How to Score Maximum Marks in Cloze Test<\/a><\/strong> & Ratio & Proportion Concepts and Shortcuts for RBI Grade B Exam<\/a><\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n The biggest advantage of alligation is speed. A normal average calculation takes more time, but the alligation rule gives you the ratio directly. This is exactly why exam setters use this topic \u2014 it tests both speed and understanding.<\/p>\n\n\n\n Here are some types of questions that appear in the exam:<\/p>\n\n\n\n Example: A shopkeeper mixes tea worth \u20b9200\/kg with tea worth \u20b9280\/kg to get tea worth \u20b9240\/kg. Find the ratio.<\/p>\n\n\n\n Using alligation: High = 280, Low = 200, Mean = 240.<\/p>\n\n\n\n Ratio = (280 \u2013 240) : (240 \u2013 200) = 40 : 40 = 1 : 1.<\/p>\n\n\n\n Example: A container has 30 litres of milk (100%). How much water should be added to make it 80% milk?<\/p>\n\n\n\n Milk quantity stays 30.<\/p>\n\n\n\n Let total mixture be x.<\/p>\n\n\n\n 80% of x = 30 \u21d2 x = 37.5 litres.<\/p>\n\n\n\n Water = 37.5 \u2013 30 = 7.5 litres.<\/p>\n\n\n\n Example: A vessel has 60 litres of milk. 6 litres are removed and replaced with water. This process is repeated 2 more times. Find remaining milk.<\/p>\n\n\n\n Formula: <\/strong>Final milk = 60 \u00d7 (1 \u2013 6\/60)^3 = 60 \u00d7 (0.9)^3 = 60 \u00d7 0.729 = 43.74 litres.<\/p>\n\n\n\n <\/p>\n\n\n\n ALSO READ: Word Swap Tricks for RBI Grade B Phase 1 Exam<\/a><\/strong><\/p>\n\n\n\n <\/p>\n\n\n\n <\/p>\n\n\n\n Some tricks make your calculations easy. Here are some tricks that will help you in solving all types of questions related to Mixture & Alligation:<\/p>\n\n\n\n 1. Always place the mean in the middle: <\/strong>Draw the alligation cross with high value at top left, low value at bottom left, and mean in the middle right. The differences automatically give you the ratio.<\/p>\n\n\n\n 2. For concentration, use percentage values directly: <\/strong>If milk = 100% and water = 0%, just put these into the alligation formula without converting to decimals.<\/p>\n\n\n\n 3. For repeated replacement, don\u2019t re-calculate each step: <\/strong>The (1 \u2013 x\/V)^n formula directly gives you the final concentration. Saves time in multiple replacement questions.<\/p>\n\n\n\n 4. Double-check ratios with a quick average: <\/strong>After finding the ratio, take the weighted average to confirm it matches the given mean. This prevents silly mistakes.<\/p>\n\n\n\n 5. Learn to spot \u201chidden\u201d alligation questions: <\/strong>Sometimes a question looks like average or ratio but can be solved in one step with alligation. This can save 30\u201340 seconds per question.<\/p>\n\n\n\n Example 1:<\/strong> Ratio = (45 \u2013 40) : (40 \u2013 30) = 5 : 10 = 1 : 2.<\/p>\n\n\n\n Example 2:<\/strong> Ratio = (50 \u2013 40) : (40 \u2013 20) = 10 : 20 = 1 : 2.<\/p>\n\n\n\n Example 3:<\/strong> Milk = 30 litres, Water = 20 litres. <\/p>\n\n\n\n Question 1:<\/strong> Mixture A contains milk and water in the ratio of 15:11 respectively while mixture B contains milk and water in the ratio of 13:9 respectively. Find the ratio in which mixture A should be mixed with mixture B so that ratio of milk to water in the resultant mixture becomes 7:5 respectively.<\/p>\n\n\n\n A) 17:11<\/p>\n\n\n\n B) 11:15<\/p>\n\n\n\n C) 12:11<\/p>\n\n\n\n D) 13:11<\/p>\n\n\n\n E) Can\u2019t be determined<\/p>\n\n\n\n Question 2:<\/strong> 25% of a 320 litres mixture \u2018A\u2019 (milk and water) is drawn in container \u2018P\u2019. Mixture \u2018B\u2019 which contains milk and water, only in the ratio 3:5, respectively is also added to the container \u2018P\u2019 such that ratio of milk to water in container \u2018P\u2019 becomes 11:17. Which of the following can be possible quantity (in litres) of milk in mixture \u2018A\u2019 and mixture \u2018B\u2019?<\/p>\n\n\n\n A) 140 and 75<\/p>\n\n\n\n B) 120 and 60<\/p>\n\n\n\n C) 160 and 100<\/p>\n\n\n\n D) 200 and 40<\/p>\n\n\n\n E) 80 and 15<\/p>\n\n\n\n Question 3:<\/strong> Can \u2018A\u2019 contain mixture of milk and water, only such that quantity of milk is 120 litres more than that of water. 60% of the mixture from can \u2018A\u2019 is withdrawn in an empty can \u2018B\u2019. When \u2018y\u2019 litres of milk and (y + 12) litres of water is added to can \u2018B\u2019, the ratio of milk to water in it becomes 3:2. Find the sum of quantity of water withdrawn from can \u2018A\u2019 and quantity of milk added to can \u2018B\u2019.<\/p>\n\n\n\n A) 112 litres<\/p>\n\n\n\n B) 108 litres<\/p>\n\n\n\n C) 72 litres<\/p>\n\n\n\n D) 96 litres<\/p>\n\n\n\n E) Cannot be determined<\/p>\n\n\n\n Question 4:<\/strong> A mixture of milk and water contains ______% more milk than water in it. If the quantity of water would have been _____ litres more, then the quantity of milk would be ______% more\/less than that of water. Initial quantity of mixture is 480 litres.<\/p>\n\n\n\n The values given in which of the following options will fill the blanks in the same order in which is it given to make the statement true:<\/p>\n\n\n\n I. 100, 40, 60<\/p>\n\n\n\n II. 40, 200, 30<\/p>\n\n\n\n III. 120, 50, 65<\/p>\n\n\n\n A) Only I<\/p>\n\n\n\n B) Only I and III<\/p>\n\n\n\n C) All I, II and III<\/p>\n\n\n\n D) Only II and III<\/p>\n\n\n\n E) Only II<\/p>\n\n\n\n \u092a\u094d\u0930\u0936\u094d\u0928 1:<\/strong> None<\/p>\n\n\n\n A) 17:11<\/p>\n\n\n\n B) 11:15<\/p>\n\n\n\n C) 12:11<\/p>\n\n\n\n D) 13:11<\/p>\n\n\n\n E) Can\u2019t be determined<\/p>\n\n\n\n \u092a\u094d\u0930\u0936\u094d\u0928 2:<\/strong> None<\/p>\n\n\n\n A) 140 and 75<\/p>\n\n\n\n B) 120 and 60<\/p>\n\n\n\n C) 160 and 100<\/p>\n\n\n\n D) 200 and 40<\/p>\n\n\n\n E) 80 and 15<\/p>\n\n\n\n \u092a\u094d\u0930\u0936\u094d\u0928 3:<\/strong> None<\/p>\n\n\n\n A) 112 litres<\/p>\n\n\n\n B) 108 litres<\/p>\n\n\n\n C) 72 litres<\/p>\n\n\n\n D) 96 litres<\/p>\n\n\n\n E) Cannot be determined<\/p>\n\n\n\n \u092a\u094d\u0930\u0936\u094d\u0928 4:<\/strong> None<\/p>\n\n\n\n A) Only I<\/p>\n\n\n\n B) Only I and III<\/p>\n\n\n\n C) All I, II and III<\/p>\n\n\n\n D) Only II and III<\/p>\n\n\n\n E) Only II<\/p>\n\n\n\n ANSWER KEYS and SOLUTIONS:<\/strong><\/p>\n\n\n\n Solution 1: D)<\/strong><\/p>\n\n\n\n Quantity of milk in mixture A = 15\/26 \u00d7 total quantity of mixture A<\/p>\n\n\n\n Quantity of milk in mixture B = 13\/22 \u00d7 total quantity of mixture B<\/p>\n\n\n\n Quantity of milk in resultant mixture = 7\/12 \u00d7 total quantity of resultant mixture<\/p>\n\n\n\n By Alligation method we get;<\/p>\n\n\n\n <\/p>\n\n\n Hence, option d.<\/p>\n\n\n\n Solution 2: A)<\/strong><\/p>\n\n\n\n Let quantity of milk in mixture \u2018A\u2019 be \u2018x\u2019 litres<\/p>\n\n\n\n Therefore, quantity of water in mixture \u2018A\u2019 = (320 \u2013 x) litres<\/p>\n\n\n\n Let the quantity of milk and water in mixture \u2018B\u2019 be 3y litres and 5y litres, respectively<\/p>\n\n\n\n According to the question,<\/p>\n\n\n\n (0.25x + 3y)\/{0.25(320 \u2013 x) + 5y} = 11\/17<\/p>\n\n\n\n Or, 4.25x + 51y = 880 \u2013 2.75x + 55y<\/p>\n\n\n\n Or, 7x \u2013 880 = 4y<\/p>\n\n\n\n Or, y = 1.75x \u2013 220<\/p>\n\n\n\n Putting x = 140 and y = 25, the above equation gets satisfied.<\/p>\n\n\n\n Therefore, quantity of milk in mixture \u2018A\u2019 and mixture \u2018B\u2019 is 140 litres and 75 litres, respectively<\/p>\n\n\n\n Hence, option a.<\/p>\n\n\n\n Solution 3: B)<\/strong><\/p>\n\n\n\n Let the quantity of water in can \u2018A\u2019 be \u2018x\u2019 litres<\/p>\n\n\n\n Therefore, quantity of milk in can \u2018A\u2019 = (x + 120) litres<\/p>\n\n\n\n According to the question,<\/p>\n\n\n\n {0.6(x + 120) + y}\/(0.6x + y + 12) = 3\/2<\/p>\n\n\n\n Or, 1.2x + 144 + 2y = 1.8x + 3y + 36<\/p>\n\n\n\n Or, 0.6x + y = 108<\/p>\n\n\n\n Or, quantity of water withdrawn from can \u2018A\u2019 + quantity of milk added to can \u2018B\u2019 = 108 litres<\/p>\n\n\n\n Hence, option b.<\/p>\n\n\n\n Solution 4: C)<\/strong><\/p>\n\n\n\n For I:<\/p>\n\n\n\n Let initial quantity of water in the mixture be \u2018x\u2019 ml<\/p>\n\n\n\n So, initial quantity of milk in the mixture = 2 \u00d7 x = 2x ml<\/p>\n\n\n\n So, x + 2x = 480<\/p>\n\n\n\n Or, 3x = 480<\/p>\n\n\n\n Or, x = 160<\/p>\n\n\n\n Initial quantity of water in the mixture = x = 160 litres<\/p>\n\n\n\n Quantity of milk in the mixture = 2 \u00d7 160 = 320 litres<\/p>\n\n\n\n Final quantity of water = 160 + 40 = 200 litres<\/p>\n\n\n\n Required percentage = {(320 \u2013 200)\/200} \u00d7 100 = 60%<\/p>\n\n\n\n Therefore, \u2018I\u2019 is true.<\/p>\n\n\n\n For II:<\/p>\n\n\n\n Let initial quantity of water in the mixture be \u2018x\u2019 ml<\/p>\n\n\n\n So, initial quantity of milk in the mixture = 1.40 \u00d7 x = 1.4x ml<\/p>\n\n\n\n So, x + 1.4x = 480<\/p>\n\n\n\n Or, 2.4x = 480<\/p>\n\n\n\n Or, x = 200<\/p>\n\n\n\n Initial quantity of water in the mixture = x = 200 litres<\/p>\n\n\n\n Quantity of milk in the mixture = 1.4 \u00d7 200 = 280 litres<\/p>\n\n\n\n Final quantity of water = 200 + 200 = 400 litres<\/p>\n\n\n\n Required percentage = {(400 \u2013 280)\/400} \u00d7 100 = 30%<\/p>\n\n\n\n Therefore, \u2018II\u2019 is true.<\/p>\n\n\n\n For III:<\/p>\n\n\n\n Let initial quantity of water in the mixture be \u2018x\u2019 ml<\/p>\n\n\n\n So, initial quantity of milk in the mixture = 2.2 \u00d7 x = 2.2x ml<\/p>\n\n\n\n So, x + 2.2x = 480<\/p>\n\n\n\n Or, 3.2x = 480<\/p>\n\n\n\n Or, x = 150<\/p>\n\n\n\n Initial quantity of water in the mixture = x = 150 litres<\/p>\n\n\n\n Quantity of milk in the mixture = 2.2 \u00d7 150 = 330 litres<\/p>\n\n\n\n Final quantity of water = 150 + 50 = 200 litres<\/p>\n\n\n\n Required percentage = {(330 \u2013 200)\/200} \u00d7 100 = 65%<\/p>\n\n\n\n Therefore, \u2018III\u2019 is true.<\/p>\n\n\n\n Hence, option c.<\/p>\n\n\n\n <\/p>\n\n\n\n Do this for 10 days in a row and you\u2019ll notice your accuracy and speed improving.<\/p>\n\n\n\n <\/p>\n\n\n\n Are you preparing for the RBI Grade B exam 2025? If so, it’s the ideal time to start and accelerate your exam preparation. The notification can be released anytime soon! <\/strong><\/p>\n\n\n\n Start preparing with the course that best suits you below!<\/a><\/strong><\/p>\n\n\n\nWhat Is Mixture & Alligation?<\/strong><\/h2>\n\n\n\n
\n
Main Formula: Alligation Rule<\/strong><\/h2>\n\n\n\n
\n
Why This Is Important for RBI Grade B<\/strong><\/h2>\n\n\n\n
Important Formulas to Remember<\/strong><\/h2>\n\n\n\n
\n
Average = (Sum of quantities \u00d7 values) \u00f7 (Total quantity)<\/li>\n\n\n\n
Ratio = (High value \u2013 Mean value) : (Mean value \u2013 Low value)<\/li>\n\n\n\n
If a quantity x is replaced from a mixture of volume V repeatedly:
Final concentration = Initial concentration \u00d7 (1 \u2013 x\/V)^n<\/li>\n<\/ul>\n\n\n\nTypes of Questions and Examples<\/strong><\/h2>\n\n\n\n
1. Price-Based Mixture<\/strong><\/h4>\n\n\n\n
<\/p>\n\n\n\n2. Concentration-Based Mixture<\/strong><\/h4>\n\n\n\n
3. Replacement Problem<\/strong><\/h4>\n\n\n\n
5 Smart Tricks for Fast Solving<\/strong><\/h2>\n\n\n\n
Practice Examples<\/strong><\/h3>\n\n\n\n
<\/strong> Mix sugar worth \u20b930\/kg with sugar worth \u20b945\/kg so that mixture costs \u20b940\/kg.<\/p>\n\n\n\n
<\/strong> A solution has 20% alcohol. Another has 50% alcohol. In what ratio should they be mixed to get 40% alcohol?<\/p>\n\n\n\n
<\/strong> A 50-litre mixture has milk and water in ratio 3:2. 10 litres of mixture is replaced by pure milk. Find final ratio.<\/p>\n\n\n\n
Remove 10 litres: milk removed = 6, water removed = 4.
Now milk = 24, water = 16. Add 10 litres milk \u2192 Milk = 34, Water = 16.
Ratio = 34 : 16 = 17 : 8.<\/p>\n\n\n\nExam-Like Questions for Practice<\/h2>\n\n\n\n
1) – D)<\/td> 2) – A)<\/td> 3) – B)<\/td> 4) – C)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n ![\"\"](\"https:\/\/www.practicemock.com\/blog\/wp-content\/uploads\/2025\/08\/image-16.png\")
<\/figure><\/div>\n\n\nHow to Practise Mixture & Alligation Well<\/strong><\/h2>\n\n\n\n
\n
Daily Mini Task<\/strong><\/h2>\n\n\n\n
\n
![\"\"](\"https:\/\/www.practicemock.com\/blog\/wp-content\/uploads\/2025\/06\/How-to-Make-RBI-Grade-B-2025-Exam-Preparation-Notes-for-Phase-1-and-Phase-2.png\")
<\/a><\/figure>\n\n\n\n