Quantitative Aptitude

Mixtures and Alligation

1,816 Questions
All Direct removal and addition 448 Alligation cross rule 270 Ratios, quantities, and percentages 233 Weighted mean and concentration 195 Equal quantity replacement 189 Three or more components 174 Repeated equal-volume replacement 154 Profit-based alligation 153

Mixtures and Alligation Questions

Multiple choice

$In each of the following questions given below there are two blanks, each blank indicates that something has been omitted. Choose the answer in order. 45 liter of a mixture from a cane containing petrol and kerosene in the ratio __________ is removed and replaced by 45 liter of kerosene. Again 45 liters of the mixture thus formed is removed and 45 liters of kerosene is added. This process is repeated once again, the ________________ is the volume of the petrol in the solution thus formed, if it is known that the initial volume of the mixture in the tank is 180 liters.

  1. 3:4, 35

  2. 4:5, 60

  3. 4:5, 33.75
  4. 2:7, 50$

  5. Only A

  6. Only B

  7. Any Two

  8. Any Three

  9. None of these
Reveal answer Fill a bubble to check yourself
I Correct answer
Explanation

Testing all options: For 3:4 initial ratio with 180L total (77.14L petrol), after three 45L replacements with kerosene, final petrol = 77.14 × (1 - 45/180)^3 = 77.14 × (3/4)^3 = 77.14 × 27/64 = 32.56L, not matching any option. For 4:5 ratio (80L petrol), final petrol = 80 × (3/4)^3 = 33.75L, which matches option C's second value. However, the 'Only B' option format is incorrect as C also works.

Multiple choice

Given below are two quantities named I and II. Based on the given data, you have to determine the relation between them and mark the answer. \textbf{Quantity I-} in a 40 L mixture of milk and water , the water is only 10%, then find amount of water to be added to make the concentration 50%. \textbf{Quantity II-} in a 100 L mixture of petrol and spirit , the spirit is only 2%, then find the amount of spirit to be added to make spirit concentration 30%.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relation can not be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quantity I: In 40L with 10% water (4L water, 36L milk), let x be water added. New concentration = (4+x)/(40+x) = 0.5, so 4+x = 20+x/2, giving x = 32L. Quantity II: In 100L with 2% spirit (2L spirit, 98L petrol), let y be spirit added. (2+y)/(100+y) = 0.3, so 2+y = 30+0.3y, giving y = 40L. Thus Quantity I (32) < Quantity II (40).

Multiple choice

Given below are two quantities named I and II. Based on the given data, you have to determine the relation between them and mark the answer Quantity I- there is 64 litres of mixture of milk and water having the ratio 5:3. By adding more water, concentration of the mixture reduces and the volume increases to 75 lires. What is the new concentration of milk. Quantity II- in a 70 litres of mixture of milk and water, the quantity of milk is 40 litre. The concentration was reduced, by adding more water and the volume was increased to 110 litres. The new concentration of milk

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relation can not be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: 64 liters with milk:water = 5:3 means milk = 40 liters, water = 24 liters. After adding water, total = 75 liters, milk remains 40 liters. New milk concentration = 40/75 = 53.33%. Quantity II: 70 liters contains 40 liters milk. After adding water to reach 110 liters, milk remains 40 liters. New concentration = 40/110 = 36.36%. Since 53.33% > 36.36%, Quantity I > Quantity II.

Multiple choice

Each of given questions consists of a question followed by informations in four statements. You have to study the question and the statements and decide that information in which of the statement(s) is/are necessary to answer the question. Find ratio of milk and water in the resultant I. two mixtures contain milk and water in the ratio 3:2 and 4:3 II. 20 litres from 1st container is taken out and x litres from 2nd is taken out and poured in third container III. value of x is 40 litres IV. the mixture from two containers are mixed in the ratio 3:2

  1. I,II and III

  2. I and IV

  3. I,II and III or I and IV

  4. All required

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the milk:water ratio in the resultant mixture, we need either (I, II, III) OR just (I, IV). With I and IV: mixtures 3:2 and 4:3 combined in 3:2 ratio gives (3/5)(3/5)+(4/7)(2/5) for milk = 9/25+8/35 = (63+40)/175 = 103/175, so water = 72/175. With I, II, III: 20L from first and 40L from second, we can calculate the combined ratio. Either approach works.

Multiple choice

Quantity I- a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 per kg. Find the sum of numerator and denominator of shortest term of the ratio in which these varieties are mixed. Quantity II- Find 150% of sum of numerator and denominator of shortest term of the ratio in which rice at Rs. 7.20 per kg must be mixed with rice at Rs. 5.70 per kg to produce a mixture worth Rs. 6.30 per kg.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Using alligation, the ratio of Rs. 15 and Rs. 20 pulses to get Rs. 16.50 mixture is |16.50 - 15| : |16.50 - 20| = 1.50 : 3.50 = 3 : 7. Sum = 3 + 7 = 10. Quantity II: For Rs. 7.20 and Rs. 5.70 rice to get Rs. 6.30 mixture, the ratio is |6.30 - 5.70| : |6.30 - 7.20| = 0.60 : 0.90 = 2 : 3. Sum = 2 + 3 = 5. 150% of 5 = 7.5. Comparing: 10 > 7.5, so Quantity I > Quantity II.

Multiple choice

Find the value of both quantities and then state the correct relationship. (10) litres of water were drawn from a cask full of water and it was filled with (30) litres milk then the concentration of milk in the mixture become (20\%). ()(\textbf{Quantity I :} ) From initial water, how many litres of mixture should be replaced with (10) litres milk so the concentration of water in the mixture will become (60\%). ()(\textbf{Quantity II :} ) What was the original quantity of water in the cask?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let original water = W liters. After removing 10L water and adding 30L milk, total = W + 20L. Milk concentration = 20%, so 30/(W+20) = 0.2, giving W = 130L. For Quantity I: let M be mixture to replace. After removing M and adding 10L milk, water = (130-M)/140 × 100 = 60%. Solving gives M = 46L. Quantity I = 46, Quantity II = 130. Since 46 < 130, Quantity II > Quantity I.

Multiple choice

In each of the following questions (quantity) two questions are given. Solve these questions and give answer: $I. In a mixture of 40 liters, the ratio of milk and water is 4:1. How much water must be withdraw from this mixture so that the ratio of milk and water becomes 16:3?\\II. Aman crosses 45 km long Still River by swimming in 20 hours but it takes less than 55% time to him to cross the same river from the boat. What is the speed of the boat?$

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: 40L mixture in 4:1 has 32L milk, 8L water. Removing x water gives ratio 32:(8-x) = 16:3, so 96 = 128 - 16x, x = 2. Answer: 2L water removed. Quantity II: 55% of 20 hours = 11 hours. Boat takes <11 hours for 45km, so speed > 45/11 ≈ 4.09 km/h. Comparing: 2 < 4.09, so Quantity II is greater. Key distractor: Quantity I might seem larger if you miscalculate the water removal.

Multiple choice

Find the correct relationship between given quantities. There are two containers. First container contains 600 ml. of Milk, while the second container contains 600 ml. of water. Three cups of Milk from the first container is taken out and is mixed well in the second container. Then, three cups of this mixture is taken out and is mixed in the first container. Quantity 1: Proportion of water in first container Quantity 2: Proportion of Milk in second container

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or No relationship can be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

This is a mixture transfer problem. Container 1: 600 ml Milk. Container 2: 600 ml Water. After transferring 3 cups milk to container 2 and mixing, then transferring 3 cups of mixture back, due to the symmetric transfers and equal initial volumes, the final proportion of water in container 1 equals the final proportion of milk in container 2. Quantity I = Quantity II.

Multiple choice

A certain mixture of paint requires blue, red, and yellow in the ratio of 2: 3: 4 respectively and no other ingredients. If there are ample quantity of blue and red paints are available then is there enough quantity of yellow paint is available to get the desired amount of the mixture? I: Exactly 180 litres of the mixture is needed. II: The difference between the quantity of blue paint available and the red paint available is 60 litres III: Exactly 180 litres of red paint are available.

  1. The data in statements I and III together are sufficient to answer the question, while the data in statement II are not sufficient to answer the question.

  2. The data in statements I and II together are sufficient to answer the question, while the data in statement III are not sufficient to answer the question.

  3. The data in statement I, II and III together are not sufficient to answer the question.

  4. The data in statement only I and II together or only statement III are sufficient.

  5. The data in all the statements I, II and III together are necessary to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Paint ratio is 2:3:4 (blue:red:yellow), so yellow is 4/9 of total mixture. Statement I: 180 L mixture needed, so yellow needed = 180 × 4/9 = 80 L. Statement III: 180 L red available (not mixture!). But Statement II says difference between blue and red available is 60 L. The statements seem contradictory - we need to know how much yellow is available, not how much red. Statements don't tell us the available yellow quantity, so data is insufficient.

Multiple choice

The question below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer. There are two mixtures A and B of milk and water which are mixed together to form another mixture C. In what ratio mixtures A and B are mixed to form another mixture C? Statement I: Quantity of milk in both the mixtures is 10 litres more than the quantity of water in those two mixtures. Statement II: When mixture B is sold at the cost of pure milk, then profit percent earned is 77(7/9)%. Statement III: When mixture C is sold at the cost equal to 75% cost of the pure milk, then profit percent earned is 31.25%.

  1. Any two of them together are sufficient

  2. All three of them together are sufficient

  3. All three of them together are not sufficient

  4. Only I and II together or only II and III together are sufficient

  5. Only I and III together are sufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement II reveals the milk-to-water ratio in mixture B through the profit percentage (77.77%) when sold as pure milk - this profit directly converts to the mixture's composition. Statement III provides the milk-to-water ratio in mixture C using the 31.25% profit when sold at 75% of pure milk's cost. Statement I establishes that total milk in both A and B exceeds total water by 10 litres, creating the crucial linking equation. Together, all three statements enable solving the ratio A:B through the volume balance equation.

Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. (Only quantity is to be considered) Quantity 1- A vessel is filled with liquid, 4 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup? Quantity 2- An alloy contains Brass, Iron and Zinc in the ratio 2:3:1 and another contains Iron, zinc and lead in the ratio 5:4:3.If equal weights of both alloys are melted together to form a third alloy, then what will be the part of lead per kg in new alloy?

  1. Quantity 1 > Quantity 2

  2. Quantity 1 < Quantity 2

  3. Quantity 1 ≥ Quantity 2

  4. Quantity 1 ≤ Quantity 2

  5. Quantity 1 = Quantity 2 or Relation can’t be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quantity 1: 4 parts water, 5 parts syrup (total 9). To make 1:1 ratio, remove some syrup and replace with water. Let x be fraction removed. New water = 4/9(1-x) + x, new syrup = 5/9(1-x). Set equal: 4/9 + 5x/9 = 5/9(1-x). Solving gives x = 1/9. Quantity 2: Alloy 1 (2:3:1), Alloy 2 (5:4:3). Combined alloy lead fraction = 3/19. 1/9 < 3/19, so Quantity 1 < Quantity 2.

Multiple choice

In the given questions, two quantities are given, one as ‘Quantity I’ and another as ‘Quantity II’. You have to determine relationship between two quantities and choose the appropriate option: Quantity I: A mixes milk and sugar in an empty container in the ratio of 4: 9, respectively. If 39 litres of mixtures is taken out and 4 litres of sugar is mixed, then the ratio of milk and sugar becomes 3: 7, respectively. Find the amount of milk mixed initially. Quantity II: A tank contains mixture of water and alcohol in the ratio of 3: 7, respectively. 40 litres of mixture is sold and 4 litres of alcohol is mixed in the container. If the ratio of water and alcohol in container becomes 2: 5, then find the difference between the amount of water and alcohol present in the container initially.

  1. Quantity I < Quantity II

  2. Quantity I > Quantity II

  3. Quantity I ≤ Quantity II

  4. Quantity I ≥ Quantity II

  5. Quantity I = Quantity II or relationship cannot be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quantity I: Let milk=4x, sugar=9x. After removing 39 litres (4/13 milk, 9/13 sugar) and adding 4 litres sugar: (4x-12)/(9x-27+4) = 3/7. Solving: 7(4x-12) = 3(9x-23), 28x-84 = 27x-69, x=15. So milk=60 litres. Quantity II: Let water=3x, alcohol=7x. After selling 40 litres (3/10 water, 7/10 alcohol) and adding 4 alcohol: (3x-12)/(7x-28+4) = 2/5. Solving: 5(3x-12) = 2(7x-24), 15x-60 = 14x-48, x=12. So water=36, alcohol=84, difference=48. Therefore Quantity I (60) > Quantity II (48). Answer B is correct.

Multiple choice

18 litres water was added to a vessel containing 80 litres of pure milk. 49 litres of the resultant mixture was then sold. After that ____ litre pure milk and ____ litre pure water was added to the vessel in the respective ratio of 2:1. The respective ratio of milk and water in the resultant mixture is 4:1. Find the missing data? 80 लीटर शुद्ध दूध वाले बर्तन में 18 लीटर पानी डाला गया। तब परिणामी मिश्रण के 49 लीटर बेचा गया। उसके बाद बर्तन में 2:1 के अनुपात में ____ लीटर शुद्ध दूध और ____ लीटर शुद्ध पानी की कुछ और मात्रा मिलायी गयी। परिणामी मिश्रण में दूध और पानी का अनुपात क्रमशः 4:1 है। विलुप्त आँकड़ों का पता लगाएँ।

  1. 16, 18

  2. 2, 1

  3. 4, 2

  4. 20, 10

  5. None of these इनमे से कोई नही
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial: 80L milk + 18L water = 98L mixture (ratio 80:18 = 40:9). After selling 49L: remaining = 49L with 40L milk, 9L water (same ratio). Adding milk and water in 2:1 ratio to get 4:1 final ratio. Let 2x milk and x water be added. Final: (40+2x)/(9+x) = 4/1. Solving: 40+2x = 36+4x, so 2x = 4, x = 2. Add 4L milk and 2L water. Answer: 4, 2 matches option C.

Multiple choice

Find the value of x and y from Q1 and Q2 and choose correct option. Q1 और Q2 से x और y का मान ज्ञात कीजिए और सही विकल्प चुनिए। Q1: In a certain quantity of syrup; 5 parts is honey while 3 parts is water. x part of syrup is removed and replenished with water in order to get a syrup having half honey and half water? सिरप के किसी निश्चित मिश्रण में; 5 भाग शहद है और 3 भाग पानी है. आधा शहद और आधा पानी वाला सिरप प्राप्त करने के लिए सिरप का x हिस्सा निकाला गया और प्रतिपूर्ति पानी से कर दिया गया? Q2: A bottle contains 0.75 whisky and the rest water. y part of the mixture is taken away and substituted by equal quantity of water so as to have half whiskey and half water? एक बोतल में 0.75 मदिरा और बाकी पानी है। आधी मदिरा और आधा पानी होने के लिए मिश्रण का y भाग लिया गया और समान मात्रा में पानी द्वारा प्रतिस्थापित किया गया।

  1. y≤x

  2. x<y

  3. x>y

  4. x≤y

  5. x= y or relation can’t be determined x=y अथवा संबंध निर्धारित नहीं किया जा सकता
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Q1: Initial honey:water = 5:3 (5/8 honey). To get 1:1 (1/2 honey), remove fraction x where (5/8)(1-x) = 1/2. Solving: (5/8)(1-x) = 1/2, so 1-x = 4/5, x = 1/5. Q2: Initial whisky:water = 0.75:0.25 = 3:1 (3/4 whisky). To get 1:1, remove fraction y where (3/4)(1-y) = 1/2. Solving: 1-y = 2/3, y = 1/3. Comparing: x = 0.2, y = 0.333..., so x < y. Answer B is correct.

Multiple choice

In each of the following questions, a question is followed by two statements numbered I and II. Read both the statements and answer accordingly. What is the ratio of milk and water in the mixture? Statement I : If a trader earns a profit of 20%after adding water in milk and sold it at Cost Price. Statement II : If a trader earns some profit after selling milk at Rs.25/Litre by adding water in it. नीचे दिए गए प्रश्नों में, एक प्रश्न में दो कथन (I) और (II) दिए गए हैं । दोनों कथनों को पढ़कर उसके अनुसार उत्तर दीजिये। मिश्रण में दूध और पानी का क्या अनुपात है ? कथन I : यदि एक विक्रेता दूध में पानी मिलाकर इसे क्रय मूल्य पर बेचकर 20% का लाभ कमाता है। कथन II : यदि एक विक्रेता पानी मिलाकर इसे 25 रु. प्रति लीटर बेचकर कुछ लाभ प्राप्त करता है।

  1. Only I / केवल I

  2. Only II / केवल II

  3. Either I or II / केवल I या II

  4. Both together / दोनों एक साथ पर्याप्त है

  5. Both together are not sufficient / दोनों एक साथ पर्याप्त नहीं है
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I: If profit is 20% when selling at cost price after adding water, it means water added is 20% of milk quantity (since selling 120 units at the price of 100 units gives 20% profit). So milk:water = 100:20 = 5:1. Statement II only gives selling price (Rs.25/Litre) without cost price or profit percentage, making the ratio impossible to determine. Therefore, only Statement I is sufficient.