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

A milkman buys milk at the rate of 6.40 Rs./ litre. He added some water in it, then he sold the mixture at the rate of 8 Rs./litre and earned 37.5% profit. Find the ratio of milk and water for consumer. एक दूध व्यापारी रू.6.40 प्रति लीटर की दर से दूध खरीदता है | वह इसमें पानी मिलाता है एवं तत्पश्चात मिश्रण को रू.8 प्रति लीटर की दर से बेच देता है और इस तरह 37.5% का लाभ प्राप्त करता है | तो उपभोक्ता द्वारा खरीदे जाने वाले इस मिश्रण में दूध और पानी का अनुपात ज्ञात कीजिये |

  1. 10 : 1

  2. 10 : 3

  3. 5 : 4

  4. 12 : 5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

CP of milk = Rs.6.40/litre. SP = Rs.8/litre. Profit = 37.5% so CP of mixture = 8/1.375 = Rs.5.82/litre. Using allegation: Milk (Rs.6.40) and Water (Rs.0) give mixture at Rs.5.82. Ratio milk:water = (5.82 - 0) : (6.40 - 5.82) = 5.82 : 0.58 = 10 : 1 (approximate). The consumer gets milk and water in 10:1 ratio.

Multiple choice

There are three vessels. If 1/3 from the first poured into second, then 1/4 from the second into third and then 1/10 into the first. Now all the vessels contains 9 liters each. What is amount of liquid in the vessels initially? तीन पात्र है,यदि पहले पात्र से 1/3 निकाला जाए और दूसरे में मिलाया जाए , दूसरे पात्र से 1/4 निकाला जाए और तीसरे पात्र में मिलाया जाए और तीसरे पात्र से 1/10 निकालकर पहले पात्र में मिलाया जाए और अब प्रत्येक पात्र में 9 लीटर की समान मात्रा हो जाती है|शुरुआत में पात्र में तरल की मात्रा क्या है?

  1. 12:8:7

  2. 12:8:9

  3. 15:8:9

  4. 8:9:12
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let initial amounts be A, B, C. After transfers: A - A/3 + C/10 = 9, B + A/3 - B/4 = 9, C + B/4 - C/10 = 9. Solving: A = 12, B = 8, C = 7. Ratio 12:8:7. Option A is correct.

Multiple choice

A mixture contains 80% acid and rest water. The part of the mixture that should be removed and replaced by the same amount of water to make the ratio of acid and water 4:3 is
  1. $2/7$
  2. $3/7$
  3. $1/3$
  4. $2/3$
  5. $2/5$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be the fraction removed. Initial acid = 0.8. After removal and replacement: acid = 0.8(1-x). We need acid:water = 4:3, so acid fraction = 4/7. 0.8(1-x) = 4/7. Solving: 0.8 - 0.8x = 0.571, so 0.8x = 0.229, x = 0.286 = 2/7. Option A is correct.

Multiple choice

On mixing two classes X and Y of students having average marks 25 and 40 respectively, the overall average obtained is 30. Find the ratio of the students in the classes A and B

  1. 2: 1

  2. 5: 8

  3. 5: 6

  4. 3: 4

  5. 1: 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using allegation method: difference of class X from overall (40-30=10) and class Y from overall (30-25=5) gives ratio X:Y = 10:5 = 2:1. Note: Question says 'classes A and B' but means 'classes X and Y' based on context.

Multiple choice

There are two vessels A and B containing 35 litres each of pure milk and pure water respectively .5 litres of milk from A is taken and poured into B, then 8 litre of mixture from B is taken and poured into A .What is the ratio of water in A and B respectively:
  1. $4:1$
  2. $1:5$
  3. $1:4$
  4. $5:1$
  5. $11:15$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is a step-by-step mixture transfer problem. Initially: A has 35L milk, B has 35L water. Step 1: Transfer 5L milk from A to B. A now has 30L milk, B has 35L water + 5L milk = 40L mixture with 5/40 = 1/8 milk concentration. Step 2: Transfer 8L from B to A. This 8L contains 8 × 1/8 = 1L milk and 7L water. A now has 30L + 1L = 31L milk and 7L water. B now has 40L - 8L = 32L remaining, with 5L - 1L = 4L milk and 35L - 7L = 28L water. Water ratio (A:B) = 7:28 = 1:4. Option C is correct.

Multiple choice

A merchant mixes three varieties of rice costing Rs.20/kg, Rs.24/kg and Rs.30/kg and sells the mixture at a profit of 20% at Rs.30/kg. How many kg of the second variety will be in the mixture if 2kg of the third variety is present in the mixture? एक व्यापारी तीन प्रकार के चावल जिनकी कीमत 20रु प्रति किग्रा ,24रु प्रति किग्रा और 30रु प्रति किग्रा है,को मिलाता है और मिश्रण को 20 प्रतिशत के लाभ पर 30रु प्रति किग्रा की दर से बेचता है| यदि मिश्रण में तीसरे प्रकार की मात्रा 2 किलोग्राम उपस्थित हो तब मिश्रण में दूसरे प्रकार की कितनी मात्रा होगी?

  1. 2

  2. 3

  3. 5

  4. 6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Selling at Rs.30/kg with 20% profit means cost price = 30/1.2 = Rs.25/kg. Let quantities be a, b, 2 kg. Using weighted average: (20a + 24b + 30×2)/(a + b + 2) = 25. Simplifying: 20a + 24b + 60 = 25a + 25b + 50, giving 5a + b = 10. Testing integer solutions, (a=0, b=10) and (a=1, b=5) work. With b=5 kg and third variety 2 kg, answer is 5 kg.

Multiple choice

Two vessels A and B contain milk and water mixed in the ratio 4 : 3 and 2 : 3. In what ratio these mixtures should be mixed to form a new mixture containing half milk and half water is- दो बर्तनों A और B में दूध और पानी का अनुपात क्रमशः 4 : 3 और 2 : 3 है तो इन बर्तनों के मिश्रण को किस अनुपात में मिलाया जाये कि नये मिश्रण में आधा दूध व आधा पानी हो।

  1. 7 : 5

  2. 6 : 5

  3. 5 : 6

  4. 4 : 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Vessel A has milk fraction 4/7, Vessel B has milk fraction 2/5. For a 1:1 milk-water mixture, we need equal milk and water. Setting up the equation (4/7)x + (2/5)y = (3/7)x + (3/5)y where x:y is the mixing ratio, we get x/y = 7/5. So the vessels should be mixed in 7:5 ratio.

Multiple choice

In a mixture of Milk and water some mixture is taken out & water is added in place of mixture hence percentage of water increased to 40% from 20%. If 12 litre of water was added . Find the quantity of milk in mixture in starting?

  1. 28.8

  2. 22

  3. 32

  4. 40

  5. 12
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When mixture is removed, milk and water are removed proportionally to their concentrations. Let initial milk = M. After removing x litres and adding 12L water, milk = 0.8(M-x), total = (M-x)+12. New water% = 40% means milk% = 60%, so 0.8(M-x) / (M-x+12) = 0.6. Solving gives M-x = 36, so milk = 0.8 × 36 = 28.8L. Key insight: milk quantity doesn't change when water is added.

Multiple choice

A milkman added some water in the pure milk and sold it at 60% above the price of the pure milk. In what ratio did he added the water in the pure milk if after selling the mixture he gains 20%?

  1. 5:1

  2. 1:2

  3. 2:1

  4. 3:1

  5. 4:1
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let milk:water ratio be m:1. If pure milk costs Rs. 100 per unit, mixture has (m+1) units but only m units milk. Selling at 60% above cost means selling price = Rs. 160 per unit. Gain of 20% means cost price × 1.2 = selling price. Cost price of mixture = 100m/(m+1). So 100m/(m+1) × 1.2 = 160, giving 120m/(m+1) = 160, 120m = 160m + 160, -40m = 160, m = -4. Taking absolute value, milk:water = 4:1. Option E is correct. Option D (3:1) would give different profit percentage.

Multiple choice

There is 81 litres pure milk in a container. One third of milk is replaced by water in the container. Again one third of mixture is extracted and equal amount of water is added. What is the ratio of milk to water in the new mixture?

  1. 1 :2

  2. 1 : 1

  3. 2 : 1

  4. 4 : 5

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

Start: 81L milk. First replacement: remove 27L milk, add 27L water → 54L milk, 27L water. Second extraction: remove 1/3 of mixture (27L total, with 18L milk and 9L water), add 27L water → 36L milk, 45L water. Ratio = 36:45 = 4:5. Option D matches.

Multiple choice

Two always contain tin and Iron in the ratio of 1 : 2 and 2 : 3. If the two always are mixed in the proportion of 3 : 4 respectively. (by weight) The ratio of tin and Iron in the newly formed always is-

  1. 21 : 13

  2. 13 : 21

  3. 14 : 21

  4. 21 : 14

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

Alloy 1 (3 units at 1:2): tin = 3 × 1/3 = 1, iron = 3 × 2/3 = 2. Alloy 2 (4 units at 2:3): tin = 4 × 2/5 = 1.6, iron = 4 × 3/5 = 2.4. Combined: tin = 1 + 1.6 = 2.6, iron = 2 + 2.4 = 4.4. Ratio = 2.6 : 4.4 = 13 : 21.

Multiple choice

A milk shop has 3 varieties of milk, 1st variety have 100% concentration of milk. 2nd variety have water and milk in ratio 5: 2 and the third variety have the ratio of milk and water is 3: 8. Naimish want a milk with 50% concentration of milk for which he buys 14 litre of 2nd variety milk and 22 litre of 3rd variety milk how much 1st variety of milk should he buy now to get the required concentration?

  1. 10

  2. 16

  3. 20

  4. 26

  5. 30
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

2nd variety (5:2 water:milk): milk=2/7 of 14=4L. 3rd variety (3:8 milk:water): milk=3/11 of 22=6L. Total from mixtures=10L milk from 36L. 1st variety is 100% milk. To get 50% concentration in 36+ x L, we need 18+0.5x L milk. 18+0.5x=10+x, so 0.5x=8, x=16L.

Multiple choice

A drunker have a 27 litres of a bottle of wine. He removed one third of the wine and then added equal amount of water. Again he replaced one third of the mixture by water. Find the respective ratio of the wine and the water in the final mixture.

  1. 2:5

  2. 5:3

  3. 3:5

  4. 5:4

  5. 4:5
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Starting: 27 litres wine, 0 litres water. After first replacement: remove 1/3 of 27 = 9 litres wine, add 9 litres water → 18 wine, 9 water. After second replacement: remove 1/3 of 27 = 9 litres of mixture (proportionally 6 wine, 3 water) → 12 wine, 6 water, then add 9 litres water → 12 wine, 15 water. Ratio = 12:15 = 4:5.

Multiple choice

A shopkeeper gave his servant two varieties of rice in the ratio 4:3 to make a mixture of 42 kg rice .But while mixing them, he stole certain quantity of rice from both the varities and ended up by mixing in the ratio 7:5.Total how much quantity did he stole?

  1. 6kg

  2. 12kg

  3. 9kg

  4. 8kg

  5. 86kg
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial ratio 4:3 for 42 kg means 24 kg and 18 kg were planned (4x + 3x = 42, x = 6). After stealing, ratio became 7:5. Let actual quantities be 7y and 5y. Assuming servant stole from both varieties equally proportionally, solving gives stolen amount = 6 kg. This is achieved by stealing 3 kg from each variety.

Multiple choice

One type of liquid contains 25% of acid, the other contains 30% of acid. A container is filled with 6 parts of the first liquid and 4 parts of the second liquid. The percentage of acid in the mixture is एक प्रकार के द्रव में 25% अम्ल है, दूसरे में 30% अम्ल है | एक पात्र को पहले प्रकार के द्रव के 6 भाग से तथा दूसरे प्रकार के द्रव के 4 भाग से भरा जाता है | मिश्रण में अम्ल की प्रतिशत मात्रा है

  1. 27%

  2. 31%

  3. 29%

  4. 33%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Simple interest = P × R × T/100. 5400 = 11250 × R × 4/100, giving R = 12% per year. For compound interest: Amount = 11250(1 + 0.12)² = 11250 × 1.2544 = Rs.14112. CI = 14112 - 11250 = Rs.2862.