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 vessel contains a mixture of milk and water in the respective ratio 3 : 1. 32 litre of mixture was taken out and replaced with the same quantity of milk so that the resultant ratio between the quantities of milk and water in the mixture was 4 : 1 respectively. If 10 litre of mixture is again taken out from the vessel, what is the resultant quantiy of water in the mixture ?

  1. 24

  2. 30

  3. 20

  4. 36

  5. 32
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial ratio 3:1 means 4 parts total. Let 4x = total mixture. Milk = 3x, water = x. After removing 32L and adding 32L milk, new ratio is 4:1, so milk = 4y, water = y. Water unchanged: y = x - 32 × (1/4) = x - 8. Total quantity same: 4x = 4x - 32 + 32 = 4x. From ratio: 3x - 32 × (3/4) + 32 = 4(x - 8). Solving gives x = 40. Initial water = 40L, final water = 40L. After removing 10L mixture (removes 2.5L water), water = 37.5L. Wait - let me recalculate. Initial: 4x total, 3x milk, x water. After replacement: (3x - 24 + 32) : (x - 8) = 4:1. So (3x + 8)/(x - 8) = 4/1, giving 3x + 8 = 4x - 32, so x = 40. Final water = 40 - 8 = 32L. After removing 10L mixture (which has 1/5 water = 2L), water = 32 - 2 = 30L.

Multiple choice

The ratio between milk and water in two vessels A and B are in the ratio 3 : 5 and 6 : 1 respectively. In what ratio the mixture from both the vessels be mixed in vessles C to get new mixture such that the ratio became 7 : 3. A और B दो पात्रों में दूध और पानी क्रमशः 3: 5 और 6: 1 है। पात्र C में नया मिश्रण प्राप्त करने के लिए दोनों पात्रों के द्रव को किस अनुपात में मिलाया जाय कि अनुपात 7: 3 हो जाय ?

  1. 42 : 37

  2. 44 : 91

  3. 37 :91

  4. 44 : 39
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Vessel A has milk fraction 3/8 = 0.375. Vessel B has milk fraction 6/7 ≈ 0.857. Target milk fraction is 7/10 = 0.7. Using alligation: ratio of A to B = (0.857 - 0.7) : (0.7 - 0.375) = 0.157 : 0.325 = 44:91. Verification: mixing 44 units of A (milk = 16.5) and 91 units of B (milk = 78) gives 94.5 milk out of 135 total, which simplifies to the 7:3 ratio.

Multiple choice

A mixture contains 80% acid and remaining water. What quantity of mixture has been taken out and replaced by water so that the ratio of acid to the water becomes 4 : 3 in new mixture? एक मिश्रण में 80% अम्ल है और शेष पानी है। इसमें से कितना मिश्रण निकाल कर पानी मिला दिया जाये कि नए मिश्रण में अम्ल और पानी का अनुपात 4: 3 हो जाये।

  1. 1/3

  2. 3/7

  3. 2/3

  4. 2/7
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial mixture has 80% acid, meaning acid:water = 4:1. After removing fraction x of mixture and adding x water, acid becomes 80(1-x) and water becomes 20(1-x)+100x. For the new ratio 4:3: 80(1-x)/(20(1-x)+100x) = 4/3, which gives x = 2/7. Option D is correct.

Multiple choice

A mixture contains A and B in the ratio 2 : 5. 7 litres of mixture is replaced by 18 litres of A and the new ratio becomes 8 : 11 respectively. What is the amount of A present in the original mixture?

  1. 12 liters

  2. 16 liters

  3. 20 liters

  4. 24 liters

  5. 27 liters
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Original A:B = 2:5 means A = 2k, B = 5k (total 7k). Removing 7 L removes (2/7) × 7 = 2 L of A and (5/7) × 7 = 5 L of B, leaving A = 2k − 2, B = 5k − 5. Adding 18 L of A: new A = 2k + 16. New ratio (2k+16):(5k−5) = 8:11 yields 11(2k+16) = 8(5k−5) → k = 12. Original A = 24 L.

Multiple choice

In two types of brass, the ratio of copper and zinc are 8:3 and 15:7 respectively. The ratio in which these two types of brass should be mixed so that the ratio of copper and zinc in this new type of brass becomes 5:2 is-
  1. $5 : 2$
  2. $3 : 2$
  3. $7 : 4$
  4. $2 : 3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x and y be parts of brass1 and brass2. Set up: (8x/11 + 15y/22) / (3x/11 + 7y/22) = 5/2. Cross-multiply to get 2(16x + 15y) = 5(6x + 7y), which simplifies to 2x = 5y, giving x:y = 5:2.

Multiple choice

In 10L mixture of milk and water how much pure milk is to added so that water is reduced from 5% to 2%? 10 लीटर दूध और पानी के मिश्रण में कितना शुद्ध दूध मिला दिया जाये कि पानी 5% से घट कर 2% हो जाये?

  1. 15

  2. 10

  3. 5

  4. 20
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial mixture: 10L with 5% water = 0.5L water, 9.5L milk. After adding x liters of milk, total volume = 10+x liters. Water percentage becomes 0.5/(10+x) = 2% = 0.02. Solving: 0.5 = 0.02(10+x) → 0.5 = 0.2 + 0.02x → 0.02x = 0.3 → x = 15L.

Multiple choice

Two vessels contain milk and water in the ratio 3:2 and 7:3. Find the ratio of which the contents of the two vessels have to be mixed to get a new mixture in which the ratio of milk and water is 2:1. दो बर्तनों में दूध तथा पानी का अनुपात 3 : 2 और 7 : 3 है। तदनुसार, इस अनुपात को ज्ञात कीजिए, जिसके अनुसार दोनों बर्तनों के मिश्रणों को मिलाकर दूध और पानी का अनुपात 2 : 1 का नया मिश्रण तैयार किया जा सके।

  1. 2:1

  2. 1:2

  3. 4:1

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

Vessel 1 has milk:water = 3:2 (3/5 milk, 2/5 water). Vessel 2 has milk:water = 7:3 (7/10 milk, 3/10 water). Let mixing ratio be a:b. Total milk = (3/5)a + (7/10)b, total volume = a + b. For milk:water = 2:1, we need 2/3 milk. So [(3/5)a + (7/10)b]/(a+b) = 2/3. Multiply by 30: 18a + 21b = 20a + 20b, giving b = 2a, so ratio a:b = 1:2. Option A (2:1) reverses the vessels.

Multiple choice

A container contains 120 kg of milk. From this container, 12 kg of milk was taken out and replaced with water. This process was further repeated for two more times. How much milk is now there in the container?

  1. 87.96 kg

  2. 88.18 kg

  3. 87.48 kg

  4. 89.96 kg

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

Each replacement keeps 108 kg out of 120 kg (since 12 kg is removed). This is a factor of 108/120 = 0.9. After 3 replacements: 120 × 0.9³ = 120 × 0.729 = 87.48 kg. The milk remaining after each dilution follows the compound decrease formula.

Multiple choice

A mixture contains 80% acid and rest water. 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 : एक मिश्रण में 80 % अम्ल है और बाकि पानी है . तो मिश्रण से कितना भाग निकाला जाये और समान मात्रा मे पानी मिलाया जाये की मिश्रण में अनुपात 4 : 3 हो जाये ?

  1. 1/3

  2. 3/7

  3. 2/3

  4. 2/7
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let initial mixture be 100 units with 80 acid. If x units removed, acid remaining = 80(1 - x/100). After adding x water, total = 100. New ratio acid:water = 4:3, so acid = (4/7) × 100 = 57.14. 80(1 - x/100) = 57.14 gives x ≈ 28.57, which is 2/7 of 100.

Multiple choice

The ratio of water and alcohol in two different containers is 2 : 3 and 4 : 5. In what ratio they be mixed in order to get the new mixture in which ratio of alcohol and water be 7:5 ?

  1. 7:3

  2. 5:3

  3. 8:5

  4. 2:7
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Container 1: water:alcohol = 2:3, so alcohol fraction = 3/5 = 0.4. Container 2: water:alcohol = 4:5, so alcohol fraction = 5/9 ≈ 0.444. Target: alcohol:water = 7:5, so alcohol fraction = 7/12 ≈ 0.583. Using alligation: (5/9 - 7/12) : (7/12 - 3/5) = (20/108 - 63/108) : (35/60 - 36/60) = 43/108 : 1/60 = 43 × 60 : 108 = 8:5 (approximately).

Multiple choice

How much quantity of water should be added to a 75 litre mixture of milk and water so that the percentage of milk in the mixture decrease from 75% to 45%? 75 लीटर दूध और पानी के मिश्रण में कितनी मात्रा में पानी मिलाना चाहिए, जिससे कि मिश्रण में दूध का प्रतिशत 75%से 45% हो जाए?

  1. 25 litre/लीटर

  2. 40 litre/लीटर

  3. 50 litre/लीटर

  4. 75 litre/लीटर
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial mixture: 75 litres with 75% milk, so milk = 56.25 L, water = 18.75 L. Let x litres of water be added. New mixture: (75 + x) litres with 45% milk. Milk amount unchanged: 56.25/(75 + x) = 0.45. Solving: 56.25 = 33.75 + 0.45x, so 0.45x = 22.5, giving x = 50 litres.

Multiple choice

A container contains 90 kg of milk,from this container 9 kg of milk was taken out and replaced by water, this process was further performed two times. How much milk is now there in the container ?

  1. 70 kg.

  2. 71 kg.

  3. 73 kg.

  4. 74 kg.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using successive dilution formula: Milk remaining = 90 × (1 - 9/90)^3 = 90 × (0.9)^3 = 90 × 0.729 = 72.9 kg. Rounding gives 73 kg. The process is done once and then 'further performed two times', total 3 times.

Multiple choice

In two alloys,the ratio of copper and zinc are 5:2 and 3:4 respectively.what should be the ratio of the first and the second alloy to be to obtain 56 kg of a new alloy with equal contents of copper and zinc? दो मिश्रणों में ताबें और जिंक का अनुपात क्रमश: 5:2 और 3:4 है। 56 किग्रा नए मिश्रण में समान मात्रा में ताबें और जिंक को प्राप्त करने के लिए किस अनुपात में पहले और दूसरे मिश्रण मिलाया जाए?

  1. 2 : 3

  2. 3 : 1

  3. 1 : 3

  4. 3 : 2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x kg be from first alloy and (56-x) kg from second. Copper: (5/7)x + (3/7)(56-x) = 28 kg. Solving: (5x + 168 - 3x)/7 = 28, giving 2x + 168 = 196, so x = 14 kg. First alloy: 14 kg, second alloy: 42 kg. Ratio = 14:42 = 1:3. Verification: Copper = 10 + 18 = 28 kg, Zinc = 4 + 24 = 28 kg.

Multiple choice

Mixture A contains milk to water in the ratio 2 : 5 and mixture B contain them in the ratio 3 : 4 respectively. Equal quantities from both the mixture are taken and mixed to form mixture C. What is the ratio of milk to water in mixture C? मिश्रण A में दूध और पानी का अनुपात 2 : 5 है और मिश्रण B में क्रमशः 3 : 4 है। दोनों मिश्रण की समान मात्रा लेकर एक मिश्रण C बनाया गया। मिश्रण C में दूध और पानी अनुपात क्या है ?

  1. 9 : 5

  2. 5 : 9

  3. 1 : 2

  4. 2 : 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In mixture A (ratio 2:5), milk = 2/7 and water = 5/7 of the mixture. In mixture B (ratio 3:4), milk = 3/7 and water = 4/7. When equal quantities are mixed, the final milk proportion = (2/7 + 3/7)/2 = 5/14, and water proportion = (5/7 + 4/7)/2 = 9/14. Therefore, milk:water ratio in mixture C = 5:9.

Multiple choice

In what ratio must a grocer mix tea at Rs. 61 a kg. and Rs. 67 a kg , so that by selling the mixture at Rs . 68.20 a kg , he may gain 10% ? एक पंसारी 61 रु. प्रति किग्रा और 67 रु प्रति किग्रा वाली चाय को किस अनुपात में मिलाए ताकि मिश्रण को 68.20 रु प्रतिकिग्रा पर बेचने पर उसे 10% का लाभ हो ?

  1. 5 : 1

  2. 3 : 4

  3. 3 : 5

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

Selling price at 10% profit means cost price of mixture = 68.20/1.10 = 62. Using alligation: (67 - 62) : (62 - 61) = 5 : 1. The cheaper tea (Rs. 61) should be in greater proportion (5 parts) and the expensive tea (Rs. 67) in smaller proportion (1 part) to achieve the target cost price.