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

How many litres of a 12 litre mixture containing milk and water in the ratio of 2 : 3 be replaced with pure milk so that the resultant mixture contains milk and water in equal proportion? 2 : 3 के अनुपात में दूध और पानी वाले 12 लीटर मिश्रण में से कितने लीटर को शुद्ध दूध से बदल दिया जाए ताकि परिणामी मिश्रण में दूध और पानी समान अनुपात में हो?

  1. 4 liter 4 लीटर

  2. 3 liter 3 लीटर

  3. 2 liter 2 लीटर

  4. 6 liter 6 लीटर

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

Initial mixture has milk:water = 2:3 in 12L, so milk = (2/5)×12 = 4.8L and water = 7.2L. If x litres is removed and replaced with pure milk, milk becomes 4.8 - (2/5)x + x = 4.8 + (3/5)x, and water becomes 7.2 - (3/5)x. For equal proportions: 4.8 + 0.6x = 7.2 - 0.6x, giving 1.2x = 2.4, so x = 2L. The key is maintaining concentration when removing mixture.

Multiple choice

A mixture has milk and water in the ratio of 8:3. If 4 litres of water is added to it ,the new ratio of milk and water becomes 2:1.What are the quantities of milk and water respectively in the original mixture ? (in litres)

  1. 32,12

  2. 24,9

  3. 40,15

  4. 16,6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let original quantities be 8x milk and 3x water. After adding 4 L water, ratio becomes 8x:(3x + 4) = 2:1. Solving 8x = 2(3x + 4) gives x = 4, so original quantities are 32 L milk and 12 L water.

Multiple choice

A merchant purchased two qualities of pulses at the rate of 200 per quintal and 260 per quintal. In 52 quintals of the second quality, how much pulse of the first quality should be mixed so that by selling the resulting mixture at 300 per quintal, he gains profit of 25%?

  1. 25

  2. 26

  3. 27

  4. 28
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Selling price = 300/quintal with 25% profit, so cost price of mixture = 300/1.25 = 240/quintal. Using alligation: 260 at 52 quintals mixed with 200 at x quintals gives mean 240. Differences from mean: 260-240 = 20, 240-200 = 40. Ratio x:52 = 20:40 = 1:2, so x = 26 quintals.

Multiple choice

A container contains mixture of milk & water in which milk is 80%.If 10 litre of the mixture is taken out & 10 litre of water is added, now the concentration of milk becomes 60% in the mixture. Find the quantity of mixture initially present in the container. एक कंटेनर में दूध और पानी का मिश्रण है जिसमें दूध 80% है। यदि 10 लीटर मिश्रण निकाल दिया जाता है और 10 लीटर पानी मिला दिया जाता है, तो अब मिश्रण में दूध की सांद्रता 60% हो जाती है। कंटेनर में शुरू में मौजूद मिश्रण की मात्रा ज्ञात कीजिए।

  1. 40

  2. 41

  3. 42

  4. 45

  5. 50
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let initial quantity = x liters. Milk = 0.8x, Water = 0.2x. After removing 10 liters: Milk removed = 8, Water removed = 2. Remaining: Milk = 0.8x-8, Water = 0.2x-2. Adding 10 liters water: Milk = 0.8x-8, Water = 0.2x-2+10 = 0.2x+8. New concentration: (0.8x-8)/(x) = 0.6. 0.8x-8 = 0.6x. 0.2x = 8. x = 40 liters.

Multiple choice

In a 75 liters of mixture of milk and water, 20% of mixture is water. The milkman sells 25 liters of mixture and mixes equal quantity of water. What is the ratio of milk and water in the final mixture? दूध और पानी के 75 लीटर मिश्रण में, मिश्रण का 20% पानी है। दूधवाला 25 लीटर मिश्रण बेचता है और बराबर मात्रा में पानी मिलाता है। अंतिम मिश्रण में दूध और पानी का अनुपात क्या है?

  1. 4 : 3

  2. 3 : 4

  3. 4 : 1

  4. 3 : 2

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

Initial: 60L milk + 15L water in 75L. After selling 25L (proportional): remaining 45L milk + 10L water. Adding 25L water: 45L milk + 35L water. Ratio = 45:35 = 9:7, which is not in options A-D.

Multiple choice

A vessel has a milk solution in which ratio of milk and water is 4 : 1 by adding some water into it ,the ratio of milk and water become 4:3,on replacing 14 litre of this solution with pure milk the ratio of milk and water changed to 5:3.what is the volume of water added?

  1. 12ltrs

  2. 60ltrs

  3. 32ltrs

  4. 24ltrs

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

Let initial volume = x. Initial milk:water = 4:1, so milk = 4x/5, water = x/5. After adding water (32 liters), ratio becomes 4:3, so milk = 4(x+32)/7, water = 3(x+32)/7. Equating milk: 4x/5 = 4(x+32)/7 gives x = 80. Initial water = 16. Final: 80+32 = 112 liters with milk = 64, water = 48. After replacing 14 liters with pure milk: milk = 64 - 8 + 14 = 70, water = 48 - 6 = 42. Ratio 70:42 = 5:3. Correct.

Multiple choice

A jar contains a mixture of two liquids A and B in the ratio of 23 : 17. Another jar contains a mixture of the same liquids in the ratio of 11 : 9. A new mixture is formed by taking out some amount from both mixtures. Find the ratio of the amount taken out if the ratio of liquids in new mixture is 17 : 13.

  1. 4 : 1

  2. 1 : 4

  3. 1 : 2

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

Use allegation principle. Jar 1 has 23/40 = 57.5% liquid A. Jar 2 has 11/20 = 55% liquid A. Target mixture needs 17/30 ≈ 56.67% liquid A. Using allegation: |56.67 - 55| : |57.5 - 56.67| = 1.67 : 0.83 = 2 : 1. So ratio is 2:1, option D.

Multiple choice

In what ratio should water be mixed with ‘THANDA SHARBAT’ worth Rs 70 per litre so that by selling the mixture at Rs 40 per litre, the profit will be 33.33%?

  1. 4:3

  2. 3:4

  3. 5:4

  4. 4:5

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

Let water:sharbat = x:y. CP of mixture = (0x + 70y)/(x+y). SP = 40, profit = 33.33% = 1/3, so CP = 40/(4/3) = 30. Using alligation: (70-30)/(30-0) = 40/30 = 4/3. This is water:sharbat ratio. Answer B (3:4) is correct when read as water:sharbat = 3:4.

Multiple choice

Acid and water are mixed in a vessel A in the ratio of 5 : 2 and in the vessel B in the ratio 8: 5. In what proportion should quantities be taken out from the two vessels so as to form a mixture in which acid and water will be in the ratio of 9 : 4? एक बर्तन A में 5 : 2 के अनुपात में अम्ल और पानी मिलाया जाता है और बर्तन B में 8: 5 के अनुपात में मिलाया जाता है। दोनों बर्तनों से किस अनुपात में मात्रा निकालनी चाहिए ताकि एक मिश्रण बन जाए जिसमें अम्ल और पानी 9:4 के अनुपात में होंगे?

  1. 7 : 2

  2. 2 : 7

  3. 7 : 4

  4. 2 : 3

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Vessel A: acid:water = 5:2 (7 parts, 5/7 acid). Vessel B: acid:water = 8:5 (13 parts, 8/13 acid). Target: 9:4 (13 parts, 9/13 acid). Using alligation: (5/7 - 9/13):(9/13 - 8/13) = (65-63)/91 : 1/13 = 2/91 : 7/91 = 2:7. The ratio should be 7:2 from A:B.

Multiple choice

In a mixture of alcohol and water, there is only 26% water. After replacing the mixture with 16 litres of alcohol, the percentage of alcohol in the mixture become 76%. The quantity of mixture is: शराब और पानी के मिश्रण में केवल 26% पानी है। मिश्रण को 16 लीटर अल्कोहल से बदलने के बाद, मिश्रण में अल्कोहल का प्रतिशत 76% हो जाता है। मिश्रण की मात्रा है:

  1. 208 litre 208 लीटर

  2. 200 litre 200 लीटर

  3. 189 litre 189 लीटर

  4. 180 litre 180 लीटर

  5. 176 litre 176 लीटर
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let total mixture = x litres. Water = 26% of x = 0.26x, Alcohol = 74% of x = 0.74x. When 16 litres of mixture is replaced, alcohol removed = 0.74 × 16 = 11.84 litres. New alcohol = (0.74x - 11.84 + 16) litres. This equals 76% of x = 0.76x. So 0.74x + 4.16 = 0.76x, which gives 0.02x = 4.16, so x = 208 litres.

Multiple choice

Three glasses of equal volume contains acid mixed with water. The ratios of acid and water are 2 : 3, 3 : 4 and 4 : 5 respectively. Contents of these glasses are poured in a large vessel. The ratio of acid and water in the large vessel is समान मात्रा के तीन गिलास में पानी के साथ अम्ल मिश्रित होता है। अम्ल और जल का अनुपात क्रमशः 2 : 3 , 3 : 4 और 4 : 5 है। इन गिलासों की सामग्री को एक बड़े बर्तन में डाला जाता है। बड़े बर्तन में अम्ल और पानी का अनुपात है

  1. 411 : 540

  2. 401 : 544

  3. 417 : 564

  4. 407 : 560

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

Each glass has equal volume V. Glass 1: acid = 2/5 V, water = 3/5 V. Glass 2: acid = 3/7 V, water = 4/7 V. Glass 3: acid = 4/9 V, water = 5/9 V. Total acid = V(2/5 + 3/7 + 4/9) = V(126/315 + 135/315 + 140/315) = 401V/315. Total water = V(3/5 + 4/7 + 5/9) = V(189/315 + 180/315 + 175/315) = 544V/315. Ratio acid:water = 401:544. Option A (411:540), C (417:564), and D (407:560) are calculation errors.

Multiple choice

Mixture of water and alcohol is 30 liters, in which water is 33.33% less than alcohol. Find the quantity of water added in the mixture so that water becomes 50% more than the alcohol.

  1. 24

  2. 15

  3. 12

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

Let alcohol = A. Water is 33.33% less = A - (1/3)A = 2A/3. Total = A + 2A/3 = 5A/3 = 30L, so A = 18L, water = 12L. Let x be water added. New water = 12 + x. We need water to be 50% more than alcohol: 12 + x = 1.5 × 18 = 27. Solving: x = 15L. Options A (24L) and D (20L) would make water exceed alcohol by much more than 50%.

Multiple choice

A container has a 84 litres solution of milk and water in the ratio 7:5. If 24 litres of solution is taken out and then 5 litres of milk is added to it, what is the ratio of milk and water in the resulting mixture?
  1. $10:7$
  2. $7:4$
  3. $5:3$
  4. $8:5$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial: 84L in ratio 7:5 means 49L milk + 35L water. 24L removed (same ratio 7:5): removes 14L milk + 10L water. Remaining: 35L milk + 25L water. After adding 5L milk: 40L milk + 25L water = 65L total. New ratio = 40:25 = 8:5. Option A (10:7) would give 70 parts total, not matching the actual quantities.

Multiple choice

The ratio of petrol and kerosene in the container is 3: 2 when 10 litres of the mixture is taken out and is replaced by the kerosene, the ratio becomes 2: 3. The total quantity of the mixture in the container is : कंटेनर में पेट्रोल और मिट्टी के तेल का अनुपात 3: 2 है जब मिश्रण का 10 लीटर निकाल दिया जाता है और मिट्टी के तेल से बदल दिया जाता है, तो अनुपात 2: 3 हो जाता है। कंटेनर में मिश्रण की कुल मात्रा है:

  1. 25

  2. 30

  3. 45

  4. 18

  5. Cannot be determined निर्धारित नहीं किया जा सकता
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total quantity be T litres. Initial: Petrol = (3/5)T, Kerosene = (2/5)T. After removing 10 litres: Petrol removed = (3/5)×10 = 6 litres, Kerosene removed = (2/5)×10 = 4 litres. Remaining: Petrol = (3/5)T - 6, Kerosene = (2/5)T - 4. After adding 10 litres kerosene: New Kerosene = (2/5)T - 4 + 10 = (2/5)T + 6. New ratio is 2:3, so Petrol/Kerosene = 2/3. Therefore: [(3/5)T - 6] / [(2/5)T + 6] = 2/3. Cross-multiplying: 3[(3/5)T - 6] = 2[(2/5)T + 6]. This gives (9/5)T - 18 = (4/5)T + 12. So (5/5)T = 30, meaning T = 30 litres. This matches option B.

Multiple choice

A container contains 20 L mixture in which there is 10% sulphuric acid. Find the quantity of sulphuric acid to be added in it to make the solution to contain 25% sulphuric acid. एक कंटेनर में 20 लीटर का मिश्रण होता है जिसमें 10% सल्फ्यूरिक एसिड होता है। 25% सल्फ्यूरिक एसिड युक्त घोल बनाने के लिए इसमें सल्फ्यूरिक एसिड की मात्रा मिलानी चाहिए?

  1. 3L 3 लीटर

  2. 5L 5 लीटर

  3. 4L 4 लीटर

  4. 2L 2 लीटर

  5. 8L 8 लीटर
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial mixture: 20 L with 10% acid = 2 L acid, 18 L other. Add x L pure acid: final volume = 20 + x, acid = 2 + x. We need (2 + x) / (20 + x) = 25% = 1/4. Cross multiply: 4(2 + x) = 20 + x, so 8 + 4x = 20 + x, giving 3x = 12 and x = 4 L.