Quantitative Aptitude

Mixtures and Alligation

1,816 Questions
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Mixtures and Alligation Questions

Multiple choice

The quantity of water that should be added to reduce 18 ml lotion containing 50\% alcohol to a lotion containing 30\% alcohol is-

  1. 6 ml

  2. 8 ml

  3. 10 ml

  4. 12 ml
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial alcohol = 50% of 18 ml = 9 ml. Let x ml water be added. Total volume = (18+x) ml, alcohol = 9 ml. For 30% concentration: 9/(18+x) = 0.3, so 9 = 0.3(18+x), giving 9 = 5.4 + 0.3x, therefore x = 3.6/0.3 = 12 ml. Option A (6 ml) might result from incorrectly solving 9/(18+x) = 0.5.

Multiple choice

Pramod mixes milk and water in the ratio 9 : 4. And after taking out 13 liters of mixture and adding 16 liters of water, the ratio of milk to water becomes 5:4. How many liters of the mixture was used by Pramod initially?

  1. 78

  2. 65

  3. 80

  4. 52
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let initial mixture be 13x liters (9x milk, 4x water). Removing 13L maintains ratio, so remaining: 9x-9 milk, 4x-4 water. After adding 16L water: milk = 9x-9, water = 4x+12. Given (9x-9)/(4x+12) = 5/4. Cross-multiply: 4(9x-9) = 5(4x+12), so 36x-36 = 20x+60, giving 16x = 96 and x = 6. Initial mixture = 13x = 78 liters.

Multiple choice

A container contains 10 litres mixture in which there is 10 \% sulphuric acid. How much sulphuric acid is to be added to make the solution to contain 25 \% sulphuric acid ?

  1. 1 litre

  2. 2 litre

  3. 3.5 litre

  4. 2.5 litre
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture: 10 litres with 10% acid = 1 litre acid, 9 litres other. Let x litres of pure acid be added. New volume = 10 + x litres. New acid = 1 + x litres. We need 25% acid: (1 + x)/(10 + x) = 25/100 = 1/4. Cross-multiplying: 4(1 + x) = 10 + x. 4 + 4x = 10 + x. 3x = 6. x = 2 litres.

Multiple choice

A vessel contains milk and water in which 20% water. 20 litre of mixture was taken and replaced by water and the ratio becomes 12: 13. Then find the initial quantity of milk in the vessel. एक बर्तन में दूध और पानी रखा है| जिसमें 20% पानी है। 20 लीटर मिश्रण को निकाला जाता है और इसे पानी से बदल दिया जाता है, तो नया अनुपात 12: 13 हो जाता है। तो बर्तन में दूध की प्रारंभिक मात्रा ज्ञात करें।

  1. 30 litres 30 लीटर

  2. 40 litres 40 लीटर

  3. 50 litres 50 लीटर

  4. 56 litres 56 लीटर

  5. 60 litres 60 लीटर
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture: 20% water, 80% milk. After removing 20L and adding water, milk ratio becomes 12/25 = 48%. Let total = x. Milk after replacement = 0.8(x - 20). So 0.8(x - 20)/x = 0.48, giving x = 100. Initial milk = 80% of 100 = 40L.

Multiple choice

In a 160-litres mixture of milk and water, the percentage of water is only 35%. The milkman gave 40 litres of this mixture to a customer and then added 'X' litres of pure milk to the remaining mixture. As a result the percentage of water in the final mixture becomes 30%. What is the value of 'X'? दूध और पानी के 160-लीटर मिश्रण में, पानी का प्रतिशत केवल 35% है। दूधवाले ने इस मिश्रण का 40 लीटर एक ग्राहक को दिया और फिर शेष मिश्रण में 'X' लीटर शुद्ध दूध मिलाया। परिणामस्वरूप अंतिम मिश्रण में पानी का प्रतिशत 30% हो जाता है। 'X' का मूल्य क्या है'?

  1. 20

  2. 25

  3. 30

  4. 15

  5. 10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial mixture: 160 L with 35% water = 56 L water, 104 L milk. After removing 40 L (which contains 0.35 × 40 = 14 L water), remaining water = 56 - 14 = 42 L, remaining milk = 104 - 26 = 78 L. Total remaining = 120 L. Adding X litres of pure milk, total volume = 120 + X, water stays at 42 L. For 30% water: 42/(120 + X) = 0.30, so 42 = 36 + 0.30X, which gives 0.30X = 6, therefore X = 20.

Multiple choice

Three containers A, B and C are having mixtures of milk and water in the ratio 1: 5, 3: 5 and 5: 7 respectively. If the capacities of the containers are in the ratio 5: 4: 5, then find the ratio of the milk to the water, if the mixtures of all the three containers are mixed together. तीन कंटेनर A, B और C में दूध और पानी का मिश्रण क्रमशः 1:5, 3:5 और 5:7 के अनुपात में है। यदि कंटेनरों की क्षमता 5: 4: 5 के अनुपात में है, तो दूध का पानी से अनुपात ज्ञात करें, यदि तीनों कंटेनरों के मिश्रण को एक साथ मिलाया जाता है।

  1. 53: 115

  2. 47: 56

  3. 42: 37

  4. 58: 119

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

Container A has milk:water = 1:5, capacity ratio 5. Milk in A = 1/(1+5) × 5k = 5k/6. Container B has 3:5, capacity ratio 4. Milk in B = 3/(3+5) × 4k = 12k/8 = 3k/2. Container C has 5:7, capacity ratio 5. Milk in C = 5/(5+7) × 5k = 25k/12. Total milk = 5k/6 + 3k/2 + 25k/12 = 53k/12. Total water = 25k/6 + 5k/2 + 35k/12 = 115k/12. Ratio milk:water = 53:115.

Multiple choice

Three utensils of 10 liters in which the ratio of petrol and kerosene is 2: 1, 3: 1, and 3: 2, respectively. If all the three utensils are given in a large pot, then find the ratio of petrol and kerosene in the new mixture? 10 लीटर के तीन बर्तनों में जिनमे पेट्रोल तथा केरोसिन का अनुपात क्रमशः 2:1, 3:1, और 3:2 है| अगर तीनो बर्तनों को एक बड़े बर्तन में डाल दिया जाए तो नए मिश्रण में पेट्रोल तथा केरोसिन का अनुपात ज्ञात कीजिए?

  1. 79:86

  2. 85:78

  3. 59:121

  4. 121:59

  5. 78: 85
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Calculate the amount of petrol and kerosene in each utensil separately. Utensil 1 (2:1) has petrol = 10 × 2/3 = 20/3 L and kerosene = 10/3 L. Utensil 2 (3:1) has petrol = 10 × 3/4 = 7.5 L and kerosene = 2.5 L. Utensil 3 (3:2) has petrol = 10 × 3/5 = 6 L and kerosene = 4 L. Total petrol = 20/3 + 7.5 + 6 = 20/3 + 15/2 + 6 = (40 + 45 + 36)/6 = 121/3 L. Total kerosene = 10/3 + 2.5 + 4 = 10/3 + 5/2 + 4 = (20 + 15 + 24)/6 = 59/3 L. Ratio = 121/3 : 59/3 = 121:59. Option D matches this calculation.

Multiple choice

A 10 kg mixture of sand and salt 40% is sand. How much salt should be added so that ratio of salt and sand became 4 : 1 in new mixture? बालू और नमक के 10 किलो मिश्रण में 40% बालू है, इसमें कितना नमक और मिला दे कि मिश्रण में नमक व बालू को अनुपात 4 : 1 हो जाये?

  1. 4 kg 4 किग्रा.

  2. 10 kg 10 किग्रा.

  3. 5 kg 5 किग्रा.

  4. Can't be determined तय नहीं कर सकते है

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

In 10 kg mixture: sand = 40% of 10 = 4 kg, salt = 60% of 10 = 6 kg. Let x kg salt be added. New mixture has salt = (6+x) kg and sand = 4 kg. We need (6+x) : 4 = 4 : 1, so (6+x)/4 = 4/1, giving 6+x = 16, so x = 10 kg. Option B is correct.

Multiple choice

A dealer buys mangoes at Rs 50, Rs 40 and Rs 30 per kilogram. He mixes them in the ratio 2: 4: 9 by weight, and sells at a profit of 30%. At what approximate price per kilogram does he sell the fruit? एक व्यापारी आम को 50 रुपये, 40 रुपये और 30 रुपये प्रति किलोग्राम के हिसाब से खरीदता है। वह उन्हें वजन द्वारा 2: 4: 9 के अनुपात में मिलाता है, और 30% के लाभ पर बेचता है। प्रति किलोग्राम किस अनुमानित मूल्य पर वह फल बेचेगा?

  1. 40

  2. 44

  3. 46

  4. 48

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

Total parts = 2+4+9 = 15. CP per kg = (50×2 + 40×4 + 30×9) / 15 = (100 + 160 + 270) / 15 = 530/15 = 35.26... SP at 30% profit = 35.26 × 1.3 = 45.84, approximately 46.

Multiple choice

In a mixture of alcohol and water the proportion of water by weight was 75%. If in the 120 gms mixture 30 gms water was added, what would be the percentage of water in the new mixture? शराब और पानी के मिश्रण में वजन के हिसाब से पानी का अनुपात 75% था। यदि 120 ग्राम मिश्रण में 30 ग्राम पानी मिलाया जाता है, तो नए मिश्रण में पानी का प्रतिशत कितना होगा?

  1. 65%

  2. 80%

  3. 75%

  4. 90%

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

Original mixture: 75% water means 90g water and 30g alcohol in 120g. After adding 30g water: total mixture = 150g, water = 90+30 = 120g. New % water = 120/150 × 100 = 80%. Wait, this is wrong. If water is 75% by weight, then in 120g: water = 0.75 × 120 = 90g, alcohol = 30g. Adding 30g water: water = 90+30 = 120g, total = 120+30 = 150g. % water = 120/150 = 0.8 = 80%. This matches the claimed answer.

Multiple choice

A barrel contains a mixture of wine and water in the ratio 3 : 1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture in the barrel becomes 1 : 1 ?
  1. $1/4$
  2. $1/3$
  3. $3/4$
  4. $2/3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let barrel capacity = 4 units (3 wine + 1 water). To make ratio 1:1, we need 2 wine + 2 water. Remove x fraction: remaining wine = 3(1-x), water = 1(1-x) + x. Set 3(1-x) = 1(1-x) + x. Solve: 3-3x = 1-x+x, so 3-3x = 1, giving 2x=2 and x=1/3. Option A (1/4) is incorrect because it would leave 2.25 wine and 1.75 water.

Multiple choice

A Can contains a mixture of two liquids A and B in the ratio 7 : 5. When 12 liters of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. Find the Liters of liquid A contained by the can initially was? एक कैन में 7 : 5 के अनुपात में दो तरल पदार्थ A और B का मिश्रण होता है। जब 12 लीटर मिश्रण निकाला जाता है और कैन को B से भरा जाता है, A और B का अनुपात 7 :9 हो जाता है। प्राम्भिक मिश्रण में तरल A की लीटर में मात्रा ज्ञात कीजये ?

  1. 26

  2. 28

  3. 27

  4. 24

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

Let total mixture = 12x liters. A = 7x, B = 5x. Removing 12 liters (with A:B = 7:5): A removed = 7/12 × 12 = 7, B removed = 5. After removal: A = 7x - 7, B = 5x - 5. Adding 12 liters of B: A = 7x - 7, B = 5x - 5 + 12 = 5x + 7. New ratio: (7x-7)/(5x+7) = 7/9. Solving: 63x - 63 = 35x + 49, so 28x = 112, x = 4. Initial A = 7 × 4 = 28 liters.

Multiple choice

In what ratio a mixture containing 20% milk should be mixed with another mixture containing 75% milk so that in the resultant mixture percentage of milk becomes 40%. किस अनुपात में 20% दूध वाले मिश्रण को 75% दूध वाले दूसरे मिश्रण के साथ मिलाया जाना चाहिए ताकि परिणामी मिश्रण में दूध का प्रतिशत 40% हो जाए।

  1. 7 : 4

  2. 6 : 5

  3. 9 : 5

  4. 8 : 5

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

Use allegation method. Let ratio = x:y where x is 20% milk and y is 75% milk. Mean is 40%. Using allegation: x : y = (75 - 40) : (40 - 20) = 35 : 20 = 7 : 4. So 20% mixture : 75% mixture = 7 : 4. Correct answer is option A.

Multiple choice

A 24 litres of milk and water mixture contains milk and water in the ratio 3 : 5. What litres of the mixture should be taken out and replaced with pure milk so that the final mixture contains milk and water in equal proportions? एक 24 लीटर दूध और पानी के मिश्रण में दूध और पानी 3: 5 का अनुपात होता है। कितने मिश्रण को बाहर निकालना चाहिए और शुद्ध दूध से बदलना चाहिए ताकि अंतिम मिश्रण में समान अनुपात में दूध और पानी हो?

  1. 4.8

  2. 5.2

  3. 6.4

  4. 3.8

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

In 24 litres mixture with milk:water = 3:5, milk = (3/8) × 24 = 9 litres and water = 15 litres. Let x litres be removed and replaced with pure milk. The amount of milk becomes: 9 - (3/8)x + x = 9 + (5/8)x. Water becomes: 15 - (5/8)x. For equal proportions: 9 + (5/8)x = 15 - (5/8)x. Solving: (5/8)x + (5/8)x = 15 - 9, so (10/8)x = 6, giving x = 6 × 8/10 = 4.8 litres.

Multiple choice

In a mixture of 55 kg., the ratio of milk and water is 7:4. What is the quantity of water added to the mixture in order to make the ratio 7:6? 55 किग्रा. के एक मिश्रण में दूध और पानी का अनुपात 7 : 4 है। अनुपात को 7: 6 करने के लिए मिलाये जाने वाले पानी की मात्रा क्या है?

  1. 15 kg.

  2. 10 kg.

  3. 5 kg.

  4. 12 kg.

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

In 55 kg mixture with 7:4 ratio, milk = 35 kg, water = 20 kg (7+4=11 parts, each part = 5 kg). To make ratio 7:6, add x kg water: 20+x = 6/7 × 35 = 30, so x = 10 kg. Only water quantity changes.