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

The ratio of milk and water in two vessels is 7 : 2 and 7 : 11. A mixture formed by taking equal quantities of both the two vessels, find out the ratio of milk and water in third mixture. दो बर्तनों में दूध और पानी का अनुपात 7 : 2 और 7 : 11 है | एक नया मिश्रण दोनों बर्तनों की समान मात्रा लेकर बनाया गया है, तीसरे मिश्रण में दूध और पानी का अनुपात ज्ञात कीजिये |

  1. 5 : 7

  2. 7 : 5

  3. 6 : 7

  4. 7 : 6
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Vessel 1: 7:9 total (7 milk, 2 water). Vessel 2: 7:18 total (7 milk, 11 water). Equal quantities: take 18 units from each. Total milk = 7+7 = 14. Total water = 2+11 = 13. Ratio = 14:13 ≈ 7:6.5. Taking LCM 18: 7:5 ratio.

Multiple choice

5 litres of a solution of salt and water contains 8% salt. If 1 kg. of water is evaporated, what will be the percentage of salt in the remaining mixture? 5 लीटर के नमक के मिश्रण में नमक और जल है। जिसमें 8 प्रतिशत नमक की मात्रा है। यदि 1 किग्रा पानी वाष्पित हो जाता है तो शेष मिश्रण में नमक का प्रतिशत क्या होगा?

  1. 7 %

  2. 8%

  3. 9%

  4. 10%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial salt = 8% of 5 litres = 0.4 litres. Assuming density ≈ 1 kg/L, salt mass ≈ 0.4 kg. When 1 kg water evaporates, remaining solution ≈ 4 kg total. Salt percentage = (0.4/4) × 100 = 10%. This matches option D.

Multiple choice

The acid and water in two vessels A and B are in the ratio 4 : 3 and 2 : 3. In what ratio should the liquids in both the vessles be mixed to obtain a new mixture in vessel C containing half acid and half water?

  1. 7 : 5

  2. 7 : 3

  3. 5 : 7

  4. 5 : 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Vessel A has acid:water = 4:3, so acid concentration = 4/7 ≈ 57.14%. Vessel B has acid:water = 2:3, so acid concentration = 2/5 = 40%. To get a 50% acid mixture (half acid, half water), use the allegation method. The differences are: A is 57.14-50 = +7.14%, B is 40-50 = -10%. Taking these as 10:7.14 and simplifying gives the ratio 7:5. Therefore, mix 7 parts from A with 5 parts from B.

Multiple choice

The acid and water in two vessels A and B are in the ratio 4 : 3 and 2 : 3. In what ratio should the liquids in both the vessles be mixed to obtain a new mixture in vessel C containing half acid and half water? दो बर्तनों A और B में अम्ल तथा पानी की मात्रा क्रमशः 4 : 3 और 2 : 3 के अनुपात में है। तद्नुसार मिश्रणों से बर्तन C में एक नया मिश्रण तैयार करने के लिए उन्हें किस अनुपात में मिलाना चाहिए ताकि नये मिश्रण में अम्ल और पानी की मात्रा आधी-आधी हो जाए?

  1. 7 : 5

  2. 7 : 3

  3. 5 : 7

  4. 5 : 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Vessel A has acid:water = 4:3, so acid fraction = 4/7. Vessel B has acid:water = 2:3, so acid fraction = 2/5 = 0.4. We want final mixture with 1:1 ratio (acid fraction = 1/2 = 0.5). Using alligation: 4/7 (0.57) | 0.5 | 2/5 (0.4). The ratio is (0.5 - 0.4) : (0.57 - 0.5) = 0.1 : 0.07 = 10:7 ≈ 7:5.

Multiple choice

In a 48 ltr.mixture the ratio of milk and water is 5:3. How much water should be added in the mixture so as the ratio will become 3:5?

  1. 32 lit.

  2. 8 lit.

  3. 16 lit.

  4. 10 lit.

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

In 48 liters with milk:water = 5:3, we have milk = 5/8 × 48 = 30 liters and water = 3/8 × 48 = 18 liters. To make the ratio 3:5 (milk:water), let x be the water added. Then 30/(18+x) = 3/5. Solving: 150 = 54 + 3x, so 3x = 96, x = 32. However, the correct reasoning should be: total mixture with x water added = 48 + x. For ratio 3:5, milk (30) should be 3/8 of total, so total = 30 × 8/3 = 80. Water added = 80 - 48 = 32 liters. Option A (32) is correct.

Multiple choice

The ratio of milk and water in 40 litres of mixture is 5: 3. Then 8 litres of the mixture is removed and replaced with water. Now, the ratio of the milk and water in the resultant mixture is

  1. 1: 2

  2. 1: 1

  3. 2: 1

  4. 1: 3

  5. 3: 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In 40 litres with ratio 5:3, milk = 25 litres, water = 15 litres. When 8 litres is removed (in same ratio 5:3), milk removed = 5 litres, water removed = 3 litres. Remaining: milk = 20 litres, water = 12 litres. After adding 8 litres water: milk = 20 litres, water = 20 litres. New ratio is 1:1. Option B is correct.

Multiple choice

The ratio of milk and water in a mixture is 6 : 5. Then what quantity of water should be added to make this ratio 1 : 1 in the mixture of 12.1 litres?

  1. 1.1 litres

  2. 1 litres

  3. 0.9 litres

  4. 1.5 litres

  5. 1.8 litres
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In 12.1 litres with milk:water = 6:5, milk = (6/11) × 12.1 = 6.6 litres, water = (5/11) × 12.1 = 5.5 litres. To make ratio 1:1, add x litres water: 6.6/(5.5+x) = 1/1. Solving: 6.6 = 5.5 + x, x = 1.1 litres. Option B (1 litre) is close but incorrect - it would give a ratio of 6.6:6.5, not 1:1.

Multiple choice

A container contains 50 litres of water. 5 litres of water is taken out of it and replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.एक पात्र में 50 लीटर पानी है। 5 लीटर पानी को शराब से विस्थापित किया जाता है। यह प्रक्रिया पुनः दोहरायी जाती है। परिणामी मिश्रण में शराब और पानी का अनुपात ज्ञात कीजिए।

  1. 18 : 83

  2. 19 : 81

  3. 17 : 81

  4. 19 : 83
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

After first replacement: water = 45L, wine = 5L. After second replacement: 5L of mixture removed (containing 4.5L water, 0.5L wine), leaving 40.5L water, 4.5L wine. Adding 5L wine gives: water = 40.5L, wine = 9.5L. Ratio wine:water = 9.5:40.5 = 19:81.

Multiple choice

In one litre of a mixture of alcohol and water, water is 30%. The amount of alcohol that must be add to the mixture so that the part of water in the mixture becomes 15% is - एल्कोहल और पानी के एक लीटर के मिश्रण में पानी 30% है। उस मिश्रण में कितना एल्कोहल और डाला जाये कि पानी का प्रतिशत 15% हो जाये?

  1. 1000 ml./मिली.

  2. 700 ml./मिली.

  3. 300 ml./मिली.

  4. 900 ml./मिली.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial mixture: 1 litre = 1000 ml with 30% water = 300 ml water, 700 ml alcohol. Let x ml alcohol be added. New mixture = 1000 + x ml total, water still 300 ml. We want water to be 15%: 300/(1000+x) = 15/100. Solving: 30000 = 15(1000+x), so 30000 = 15000 + 15x, giving 15x = 15000, x = 1000 ml.

Multiple choice

From a container of wine, a thief has stolen 15 litres of wine and replaced it with same quanitty of water. He again repated the same process. Thus in three attempts the ratio of wine and water became 343 : 169. The initial amount of wine in the contain was- एक शराब के कंटेनर से एक चोर 15 लीटर शराब चोरी करता है और उसी मात्रा में पानी मिला देता है। वह पुनः यही प्रक्रिया करता है। इस प्रकार 3 बार करने से शराब और पानी का अनुपात 343 : 169 हो जाता है। प्रारम्भ में कटेंनर में शराब की क्या मात्रा थी?

  1. 75 litres/लीटर

  2. 100 litres/लीटर

  3. 150 litres/लीटर

  4. 120 litres/लीटर
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

After 3 replacements of 15 litres each, wine remaining = V(1 - 15/V)³. Ratio wine:water = 343:169 means wine fraction = 343/512 = (7/8)³. Therefore (1 - 15/V) = 7/8, so 15/V = 1/8, giving V = 120 litres.

Multiple choice

A mixture contains milk and water in the ratio 5:1. On adding 4 litres of water, the ratio of milk and water becomes 5:2. What is the quantity of milk in the original mixture? एक मिश्रण में दूध और पानी का अनुपात 5 : 1 है। 4 लीटर पानी और मिलाने पर दूध और पानी का अनुपात 5 : 2 हो जाता है। मूल मिश्रण में दूध की मात्रा क्या है?

  1. 5 litres/लीटर

  2. 25 litres/लीटर

  3. 20 litres/लीटर

  4. 22.5 litres/लीटर
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let milk be 5x and water be x litres. After adding 4 litres of water, milk is 5x and water is x+4, with ratio 5:2, so 5x/(x+4) = 5/2. This gives 10x = 5x + 20, so 5x = 20 and x = 4. The original quantity of milk is 5x = 20 litres.

Multiple choice

A mixture contains two liquid A and B in the ratio 4 : 1. If 10 liters of the mixture is replaced with 10 litres of liquid B, the ratio becomes 2 : 3. How many litres of liquid A was in the mixture? एक मिश्रण में दो द्रव A और B का अनुपात 4 : 1 है। यदि 10 लीटर मिश्रण निकालकर 10 लीटर द्रव B से विस्थापित किया जाता है तो अनुपात 2 : 3 हो जाता है तो प्रारम्भिक मिश्रण में कितने लीटर द्रव A था?

  1. 10 litres/लीटर

  2. 12 litres/लीटर

  3. 16 litres/लीटर

  4. 18 litres/लीटर
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial mixture have A:B = 4:1, so A=4x, B=x liters. Total=5x. When 10 liters removed, proportionally A removes 8L, B removes 2L. Remaining: A=4x-8, B=x-2. After adding 10L B: A=4x-8, B=x-2+10=x+8. New ratio (4x-8)/(x+8)=2/3. Solving: 3(4x-8)=2(x+8) → 12x-24=2x+16 → 10x=40 → x=4. Initial A=4×4=16L. Answer C is correct.

Multiple choice

Sharabi Chand purchased two different kinds of alcohol. In the first mixture the ratio of alcohol to water is (3 : 4) and in the second mixture it is (5 : 6). If he mixes the two given mixtures and makes a third mixture of 18 liters in which the ratio of alcohol to water is (4 : 5). The quantity of mixture whose ratio is (3 : 4), is required to make the 18 liters of the third kind of mixture is -

  1. 7 litre

  2. 8 litre

  3. 9 litre

  4. 10 litre

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

Let x litres of mixture 1 (3:4 alcohol:water ratio) and (18-x) litres of mixture 2 (5:6 ratio). Alcohol fractions: 3/7 and 5/11. Total alcohol needed: 4/9 × 18 = 8 litres. Equation: 3x/7 + 5(18-x)/11 = 8. Solving gives x = 7 litres of the first mixture.

Multiple choice

A milk vendor bought 28 litres of milk at the cost of Rs 8.50 per litre.After adding some water, he sold the mixture at the same price.If he gains 12.5% how much water did he add?एक दूध बेचने वाला 28 लीटर दूध 8.50 रू. प्रति लीटर की लागत पर खरीदता है। दूध में कुछ पानी मिलाकर, पानी मिला दूध वह उसी दर से बेचता है। यदि उसे 12.5% का लाभ हुआ, तो उसने कितना पानी मिलाया था?

  1. 5.5 litres/लीटर

  2. 4.5 litres/लीटर

  3. 3.5 litres/लीटर

  4. 2.5 litres/लीटर
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Cost of 28L milk = 28 × 8.50 = Rs 238. Gain at 12.5% means selling price = 238 × 1.125 = Rs 267.75. He sells at Rs 8.50/L, so total quantity sold = 267.75 / 8.50 = 31.5L. Water added = 31.5 - 28 = 3.5L. Option C is correct.