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

Two vessels A and B filled with alcohol and sprit in the ratio 7 : 5 and 8 : 3. Find the ratio in which mixture of A & B mixed to get alcohol. दो बर्तन A और B एल्कोहल तथा स्प्रिट से भरे है जिनमें एल्कोहल तथा स्प्रिट का अनुपात क्रमशः 7 : 5 और 8 : 3 है। यदि दोनों को मिला दिया जाए तो A और B को किस अनुपात में मिलाया जाए कि मिश्रण में 70% एल्कोहल हो जाए।

  1. 77 : 55

  2. 18 : 77

  3. 23 : 24

  4. 55 : 12

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

Set the mixing ratio as A:B = x:y. Vessel A has alcohol:sprit = 7:5 (7/12 alcohol), Vessel B has 8:3 (8/11 alcohol). Final mixture has 70% alcohol. Solving (7/12)x + (8/11)y = 0.70(x+y) gives x:y = 18:77. This is the correct ratio to achieve approximately 70% alcohol concentration.

Multiple choice

A person mix 18 ltrs of water in pure milk and sells the mixture at cost price of milk and gets a profit of 12.5%. Find the initial quantity of milk. एक दुकानदार 18 ली. पानी को शुद्ध दूध में मिलाता है तथा मिश्रण को दूध के क्रय मूल्य पर बेचता है और 12.5% का लाभ प्राप्त करता है। दूध की प्रारम्भिक मात्रा ज्ञात कीजिए।

  1. 120 lt. 120 ली.

  2. 124 lt. 124 ली.

  3. 160 lt. 160 ली.

  4. 144 lt. 144 ली.

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

12.5% profit means 18L water equals 12.5% of milk quantity. If 18 = 12.5% of milk, then milk = 18 × 8 = 144L (since 12.5% = 1/8). Water added creates profit equal to its proportion of milk.

Multiple choice

In a mixture 12 litre water is mixed so percentage of water changed from 20 to 40%. Find initial quantity of mixture. एक मिश्रण में 12 लीटर पानी मिलाने पर पानी 20 प्रतिशत से बढ़कर 40% हो गया। मिश्रण की प्रारम्भिक मात्रा ज्ञात कीजिए।

  1. 24 lt. 24 ली.

  2. 48 lt. 48 ली.

  3. 36 lt. 36 ली.

  4. 40 lt. 40 ली.

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

Initial water = 20% of mixture. Adding 12L increases water to 40% of NEW total. Let initial mixture = x. 0.2x + 12 = 0.4(x+12). Solve: 0.2x = 12 - 4.8 = 7.2, so x = 36L.

Multiple choice

In a mixture of milk and water ratio of milk and water is 5 : 3. When 12 litre water is added in mixture, milk becomes 50%. Find the initial quantity of mixture. दूध और पानी के मिश्रण में दूध और पानी का अनुपात 5 : 3 है। जब मिश्रण में 12 लीटर पानी मिलाया गया तो दूध 50% हो गया। मिश्रण की प्रारम्भिक मात्रा ज्ञात कीजिए ?

  1. 36 litre 36 लीटर

  2. 18 litre 18 लीटर

  3. 45 litre 45 लीटर

  4. 48 litre 48 लीटर

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

Initial ratio milk:water = 5:3. Let initial quantities be 5x milk and 3x water (total 8x). After adding 12 liters water: milk = 5x, water = 3x + 12. Since milk becomes 50%, milk = water. So 5x = 3x + 12, giving 2x = 12, x = 6. Initial mixture = 8x = 48 liters.

Multiple choice

In a mixture percentage of water is 65%. When 18 liter mixture containing 30% water is mixed in this the percentage of water becomes 50%. Find the initial quantity of mixture. (in liters) पानी के मिश्रण में प्रतिशत 65% है। जब 30 % पानी वाले 18 लीटर मिश्रण को इसमें मिलाया जाता है तो पानी का प्रतिशत 50% हो जाता है। मिश्रण की प्रारंभिक मात्रा ज्ञात कीजिये। (लीटर में)

  1. 18

  2. 36

  3. 27

  4. 30

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

Let initial mixture be x liters. Water in it = 0.65x. Added water = 30% of 18 = 5.4L. Total water = 0.65x + 5.4, total mixture = x + 18. New concentration: (0.65x + 5.4)/(x + 18) = 0.5. Solving: 0.15x = 3.6, x = 24L.

Multiple choice

A container of 108 litre capacity is filled with pure milk. From this 18 litres is taken out and replaced with water. If this process is repeated two times more then find the quantity of water in container. एक 108 लीटर क्षमता का पात्र शुद्ध दूध से भरा हुआ है। इसमें से 18 लीटर निकाला जाता है तथा उसके स्थान पर पानी मिला दिया जाता है। यदि इस प्रक्रिया को दो बार और दोहराया जाय तो पात्र में पानी की मात्रा ज्ञात कीजिए।

  1. 45.5

  2. 41.4

  3. 50.25

  4. 46.45

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

This is a dilution problem. Each operation: remove 18L from 108L, so fraction removed = 18/108 = 1/6. After each replacement, milk multiplies by (1 - 1/6) = 5/6. After 3 operations: milk = 108 × (5/6)³ = 108 × 125/216 = 62.5L. Water = 108 - 62.5 = 45.5L. The claimed answer A (45.5) is correct.

Multiple choice

From a container, 6 liters milk was drawn out and was replaced by water. Again 6 liters of mixture was drawn out and was replaced by the water. Thus the quantity of milk and water in the container after these two operations is 8 : 10. The quantity of mixture is: एक कंटेनर से 6 लीटर दूध निकालकर उसे पानी से प्रतिस्थापित कर दिया गया । पुनः मिश्रण से 6 लीटर दूध निकालकर उसे पानी से प्रतिस्थापित कर दिया गया इस प्रकार इन दो क्रियाओं के पश्चात कंटेनर में दूध और पानी का अनुपात 8 : 10 है। मिश्रण की मात्रा है-

  1. 8 liter 8 ली

  2. 10 liter 10 ली

  3. 12 liter 12 ली

  4. 15 liter 15 ली

  5. 18 liter 18 ली
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let the total quantity be V liters. After removing 6 liters of milk and replacing with water, we have V-6 liters of milk and 6 liters of water. After the second operation, we remove 6 liters of the mixture (which contains milk and water in proportion to their current amounts) and replace with water. The final ratio of milk to water is 8:10. Using the dilution formula for successive replacements: final milk quantity = V(1 - 6/V)². The ratio milk:water = (1 - 6/V)² : (1 - (1 - 6/V)²) = 8:10. Solving gives V = 18 liters.

Multiple choice

A mixture of 70 liters of alcohol and water contains 10 % of water. How much water must be added to the above mixture to make the water 12.5 % of the resulting mixture? 70 लीटर एल्कोहल और पानी के एक मिश्रण में पानी की मात्रा 10% है। उपरोक्त मिश्रण में कितना पानी अवश्य मिलाया जाय जिससे कि प्राप्त मिश्रण में पानी की मात्रा 12.5% हो जाये?

  1. 3.3 liters 3.3 लीटर

  2. 3 liters 3 लीटर

  3. 2.8 liters 2.8 लीटर

  4. 2 liters 2 लीटर

  5. 1.5 liters 1.5 लीटर
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial mixture: 70 liters with 10% water = 7 liters water, 63 liters alcohol. Let x liters water be added. New mixture: 70 + x liters total, 7 + x liters water. For water to be 12.5%: (7 + x)/(70 + x) = 0.125. Solving: 7 + x = 8.75 + 0.125x, 0.875x = 1.75, x = 2. Adding 2 liters gives: 72 total, 9 water = 12.5%. Option D is correct.

Multiple choice

The ratio of Milk to water is 5:4, if 15 liters of water is added, the ratio becomes 10:9, then find the new quantity of water in the mixture. दूध और पानी का अनुपात 5: 4 है, यदि 15 लीटर पानी मिलाया जाता है, तो अनुपात 10: 9 हो जाता है, तो मिश्रण में पानी की नई मात्रा ज्ञात कीजिये।

  1. 120

  2. 150

  3. 175

  4. 135

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

Initial ratio 5:4 means milk=5x, water=4x. After adding 15L water, new ratio is 10:9. Setting up 5x/(4x+15)=10/9 gives x=30. Initial water=4×30=120L. New water=120+15=135L.

Multiple choice

Ankit has three varieties of rice costing 18 Rs/kg,25 Rs/kg and 36 Rs/kg, In what possible ratio he should mix these three varieties so that on selling whole mixture at 23.10 Rs/kg he may get a profit of 10%? अंकित के पास तीन किस्म के चावल हैं जिनका मूल्य क्रमशः 18 रुपये / किग्रा, 25 रुपये / किग्रा और 36 रुपये / किग्रा है ,उसे किस संभावित अनुपात में इन तीन किस्मों को मिलाना चाहिए ताकि पूरे मिश्रण को 23.10 रुपये / किग्रा पर बेचकर उसे 10 प्रतिशत का लाभ हो?

  1. 5 : 4 : 2

  2. 9 : 3 : 1

  3. 3 : 2 : 1

  4. 7 : 4 : 3

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

Selling at Rs. 23.10 with 10% profit means cost price of mixture = 23.10/1.1 = Rs. 21/kg. Let quantities in ratio a:b:c for costs 18, 25, 36. Using allegation method: (18×a + 25×b + 36×c)/(a+b+c) = 21. Testing option B (9:3:1): Weighted average = (18×9 + 25×3 + 36×1)/(9+3+1) = (162 + 75 + 36)/13 = 273/13 = Rs. 21/kg. This matches the required cost price.

Multiple choice

In a mixture of milk and water milk is found to be 28%. When 16 litre water is added in the mixture new percentage of milk in mixture becomes 20%. Find the initial quantity of mixture. दूध और पानी के मिश्रण में दूध 28% है। जब मिश्रण में 16 लीटर पानी मिलाया जाता है तो मिश्रण में दूध का नया प्रतिशत 20% हो जाता है। मिश्रण की प्रारंभिक मात्रा ज्ञात कीजिये।

  1. 42 litre 42 लीटर

  2. 48 litre 48 लीटर

  3. 36 litre 36 लीटर

  4. 40 litre 40 लीटर

  5. None कोई नहीं
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let initial mixture be x liters. Milk initially = 0.28x liters. After adding 16 liters water, total = x + 16 liters, milk still = 0.28x. New milk percentage = 20%, so 0.28x/(x + 16) = 0.20. Solving: 0.28x = 0.20x + 3.2, 0.08x = 3.2, x = 40 liters.

Multiple choice

A alcohol solution has 35\% alcohol. Another solution has 25\% alcohol. How many liters of the second solution must be added to 18 liters of the first solution to make a solution of 30\% alcohol?

  1. 18 liter

  2. 36 liter

  3. 9 liter

  4. 54 liter

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

Let x liters of 25% solution be added. Total alcohol = 35% of 18 + 25% of x = 6.3 + 0.25x. Total volume = 18 + x. This should equal 30% of (18 + x): 6.3 + 0.25x = 0.30(18 + x) = 5.4 + 0.30x. Solving: 6.3 - 5.4 = 0.30x - 0.25x, so 0.9 = 0.05x, giving x = 18. You can also use allegation: (35-30):(30-25) = 5:5 = 1:1, so equal quantities.

Multiple choice

There were 120 litres of pure milk in a vessel. Some quantity of milk was taken out and replaced with 23 litres of water. thus the resultant ratio of the quantity of milk to water is 4:1. Again 23 litres of the mixture was taken out and replaced with 28 litre of water. What is the ratio of the milk to water in the resultant mixture?

  1. 15 : 13

  2. 46 : 29

  3. 48 : 29

  4. 29 : 44
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

First replacement: After removing x litres and adding 23 L water, milk:water = 4:1 with total 120 L. So milk = 96 L, water = 24 L, meaning x = 24 L milk was removed. Second replacement: From 96 L milk + 24 L water, removing 23 L mixture removes (23×96/120) = 18.4 L milk and (23×24/120) = 4.6 L water. Remaining: 77.6 L milk + 19.4 L water. Adding 28 L water: milk = 77.6 L, water = 47.4 L. Ratio = 77.6:47.4 = 46:29.

Multiple choice

Mixture A contains 12.5% water and mixture B contains 10% water. In what ratio both mixtures should be mixed in a bottle so that in bottle ratio of milk and water be 89:11. मिश्रण A में पानी 12.5% और मिश्रण B में पानी 10% पानी है । एक बोतल में दोनों को किस अनुपात में मिलाना चाहिए ताकि बोतल में दूध और पानी का अनुपात 89:11 हो जाये।

  1. 1:2

  2. 1:3

  3. 2:3

  4. 1:4

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

This is an allegation problem. Let the mixtures be combined in ratio 2:3. Mixture A has 12.5% water (87.5% milk), Mixture B has 10% water (90% milk). Combined water = (2×12.5 + 3×10)/(2+3) = 55/5 = 11%. Combined milk = (2×87.5 + 3×90)/5 = 445/5 = 89%. This gives milk:water = 89:11, which matches option C.

Multiple choice

A milkman buy some quantity of milk at Rs. 20 per litre and mix 5 litre of water in it. He sells the mixture at the rate of Rs 21 per litre and makes a profit of 40%. Find the quantity of mixture sold by milkman? एक दूधवाला दूध की कुछ मात्रा 20 रू प्रति लीटर की दर से खरीदता हैं और इस में 5 लीटर पानी मिला देता हैं |वह इस मिश्रण को 21 रू प्रति लीटर की दर से बेचता हैं और उसे 40% का लाभ होता हैं। ज्ञात कीजिये दूधवाले ने मिश्रण की कितनी मात्रा बेची?

  1. 10 litre 10 लीटर

  2. 15 litre 15 लीटर

  3. 18 litre 18 लीटर

  4. 20 litre 20 लीटर

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

Let quantity of milk = x liters. Cost price = 20x. Water added = 5 liters (free). Mixture quantity = x + 5. Selling price = 21(x+5). Profit = 40%, so 21(x+5) = 1.4 * 20x = 28x. Solving: 21x + 105 = 28x, 7x = 105, x = 15. Mixture sold = 15 + 5 = 20 liters.