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 jar contain a mixture of milk and water in the ratio 3 : 2. The volume of the contents is increased by 50% by adding water to it. From the resultant solution 30 L is withdrawn and then replaced with water. The resultant ratio of milk and water in the final solution is 3 : 7. Find the original volume of milk in the solution?

  1. 120

  2. 80

  3. 48

  4. 90

  5. 180
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let original solution be 5x (milk 3x, water 2x). After adding 50% water: 7.5x total (milk 3x, water 4.5x). Removing 30L leaves milk 3x-(12/7.5)x and water 4.5x-(18/7.5)x. Adding 30L water gives final ratio 3:7. Solving gives 3x=48L.

Multiple choice

From 5 litre of 20% solution of alcohol in water. 2 litres of solution is taken out and 2 litres water is added to it. The strength of the alcohol in new solution is :

  1. 12 %

  2. 15 %

  3. 17 %

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

Initial: 5L of 20% alcohol = 1L alcohol + 4L water. Removing 2L removes 0.4L alcohol (20% of 2L), leaving 0.6L alcohol in 3L solution. Adding 2L water gives 0.6L alcohol in 5L total. Strength = 0.6/5 = 0.12 = 12%. Key insight: removal is proportional to concentration.

Multiple choice

A solution contains 36% milk when 72 litre milk is poured in solution percentage of milk becomes 52%. Find the final quantity of solution. एक विलयन में 36% दूध है। जब 72 लीटर दूध विलयन में मिलाया जाता है दूध का प्रतिशत बढ़कर 52% हो जाता है विलयन की परिणामी मात्रा ज्ञात कीजिये।

  1. 144 liter/लीटर

  2. 188 liter/लीटर

  3. 248 liter/लीटर

  4. 288 liter/लीटर
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the initial solution quantity be x liters. Initial milk = 0.36x. After adding 72L milk: (0.36x + 72)/(x + 72) = 0.52. Solving: 0.36x + 72 = 0.52x + 37.44, so 0.16x = 34.56 and x = 216. Final quantity = 216 + 72 = 288L. Option D is correct.

Multiple choice

A mixture contains milk and water in the ratio 7:3 and another mixture of the same contains milk and water ratio 2:3. In what ratio should the mixtures be mixed in order to obtain a new mixture consisting of milk and water in the ratio 5:3? एक मिश्रण में दूध और पानी 7:3 के अनुपात में है और एक अन्य मिश्रण में दूध और पानी 2:3 के अनुपात में है। मिश्रण को किस अनुपात में मिलाना चाहिए ताकि एक ऐसा नया मिश्रण मिले जिसमें दूध और पानी 5:3 के अनुपात में है।

  1. 3 : 1

  2. 5 : 4

  3. 7 : 9

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

Let the mixtures be combined in ratio x:y. Milk from mixture 1 is (7/10)x, from mixture 2 is (2/5)y. Total milk = (7/10)x + (2/5)y. Total volume = x + y. We need milk:water = 5:3, so milk is 5/8 of total. Setting up: (7x/10 + 2y/5)/(x+y) = 5/8. Cross-multiplying: 8(7x/10 + 2y/5) = 5(x+y). Solving: 28x/10 + 16y/10 = 5x + 5y. This gives 28x + 16y = 50x + 50y, or -22x = 34y, which gives x:y = 3:1 approximately. Verification with x=3, y=1 gives milk fraction = (21/10 + 2/5)/4 = 23/40 = 0.575 = 5/8.

Multiple choice

A vessel contains a mixture of two liquid A and B is the ratio 3:4. Whe 7 liters of mixture are drawn off and the vessel is filled with 7 liter of A. Then the ratio of A and B become 16:19. How many litres of liquid B was contained by vessel initially? एक बर्तन दो द्रवों A और B के मिश्रण से भरा है। जिसमे A और B का अनुपात 3 : 4 है। यदि 7 लीटर A भर दिया गया । तो A और B का अनुपात 16 : 19 हो जाता है। तो ज्ञात कीजिए प्रारम्भ में B की मात्रा कितने लीटर थी?

  1. 60

  2. 80

  3. 140

  4. 65
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture has A:B = 3:4. Let quantities be 3x and 4x, total = 7x. When 7 liters drawn, proportion removed: A removed = 3x/7x × 7 = 3, B removed = 4x/7x × 7 = 4. Remaining: A = 3x - 3, B = 4x - 4. After adding 7 liters of A: new A = 3x - 3 + 7 = 3x + 4, new B = 4x - 4. New ratio A:B = (3x + 4):(4x - 4) = 16:19. Cross-multiplying: 19(3x + 4) = 16(4x - 4), giving 57x + 76 = 64x - 64, so 140 = 7x, x = 20. Initial B = 4x = 80 liters. This matches option B.

Multiple choice

In a solution water is 12.5\%. From this solution 50 litre is taken out and replaced with 30 litre water hence new percentage of water in solution becomes 20\%. Find the quantity of solution initially?

  1. 240 litre

  2. 175 litre

  3. 360 litre

  4. 300 litre

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

Let initial quantity be Q. Milk = 87.5% of Q. After removing 50L and adding 30L water, new quantity = Q - 20L. Milk remains 0.875Q - 43.75L. This equals 80% of (Q - 20L). So 0.875Q - 43.75 = 0.8Q - 16, giving 0.075Q = 27.75, so Q = 370L. Since 370L is not among options A-D, the answer is E (None of these).

Multiple choice

The ratio of milk and water in a vessel is 5:3. 6 litre water mixed in vessel then ratio of milk and water becomes 5:4 find the initial quantily of milk? एक बर्तन में दूध और पानी का अनुपात 5:3 है। बर्तन में 6 लीटर पानी मिलाने पर यह अनुपात 5:4 हो जाता है। दूध की मात्रा प्रारम्भिक मात्रा ज्ञात कीजिए?

  1. 24 litre/लीटर

  2. 30 litre/लीटर

  3. 26 liter/लीटर

  4. 54 litre/लीटर
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let milk=5x, water=3x. After adding 6L water: milk=5x, water=3x+6. New ratio 5x:(3x+6) = 5:4. Cross-multiplying: 20x = 15x+30, so 5x=30, x=6. Initial milk = 5×6 = 30L.

Multiple choice

How much water be added to 88 litres of milk so that the price of the mixture becomes Rs. 22 per litre. Given that price of the milk is Rs. 25 per litre. 88 लीटर दूध में कितना पानी मिलाया जाए जिससे मिश्रण का मूल्य 22 रुपए प्रति लीटर हो जाये। यह ज्ञात है कि दूध का मूल्य 25 रुपए प्रति लीटर है ।

  1. 12 litre/लीटर

  2. 15 litre/लीटर

  3. 18 litre/लीटर

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

Using alligation: milk cost Rs 25/L, target price Rs 22/L (effectively water at Rs 0/L). Ratio milk:water = (22-0):(25-22) = 22:3. For 88L milk, water = 88 × 3/22 = 12L. Total mixture = 100L at Rs 22/L.

Multiple choice

An alloy contains the Copper and Aluminium in the ratio of 7 : 4. While making the weapons from this alloy, 12% of the alloy gets destroyed. If there is 12 kg of aluminium in the weapon, then the weight of the alloy required will be ?

  1. 32.5 kg.

  2. 37.5 kg.

  3. 42.5 kg.

  4. 45 kg.

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

Alloy has Cu:Al = 7:4, so Al is 4/11 of total alloy. 12% is destroyed, so remaining is 88%. If 12 kg Al is in weapon: original Al needed = 12/0.88 = 13.636 kg. Since Al is 4/11 of total, total alloy = 13.636 × (11/4) = 37.5 kg. Option B is correct. Account for loss first, then use ratio.

Multiple choice

In three mixtures, water and milk is in the ratio of 1: 3, 2: 3 and 2:5 respectively. If all three mixtures are mixed in the ratio of 1: 2: 3 respectively, then what will be the ratio of water and spirit in the resulting mixture? तीन मिश्रणों में, पानी और दूध क्रमशः 1 : 3, 2 : 3 और 2 : 5 के अनुपात में है। यदि सभी तीन मिश्रण को क्रमशः 1 : 2 : 3 के अनुपात में मिश्रित किया जाए, तो परिणामस्वरूप प्राप्त मिश्रण में पानी और स्पिरिट का अनुपात कितना होगा?

  1. 137 : 537

  2. 25 : 63

  3. 89 : 191

  4. 55 : 87
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Mixture 1 (1:3): water=1/4, milk=3/4. Mixture 2 (2:3): water=2/5, milk=3/5. Mixture 3 (2:5): water=2/7, milk=5/7. Mixed in 1:2:3 ratio: Total water = 1*(1/4) + 2*(2/5) + 3*(2/7) = 1/4 + 4/5 + 6/7 = 267/140. Total milk = 1*(3/4) + 2*(3/5) + 3*(5/7) = 3/4 + 6/5 + 15/7 = 573/140. Ratio = 267:573 = 89:191.

Multiple choice

From a vessel containing 100 litre of wine, 10 litre are drawn out and an equal amount of water is added. From the mixture, 10 litre is again drawn out and same quantity of water is added. What is the final ratio of wine and water? 100 लीटर शराब से युक्त एक बर्तन से, 10 लीटर बाहर निकाला जाता है और बराबर मात्रा में पानी मिला दिया जाता है । मिश्रण से, 10 लीटर फिर से निकाला जाता है और बराबर मात्रा में पानी मिला दिया जाता है। शराब और पानी का परिणामी अनुपात क्या है?

  1. 91 : 9

  2. 81 : 19

  3. 80 : 20

  4. 90 : 10
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

After first replacement: wine = 100 - 10 = 90, water = 10. Ratio 90:10. When 10L drawn from mixture, wine removed = 10 × (90/100) = 9L, water removed = 10 × (10/100) = 1L. Remaining: wine = 90 - 9 = 81L, water = 10 - 1 = 9L. Adding 10L water: wine = 81L, water = 9 + 10 = 19L. Final ratio is 81:19. This uses mixture alligation principles.

Multiple choice

A container contains 450 litres of a mixture that contains 30\% of soda and the rest is water. If 45 litres of water is added to it then what is the ratio of soda and water in the new mixture?
  1. $2 : 3$
  2. $5 : 8$
  3. $3 : 5$
  4. $3 : 8$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The mixture initially has 450 liters with 30% soda (135 liters) and 70% water (315 liters). After adding 45 liters of water, we have 135 liters soda and 360 liters water. The ratio is 135:360, which simplifies to 3:8 (divide both by 45). Option D is correct. Options A (2:3), B (5:8), and C (3:5) don't match this calculation.

Multiple choice

A container contains 8500 litres of a mixture that contains 65\% of salt and rest is water. If 650 litres of water is added to it then what is the ratio of salt and water in the new mixture?
  1. $118 : 145$
  2. $221 : 145$
  3. $445 : 661$
  4. $661 : 445$

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

Initial salt = 8500 × 0.65 = 5525 litres. Initial water = 8500 - 5525 = 2975 litres. After adding 650 litres water: new water = 2975 + 650 = 3625 litres. Ratio salt:water = 5525 : 3625. Dividing by 25: 221 : 145.