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

In a solution of spirit and water, water is 35%. When 40 litres spirit is added then percentage of spirit in solution becomes 75%. Find the quantity of water in solution initially. एक स्प्रिट तथा पानी के विलयन में, पानी 35% है । जब 40 लीटर स्प्रिट मिलाया जाता है तो विलयन में स्प्रिट का प्रतिशत 75% हो गया। प्रारम्भिक मिश्रण में पानी की मात्रा ज्ञात कीजिये।

  1. 35 litres/लीटर

  2. 22.5 litres/लीटर

  3. 67.5 litres/लीटर

  4. 72 litres/लीटर
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let initial solution volume = x liters. Water = 0.35x, spirit = 0.65x. After adding 40 liters spirit: spirit/(x+40) = 0.75. So 0.65x + 40 = 0.75(x+40), giving 0.65x + 40 = 0.75x + 30, so 0.10x = 10, x = 100 liters. Initial water = 0.35 × 100 = 35 liters.

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.

  1. 12 litre

  2. 15 litre

  3. 18 litre

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

Let x litres water be added. Total mixture = (88 + x) litres. Value of milk before = 88 × 25 = 2200. After mixing, value per litre = 2200/(88+x) = 22. Solving: 2200 = 22(88+x), 100 = 88 + x, x = 12 litres. Option A is correct.

Multiple choice

When 15 liter water is added in a solution percentage of water in solution becomes 50% from 25%. Find initial quantity of solution.

  1. 60 liter

  2. 45 liter

  3. 30 liter

  4. 75 liter
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initially, the solution is 25% water and 75% solute. Let the initial quantity be x liters. After adding 15 liters of water, water becomes 50% of (x + 15). Solving (0.25x + 15) / (x + 15) = 0.50 gives x = 30 liters. The initial water was 7.5L (25% of 30L); adding 15L makes it 22.5L out of 45L total, which is exactly 50%.

Multiple choice

A person add 1.5 liter water in a solution so that concentrations of HCI in solution becomes 60% from 72% initially. Find the quantity of HCI in solution initially.

  1. 32.2 liter

  2. 5.4 liter

  3. 4.8 liter

  4. 7.2 liter

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

Adding water dilutes the HCl concentration from 72% to 60%. Let initial HCl = x liters. Initial solution = x/0.72 (since 72% is HCl). After adding 1.5L: total = x/0.72 + 1.5, and HCl still = x. So x / (x/0.72 + 1.5) = 0.60. Solving: x = 0.60(x/0.72 + 1.5), so x = x/1.2 + 0.9. Then x - x/1.2 = 0.9, so x(1 - 1/1.2) = 0.9, so x(0.2/1.2) = 0.9, so x = 0.9 × 6 = 5.4 liters.

Multiple choice

Ratio of volumes of A and B is 2:3 and ratio of milk and water in them is 5:1 and 3:1 respectively. If they are mixed together, what will be the ratio of milk and water in the resultant mixture?
  1. $17 : 13$
  2. $32 : 17$
  3. $21 : 17$
  4. $47 : 13$
  5. $None of these$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Container A: Volume=2x, milk:water=5:1, so milk=(5/6)×2x=5x/3, water=(1/6)×2x=x/3. Container B: Volume=3x, milk:water=3:1, so milk=(3/4)×3x=9x/4, water=x/4. Total milk=5x/3+9x/4=(20x+27x)/12=47x/12. Total water=x/3+x/4=7x/12. Ratio=(47x/12):(7x/12)=47:7. Wait, this gives 47:7, not 47:13. Let me recalculate: A: 2×5/6=10/6=5/3 milk, 2×1/6=2/6=1/3 water. B: 3×3/4=9/4 milk, 3×1/4=3/4 water. Total milk=5/3+9/4=(20+27)/12=47/12. Total water=1/3+3/4=(4+9)/12=13/12. Ratio=47:13. Yes, 47:13 is correct.

Multiple choice

Several liters of acid were drawn off from a 75 litre vessel, full of acid and equal amount of water was added. Again the same volume of the mixture was drawn off and replaced by water. As a result now, the vessel contained 48 litres of pure acid. How much of the acid was drawn off initially? एसिड से भरे 75 लीटर के एक पात्र से कुछ लीटर एसिड निकाला गया तथा समान मात्रा में पानी मिला दिया गया । फिर से मिश्रण से समान मात्रा निकाली गयी और पानी से बदल दी गयी। परिणाम स्वरुप अब पात्र में 48 लीटर शुद्ध एसिड बची है । प्रारम्भ में एसिड की कितनी मात्रा निकली गयी थी?

  1. 25

  2. 27

  3. 15

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

After two operations: acid remaining = 75(1 - x/75)² = 48. Solving: (1 - x/75)² = 48/75 = 16/25, so 1 - x/75 = 4/5, x/75 = 1/5, x = 15. Each operation removes the same fraction x/75 of the current acid content. This is a standard dilution problem with sequential removal.

Multiple choice

A container has capacity of 240 litres filled with pure milk from this 48 litre milk is taken out and replaced with water. This process is repeated two more times. Find the percentage reduction in quantity of milk.

  1. 42.2%

  2. 51.2%

  3. 48.8%

  4. 37.5%

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

Each operation removes 48L of the mixture and replaces it with water. After 1st operation: 192L milk remains (48L removed). After 2nd: milk proportion is 192/240 = 0.8, so 48L mixture contains 38.4L milk, leaving 153.6L. After 3rd: milk proportion is 153.6/240 = 0.64, so 48L contains 30.72L milk, leaving 122.88L. Reduction from 240L is 117.12L, which is 117.12/240 × 100 = 48.8%.

Multiple choice

A solution has 240 liter of pure milk. From this solution 30 liter milk is taken out and replaced with water. This process is repeated one more time. Find the ratio of milk and water in resultant solution. एक विलयन में 240 लीटर शुद्ध दूध है। इस विलयन से 30 मीटर दूध निकाला जाता है और पानी से बदल दिया जाता है। इस प्रक्रिया को एक बार और दोहराया जाता है। परिणामी विलयन में दूध और पानी का अनुपात ज्ञात कीजिये।

  1. 9 : 8

  2. 49 : 15

  3. 64 : 49

  4. 8 : 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Starting with 240L pure milk. After first replacement: milk = 240 × (210/240) = 210L. After second replacement: milk = 210 × (210/240) = 183.75L. Water = 240 - 183.75 = 56.25L. Ratio milk:water = 183.75:56.25 = 49:15. Option B is correct.

Multiple choice

Dherendra purchased two different kinds of alcohol. In the first mixture the ratio of alcohol to water is 7 : 9 and in the second mixture it is 3 : 5. If he mixes the two given mixtures and makes a third mixture in which the ratio of alcohol to water is 5 : 7, find the quantity of the first mixture that is required to make 93 litre of the third kind of mixture is :

  1. 31 litre

  2. 27 litre

  3. 62 litre

  4. 33 litre

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

Mixture 1 has 7/16 alcohol (43.75%), Mixture 2 has 3/8 alcohol (37.5%), Target has 5/12 alcohol (41.67%). Using alligation: (41.67-37.5):(43.75-41.67) = 2:1. So 62 litres of first mixture and 31 litres of second give 93 litres of third.

Multiple choice

From a can full of milk, 10 liters of milk is taken out and is replaced with water and this operation is repeated one more time. If the capacity of the can is 50 liters, what is the ratio of the water and milk in the can after these operations? एक दूध से पूरे भरे हुए पात्र से, 10 लीटर दूध निकाला गया और पानी से विस्थापित कर दिया गया और यह प्रक्रिया एक बार और की गयी। यदि पात्र की धारिता 50 लीटर है, इन प्रक्रिया के बाद पात्र में दूध और पानी का अनुपात क्या है ?

  1. 9 : 16

  2. 16 : 9

  3. 8 : 12

  4. 12 : 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial: 50L milk. After first operation: 40L milk + 10L water. After second operation: removing 10L of mixture (proportionally 8L milk, 2L water) and adding 10L water gives 32L milk + 18L water. The milk:water ratio is 32:18 = 16:9. Option A reverses the ratio. Options C and D are incorrect ratios.

Multiple choice

Mixture A contains 25% 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 7:1.

  1. 1:2

  2. 1:3

  3. 2:3

  4. 1:4

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

Let the milk ratio in A and B be 75% and 90% respectively (since water is 25% and 10%). We need final mixture with milk:water = 7:1, meaning milk is 7/8 = 87.5%. Using allegation: (90 - 87.5) : (87.5 - 75) = 2.5 : 12.5 = 1:5. So A:B = 1:5.

Multiple choice

In a solution water is 45%. When 18 liters more water is added the new concentration of water becomes 60%. Find the initial quantity of water in the solution. एक विलयन में 45% पानी है। जब और 18 लीटर पानी मिलाया जाता है तो पानी की नई सान्द्रता 60% हो जाती है। विलयन में पानी की प्रारंभिक मात्रा ज्ञात कीजिये।

  1. 36 liter/लीटर

  2. 27 liter/लीटर

  3. 25.8 liter/लीटर

  4. 21.6 liter/लीटर
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Set up the equation based on water amounts. Let the initial total solution be T liters. Water increases from 45% of T to 60% of (T+18). Solving: 0.45T + 18 = 0.60(T+18) gives T = 48 L, so initial water = 0.45 × 48 = 21.6 L.

Multiple choice

From the 150 liters of a chemical solution, 15 liters of chemical solution is taken out and after it, 15 liters of water is added to the rest amount of chemical solution. Again 15 liters of chemical solution and water is drawn out and it was replaced by 15 liters of water. If this process is continued similarly for the third time, the amount of chemical solution left after the third replacement.

  1. 98.25 litres

  2. 92.4 litres

  3. 109.35 litres

  4. 90.75 litres

  5. 115.5 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Each replacement keeps 135/150 = 0.9 of the chemical solution. After 3 replacements: 150 × (0.9)³ = 150 × 0.729 = 109.35 litres of the original chemical remains.

Multiple choice

The ratio of spirit and water in two mixtures of 24 litre and 39 litre is 2 : 1 and 7 : 6 respectively. Both the mixtures are mixed together. Now the ratio of the spirit and water in the new mixture is-

  1. 37 : 26

  2. 37 : 28

  3. 26 : 37

  4. 28 : 37
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The calculation is correct. First mixture: 24L with spirit:water = 2:1 gives spirit = 16L, water = 8L. Second mixture: 39L with spirit:water = 7:6 gives spirit = 21L, water = 18L. Combined: spirit = 37L, water = 26L. Ratio = 37:26. Option B (37:28) would be incorrect.

Multiple choice

Two vessels of capacity 10 litres and 15 litres are filled with a mixture of milk and water. Vessel of capacity 10 litres contains 75% of milk while the other of capacity 15 litres contains 70% of water. The vessels are emptied into a large vessel of capacity 28 litres whose remaining part is filled with milk. Find the ratio of milk and water respectively in the large vessel.
  1. $17 : 11$
  2. $13 : 15$
  3. $11 : 13$
  4. $15 : 13$
  5. $11 : 17$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Vessel 1 (10L) has 75% milk = 7.5L milk, 2.5L water. Vessel 2 (15L) has 70% water = 10.5L water, 4.5L milk. Total milk = 12L, total water = 13L. The 28L vessel needs 3L more milk to fill completely, giving final ratio of 15:13 milk to water. Option A is incorrect as it reverses the ratio. Options B and C have incorrect values.