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 mixture of 240 lt. water is 20% and rest is Milk. What quantity of mixture should be taken out and replaced with water so that water becomes 40%.

  1. 40 liter

  2. 60 liter

  3. 45 liter

  4. 80 liter

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

Initial water: 20% of 240L = 48L. When 60L removed, water removed = 20% of 60L = 12L, remaining water = 36L. After adding 60L water, total water = 96L. Final mixture = 240L, water percentage = 96/240 × 100 = 40%. This uses the replacement formula: amount replaced = (target% - initial%) × total / target%.

Multiple choice

A shopkeeper has three varieties of pulse costing 72 Rs/Kg, 60 Rs/Kg and 90 Rs/Kg. Find the possible ratio in which he should mix these three pulses to get a mixture worth 80 Rs/Kg.

  1. 4:3:2

  2. 12:7:15

  3. 5:1:6

  4. 21:7:29

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

To get a mixture worth 80 Rs/Kg from three varieties costing 72, 60, and 90 Rs/Kg, we need to find a ratio where the weighted average equals 80. Using alligation or verification: (72×5 + 60×1 + 90×6) ÷ (5+1+6) = 960 ÷ 12 = 80. Option A (4:3:2) gives 77.5 Rs/Kg, Option B (12:7:15) gives 76 Rs/Kg, and Option D (21:7:29) gives 79.2 Rs/Kg - none of these work.

Multiple choice

Ratio of volumes of three containers containing milk and water is (4:3:6) and the ratio of milk and water in these containers is (2 : 1, 4 : 1) and (1 : 2) respectively. If all three containers are mixed together what will be the ratio of milk and water in resultant mixture?
  1. $19 : 26$
  2. $26 : 19$
  3. $27 : 14$
  4. $35 : 17$

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

Let the three containers have volumes 4x, 3x, and 6x respectively. Container 1 (4x): milk = (2/3)×4x = 8x/3, water = (1/3)×4x = 4x/3. Container 2 (3x): milk = (4/5)×3x = 12x/5, water = (1/5)×3x = 3x/5. Container 3 (6x): milk = (1/3)×6x = 2x, water = (2/3)×6x = 4x. Total milk = 8x/3 + 12x/5 + 2x = (40x + 36x + 30x)/15 = 106x/15. Total water = 4x/3 + 3x/5 + 4x = (20x + 9x + 60x)/15 = 89x/15. Ratio = 106x/15 : 89x/15 = 106:89 = 26:19 (milk:water).

Multiple choice

In a mixture of 240 litres of milk and water, water is 30%. Find the quantity of water that should be added to make the percentage of water in mixture 40%.

  1. 40 litres

  2. 45 litres

  3. 30 litres

  4. 60 litres

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

In 240 litres, water is 30% = 72 litres, milk is 168 litres. Let x litres of water be added. New mixture = (240 + x) litres with 40% water. So: (72 + x) / (240 + x) = 0.4. Solving: 72 + x = 96 + 0.4x, which gives 0.6x = 24, so x = 40 litres.

Multiple choice

The proportion of milk and water in three vessels is 2 : 1, 3 : 2 and 5 : 3. A mixture containing equal quantities of all three samples is made. The ratio of water and milk in the mixture is- तीन पात्र में दूध और पानी का अनुपात 2 : 1 , 3 : 2 और 5 : 3 है। तीनों पात्रों से समान मात्रा लेकर एक मिश्रण बनाया गया है। मिश्रण में पानी और दूध का अनुपात है-

  1. 137 : 233

  2. 227 : 133

  3. 133 : 237

  4. 133 : 227
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Taking equal quantities means each ratio contributes proportionally. Total milk = (2/3 + 3/5 + 5/8) = 133/120 parts. Total water = (1/3 + 2/5 + 3/8) = 67/120 parts. The ratio water:milk = 67:120 = 133:240. However, the question asks for water:milk ratio in the mixture made from equal quantities, so we must recalculate: For equal quantities (say 24 units each), milk total = 16+14.4+15 = 45.4, water total = 8+9.6+9 = 26.6. The simplified ratio is approximately 133:227.

Multiple choice

In two types of vessel ratio of milk and water are 8 : 3 and 15 : 7 respecetively. The ratio in which these two types of mixtures should be mixed, so that the ratio of milk and water in this new mixture become 5 : 2 is-

  1. 5 : 2

  2. 3 : 2

  3. 7 : 4

  4. 2 : 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using alligation: Vessel 1 has milk fraction 8/11 = 16/22, Vessel 2 has 15/22, target is 5/7 = 55/77 ≈ 0.714. The milk fractions are 8/11 ≈ 0.727 and 15/22 ≈ 0.682. By alligation method, the ratio is (55/77 - 15/22):(8/11 - 55/77) = (10/77):(4/77) = 5:2. This matches option A exactly.

Multiple choice

A jar contained a mixture of milk and water in the ratio 4 : 1 when 10 litres of the mixture was taken out and 10 litres of water was poured into the jar, this ratio became 2 : 3. The quantity of milk contained in the jar initially was- एक पात्र में दूध और पानी का अनुपात 4: 1 है। जब 10 लीटर मिश्रण निकाला जाता है और 10 लीटर पानी पात्र में डाला जाता है, यह अनुपात 2: 3 हो जाता है। प्रारम्भिक अवस्था में पात्र में दूध की मात्रा थी-

  1. 4 litres/लीटर

  2. 8 litres/लीटर

  3. 16 litres/लीटर

  4. 40 litres/लीटर
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial quantities be 4x and x (milk:water). After removing 10L mixture, we remove 8L milk and 2L water (maintaining 4:1 ratio). Adding 10L water gives (4x-8):(x+8) = 2:3. Solving: 3(4x-8) = 2(x+8), so 12x-24 = 2x+16, giving x=4. Initial milk = 4x = 16L. Option A (4L) would be just water, B (8L) is the water amount, and D (40L) would give wrong final ratio.

Multiple choice

If 10 litres of water is removed from a container and replaced with wine, the ratio of water to wine is 5 : 2. How much water was there originally?

  1. 35 litre

  2. 25 litre

  3. 20 litre

  4. 15 litre
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If original water was W, after removing 10L: W-10 water, 10 wine added. Ratio (W-10):10 = 5:2. So (W-10)/10 = 5/2, W-10 = 25, W = 35. Original water was 35 litres. Option B (25) is the water after removal, not original. Option C (20) comes from mis-solving the ratio.

Multiple choice

In two vessels ratio of milk and water is 5:3 and 5:7 respectively. They are mixed together in 5:4 . Find the ratio of milk and water in the final mixture.
  1. $108:101$
  2. $107:103$
  3. $115:101$
  4. $101:95$
  5. $None of these$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First find the fraction of milk and water in each vessel. Vessel 1 (5:3) has milk = 5/8, water = 3/8. Vessel 2 (5:7) has milk = 5/12, water = 7/12. When mixed in ratio 5:4, multiply each fraction by the mixing ratio and sum. Total milk = 5*(5/8) + 4*(5/12) = 115/24. Total water = 5*(3/8) + 4*(7/12) = 101/24. The ratio milk:water = 115:101.

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 more times find the quntity of water in container.

  1. 30 litre

  2. 28.8 litre

  3. 36.5 litre

  4. 45.5 litre

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

After each operation, milk remaining = Previous × (1 - 18/108) = Previous × (90/108) = Previous × (5/6). After 3 iterations: Milk = 108 × (5/6)³ = 108 × 125/216 = 62.5 L. Water added = Total - Milk = 108 - 62.5 = 45.5 L.

Multiple choice

A perfume production company prepares perfume by mixing it with water. The new mixture of 340 litre contains perfume and water in the ratio 27 : 7. Later, the company decides to further liquify the mixture to form a new mixture containing perfume and water in the ratio 3 : 1. How much water must they have to add in the previous mixture?

  1. 20 litre

  2. 15 litre

  3. 10 litre

  4. 24 litre

  5. 30 litre
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In the initial 340L mixture with perfume:water = 27:7, perfume = (27/34) × 340 = 270L and water = (7/34) × 340 = 70L. To achieve the new ratio 3:1, we need water = 270/3 = 90L. Additional water required = 90 - 70 = 20L. Option A is correct.

Multiple choice

Ratio of volumes of two containers which are filled with mixture of syrup and water is 2: 3 and the ratio of syrup and water in each contains is (5 : 1) and (3 : 1) respectively. If both containers are mixed together what will be the ratio of syrup and water in resultant mixture?
  1. $45 : 19$
  2. $12 : 5$
  3. $47 : 13$
  4. $9 : 7$

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

Container 1 has syrup:water in 5:1 ratio with total volume 2x. So syrup = 5/6 × 2x = 5x/3, water = 1/6 × 2x = x/3. Container 2 has syrup:water in 3:1 ratio with total volume 3x. So syrup = 3/4 × 3x = 9x/4, water = 1/4 × 3x = 3x/4. Total syrup = 5x/3 + 9x/4 = (20x+27x)/12 = 47x/12. Total water = x/3 + 3x/4 = (4x+9x)/12 = 13x/12. Ratio of syrup:water = 47x/12 : 13x/12 = 47:13, which is option C.

Multiple choice

In box A ratio of milk and water is 3 : 1 and in box B ratio of milk and water is 3 : 5. When both box are mixed together ratio of milk and water becomes 5 : 3. Find the ratio of volume of box A and box B respectively.

  1. 1 : 2

  2. 3 : 2

  3. 2 : 3

  4. 2 : 1

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

Box A has milk:water = 3:1 (milk fraction 3/4). Box B has milk:water = 3:5 (milk fraction 3/8). When mixed, the ratio is 5:3 (milk fraction 5/8). Using alligation method: (5/8 - 3/8) : (3/4 - 5/8) = 2/8 : 1/8 = 2 : 1. So volume ratio A:B is 2:1. Option D is correct. Options A, B, C, E are incorrect.

Multiple choice

In a mixture of salt and water of volume 30 litres, the ratio of salt and water is 7 : 3. The quantity of water to be added to the mixture to make the ratio of salt and water 1 : 2 is- 30 लीटर आयतन वाले नमक और पानी के मिश्रण में, नमक और पानी का अनुपात 7 : 3 है। पानी की किस मात्रा को मिलाने पर नमक और और पानी का अनुपात 1 : 2 हो जायेगा?

  1. 30

  2. 32

  3. 33

  4. 35
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial mixture has salt:water = 7:3. Salt = 7/10 × 30 = 21 litres, Water = 3/10 × 30 = 9 litres. After adding y litres of water, new ratio is 21:(9+y) = 1:2. Cross-multiplying: 42 = 9 + y, so y = 33 litres.