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 20% gain is made by selling the mixture of two types of ghee at Rs. 480 per kg. If the ghee costing Rs. 610 per kg was mixed with 126 kg of the other, how many kilograms of the former was mixed?

  1. 23 kg.

  2. 25 kg.

  3. 30 kg.

  4. 32 kg.

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

The mixture is sold at Rs. 480/kg with a 20% gain, so the cost price of the mixture is 480/1.2 = Rs. 400/kg. Let x kg be the quantity of Rs. 610/kg ghee and 126 kg be the quantity of the other ghee costing Rs. C/kg. The equation is (610x + 126C)/(x + 126) = 400, which simplifies to 210x = 126(400 - C). Since we don't know the cost C of the other ghee, we cannot find a unique value for x. The problem is underspecified.

Multiple choice

Sri Ram bought 60 kg. of wheat at Rs. 14.50 per kg. and 25 kg. at Rs. 15.10 per kg. He mixed them together. At what rate should he sell the mixture to earn 10% profit? (approx)

  1. Rs. 22

  2. Rs. 25

  3. Rs. 24

  4. Rs. 16

  5. Rs. 30
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total cost = (60 × 14.50) + (25 × 15.10) = 870 + 377.50 = 1247.50. Total kg = 85. Cost per kg = 1247.50/85 ≈ 14.68. For 10% profit: SP = 14.68 × 1.10 ≈ 16.15, which rounds to approximately Rs. 16. Option D is correct. Options like 22, 25, 24, 30 are too high for just 10% profit.

Multiple choice

A chemical solution contains 30% water and 70% Alkali. What quantity of water should be added to 6 litres of solution so that the water content became 40%? (In litre)

  1. 5

  2. 3

  3. 1

  4. 2

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

Initial solution: 6 litres with 30% water = 1.8 litres water, 70% alkali = 4.2 litres alkali. Let x litres of water be added. New total volume = 6 + x litres. Water content becomes (1.8 + x) litres. We want water to be 40%: (1.8 + x)/(6 + x) = 0.4. Solving: 1.8 + x = 0.4(6 + x) = 2.4 + 0.4x. So x - 0.4x = 2.4 - 1.8, giving 0.6x = 0.6, therefore x = 1 litre. Adding 1 litre water makes the solution 7 litres with 2.8 litres water = 40%.

Multiple choice

There are two mixture of honey and water, the quantity of honey in them being 25% and 75% of the mixture. If 2 gallons of the first are mixed with three gallons of the second, what will be the ratio of honey to water in the new mixture?

  1. 47%

  2. 55%

  3. 59%

  4. 60%

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

First mixture: 25% honey means 0.25 × 2 = 0.5 gallons honey and 1.5 gallons water. Second mixture: 75% honey means 0.75 × 3 = 2.25 gallons honey and 0.75 gallons water. Combined: 2.75 gallons honey and 2.25 gallons water. Total mixture = 5 gallons. Percentage honey = (2.75/5) × 100 = 55%.

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?

  1. 3.3 liters

  2. 3 liters

  3. 2.8 liters

  4. 2 liters

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

In 70 liters of mixture, water = 10% of 70 = 7 liters, alcohol = 63 liters. Let x liters of water be added. New mixture volume = 70 + x liters. Water content = 7 + x liters. Given: (7 + x)/(70 + x) = 12.5% = 0.125. Solving: 7 + x = 0.125(70 + x), 7 + x = 8.75 + 0.125x, 0.875x = 1.75, x = 2 liters.

Multiple choice

A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?

  1. 29.16 liters

  2. 30.22 liters

  3. 32.16 liters
    1. 34 liters

  5. 35.33 liters
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

After each operation, the milk quantity reduces by factor of (36/40) = 0.9. Starting with 40L, after 3 operations: 40 × 0.9³ = 40 × 0.729 = 29.16L. Option D (34.34) has a typo and should be 29.16.

Multiple choice

In a 150-litre mixture of milk and water, the percentage of milk is 84%. How much water should be added so that the percentage of milk becomes 52.5%?

  1. 50 liter

  2. 60 liter

  3. 75 liter

  4. 90 liter

  5. 100 liter
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In 150 litres, milk = 84% of 150 = 126 litres. After adding x litres water, total = 150 + x litres. Milk stays 126 litres. New percentage: 126/(150 + x) = 52.5% = 0.525. Solving: 126 = 0.525(150 + x), x = 90 litres.

Multiple choice

In a mixture of milk and water of volume 30 litres the ratio of milk and water is 7:3. How much quantity of water is to be added to the mixture to make the ratio of milk and water 1:2?

  1. 28 litres

  2. 33 litres

  3. 30 litres

  4. 24 litres

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

In 30L mixture, milk=21L (7/10 of 30), water=9L (3/10 of 30). Let x liters water be added. New ratio: 21/(9+x)=1/2. Cross-multiply: 42=9+x, so x=33 liters. Option B is correct. Verify: final water=9+33=42L, ratio 21:42=1:2.

Multiple choice

In a mixture of 42 kg. , two type of rice A & B are mixed in a ratio of 4 : 3. If there was removed x kg. from both varieties then ratio becomes 7 : 5 what is the value of x.

  1. 3 kg

  2. 5 kg

  3. 6 kg

  4. 7 kg

  5. 10 kg
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total mixture = 42 kg in ratio 4:3. Initial quantities: A = (4/7) × 42 = 24 kg, B = (3/7) × 42 = 18 kg. After removing x kg from each: (24-x)/(18-x) = 7/5. Cross-multiplying: 5(24-x) = 7(18-x), so 120-5x = 126-7x, which gives 2x = 6, so x = 3 kg. Verifying: (21)/(15) = 7/5 ✓.

Multiple choice

The milk and water in a mixture are in the ratio 7 : 5. When 15 litres of water are added to it, the ratio of milk and water in the new mixture becomes 7 : 8. The total quantity of water in the new mixture is :

  1. 35 litres

  2. 40 litres

  3. 60 litres

  4. 96 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let initial quantities be 7x milk and 5x water. After adding 15 litres water, new water is 5x + 15. New ratio 7:8 gives 7x/(5x+15) = 7/8, so 8(7x) = 7(5x+15), meaning 56x = 35x + 105, thus 21x = 105 and x = 5. New water = 5(5) + 15 = 25 + 15 = 40 litres.

Multiple choice

two containers of equal capacity are full of a mixture of oil and water. In the first, the ratio of oil to water is 4 : 7 and in the second it is 7 : 11. Now both the mixtures are mixed together in a container. What is the resulting ratio of oil to water?

  1. 149 : 247

  2. 249 : 147

  3. 247 : 149

  4. 142 : 147

  5. 149 : 147
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Container 1: ratio 4:7 means oil = 4/(4+7) = 4/11, water = 7/11. Container 2: ratio 7:11 means oil = 7/18, water = 11/18. Taking equal capacity (LCM = 198), Container 1: oil = 4/11 × 198 = 72, water = 126. Container 2: oil = 7/18 × 198 = 77, water = 121. Combined: oil = 72+77 = 149, water = 126+121 = 247. Ratio = 149:247.

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:

  1. 8 liter

  2. 10 liter

  3. 12 liter

  4. 15 liter

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

Let initial milk = x liters. After first replacement: milk = x(1 - 6/x). After second: milk = x(1 - 6/x)² = 8/18 = 4/9 of mixture. So (1 - 6/x)² = 4/9, meaning 1 - 6/x = 2/3 (positive root since 6/x < 1). Thus 6/x = 1/3, so x = 18 liters. Final milk:water ratio is 8:10 which simplifies to 4:5, confirming the calculation.