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 vessel contains a mixture of spirit & water. Spirit is 18\%. 8 litres of the mixture is taken out of the vessel, which is again filled with water. If the present percentage of spirit is 15\%, find the quantity of the mixture in the vessel?

  1. 80

  2. 70

  3. 48

  4. 75

  5. 60
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial quantity be x liters. Initial spirit = 0.18x. After removing 8 liters of mixture: spirit removed = 0.18 × 8 = 1.44 liters. Remaining spirit = 0.18x - 1.44. This is now 15% of x (since total returns to x after refilling with water): 0.15x = 0.18x - 1.44. Solving: 0.03x = 1.44, so x = 48 liters. Option C (48) is correct.

Multiple choice

Several liters of milk are taken out from a 112 liters’ vessels full of milk and replace with water. This process repeated another one time. As a result, 63 liters’ milk is remaining on that vessels. How much of milk was taken out initially?

  1. 24 liter

  2. 28 liter

  3. 32 liter

  4. 23 liter
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the replacement formula twice: remaining milk = 112(1 - x/112)² = 63. Solving: (1 - x/112)² = 63/112 = 9/16, so 1 - x/112 = 3/4, giving x/112 = 1/4 and x = 28 liters. Option B is correct. This is the milk removed in each operation.

Multiple choice

A mixture of 60 litres contains milk and water in ratio 3 : 1. How many litres of mixture must be replaced with water so that the new ratio is 1 : 1?

  1. 10 litres

  2. 20 litres

  3. 15 litres

  4. 30 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture: 60L with milk:water = 3:1, so milk = 45L, water = 15L. Let x litres be replaced with water. After removing x litres (keeping ratio 3:1), milk removed = 3x/4, water removed = x/4. Remaining: milk = 45 - 3x/4, water = 15 - x/4. Adding x litres water: milk = 45 - 3x/4, water = 15 - x/4 + x = 15 + 3x/4. New ratio 1:1 means milk = water, so 45 - 3x/4 = 15 + 3x/4. Solving: 30 = 6x/4, so x = 20 litres.

Multiple choice

A mixture contains milk and water in the ratio 5 : 3. If 16 litres of mixture is replaced by 16 litres of water, then the ratio becomes 3 : 5. How many litres of milk was there in the mixture initially.

  1. 8 litre

  2. 16 litre

  3. 24 litre

  4. 25 litre

  5. 40 litre
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial milk:water = 5:3, so milk = 5x, water = 3x, total = 8x. 16 litres removed contains milk = 5x/8x × 16 = 10 litres, water = 3x/8x × 16 = 6 litres. After removal: milk = 5x-10, water = 3x-6. Adding 16 litres water: milk = 5x-10, water = 3x-6+16 = 3x+10. New ratio (5x-10):(3x+10) = 3:5. Cross-multiplying: 5(5x-10) = 3(3x+10), 25x-50 = 9x+30, 16x = 80, x = 5. Initial milk = 5x = 5×5 = 25 litres. Options A, B, C, and E are incorrect.

Multiple choice

60 litres of mixture, the ratio of milk and water is 3 : 7 if the ratio of milk and water is to be made 2 : 5 then the amount of water further added is -

  1. 5 ltr.

  2. 2.5 ltr.

  3. 2 ltr.

  4. 3 ltr.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial mixture: 60L with milk:water = 3:7, so milk = 18L, water = 42L. After adding x liters of water, total water = 42+x L. New ratio milk:water = 2:5, so 18/(42+x) = 2/5. Cross-multiplying: 90 = 84 + 2x, so 2x = 6, and x = 3 liters. Adding 3L water gives 18:45 = 2:5, which satisfies the required ratio.

Multiple choice

An alloy X consists of 95\% copper and 5\% brass and another alloy consists of 91\% copper and 9\% brass then in which ratio both of them mixed such that it consists 6\% brass?

  1. 3:4

  2. 4:3

  3. 1:3

  4. 3:1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the ratio be x:y. Alloy X has 5% brass, Alloy Y has 9% brass. We want 6% brass. Using alligation: |5-6| : |9-6| = 1 : 3. So ratio of X:Y is 3:1 (since the part with higher brass gets lower weight). Verify: (3×5 + 1×9) ÷ 4 = 24÷4 = 6%. Option D is correct.

Multiple choice

Pure milk costs Rs. 12 per litre. A milkman add some water to 16 litres of pure milk and sells the mixture at Rs. 10 per litre by making 25% profit. How many litres of water does he added?

  1. 5 litres

  2. 6 litres

  3. 8 litres

  4. 12 litres

  5. 18 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Cost price of 16 litres milk = 16 × 12 = Rs. 192. With 25% profit, selling price = 192 × 1.25 = Rs. 240. At Rs. 10/litre, total mixture = 240/10 = 24 litres. Water added = 24 - 16 = 8 litres. Option A (5 litres) and B (6 litres) give incorrect total volumes. Option D (12 litres) would mean 28 litres sold for Rs. 280, which is 45.8% profit, not 25%. Option E (18 litres) is too high.

Multiple choice

Two vessels contain milk and water mixture in the ratio (7 : 3) and (4 : 1) respectively. The ratio in which these two mixtures should be mixed to get a new mixture containing 75% milk?

  1. 1 : 1

  2. 2 : 1

  3. 3 : 2

  4. 5 : 1

  5. 1 : 4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Use the alligation method. First mixture: milk ratio 7:3 = 7/10 = 70% milk. Second mixture: milk ratio 4:1 = 4/5 = 80% milk. Target: 75% milk. Using alligation, the differences are 80-75=5 and 75-70=5. The ratio is 5:5 = 1:1. Therefore equal quantities (1:1) of both mixtures should be combined.

Multiple choice

From a container having pure milk, 10% is replaced by water. This process was repeated thrice. At the time of third operation, the milk remained in the container is:

  1. 70% pure

  2. 90% pure

  3. 80% pure

  4. 72.90% pure
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This is a successive replacement problem. Each operation replaces 10% of the mixture with water, so 90% of the previous mixture remains. After three operations: Remaining milk = 100% × (0.90)^3 = 100% × 0.729 = 72.9%. Option D (72.90% pure) is correct.

Multiple choice

Jaydeep purchased 25 kg of rice at the rate of Rs. 16.50 per kg and 35 kg of rice at the rate of 24.50 per kg. He mixed the two and sold the mixture. Approximately at what rate per kg did he sell hte mixture to make 25% profit?

  1. Rs. 31.50

  2. Rs. 22.50

  3. Rs. 25.50

  4. Rs. 26.50
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total cost = (25 × 16.50) + (35 × 24.50) = 412.50 + 857.50 = 1270. Total kg = 60. CP per kg = 1270/60 ≈ 21.17. For 25% profit, SP = 1.25 × 21.17 ≈ 26.46. The closest option is Rs. 26.50 per kg. The profit calculation follows from the weighted average cost price.