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

Two metals 'X' and 'Y' are to be used for making two different alloys. If the ratio (by weight) of 'X' and 'Y' in the first alloy is 6 : 5 and that in the second alloy is 7 : 13, how many kilograms of metal 'X' must be melted along with 11 kg of the first alloy and 20 kg of the second, so as to produce a new alloy containing 40% of metal 'Y'?

  1. 11 kg

  2. 13 kg

  3. 14 kg

  4. 16 kg

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

First alloy: 11kg total, X:Y = 6:5 (6kg X, 5kg Y). Second alloy: 20kg total, X:Y = 7:13 (7kg X, 13kg Y). Total X = 6 + 7 + m, Total Y = 5 + 13 = 18. New alloy contains 40% Y, so 60% X. 18 is 40% of total mass, so total mass = 45kg. X = 0.6 * 45 = 27kg. 13 + m = 27, so m = 14.

Multiple choice

Two jars contain mixtures of wine and brandy in the ratio 3 : 1 and 5 : 4, respectively. If some content is to be taken out from each jar, what volume should be taken out from the first, so as to fill up a 72 litre can with wine and brandy in the ratio 1 : 1?

  1. 18

  2. 36

  3. 40

  4. Not possible

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

This is a mixture problem. You cannot determine the volume taken from each jar to get a specific ratio in a 72L can without knowing the total volume available or the specific proportions of the final mixture relative to the initial ones. It is mathematically underspecified.

Multiple choice

How many litres of a mixture in an 80-litre bottle, full of 80% concentrated milk, will have to be replaced with water to make the resultant mixture 60% concentrated?

  1. 10 litres

  2. 15 litres

  3. 20 litres

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

Let x be the amount replaced. The amount of milk initially is 0.8 * 80 = 64 litres. After replacing x litres with water, the remaining milk is 64 - 0.8x. We want this to be 60% of 80, which is 48 litres. So, 64 - 0.8x = 48, which gives 0.8x = 16, so x = 20.

Multiple choice

A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds 25 litres water to replenish the quantity that he has sold. What is the current proportion of water to milk?

  1. 2 : 3

  2. 1 : 2

  3. 1 : 3

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

Initial mixture: 80L milk, 20L water. After selling 1/4 (25L total), 75L remains (60L milk, 15L water). Adding 25L water results in 60L milk and 40L water. The ratio of water to milk is 40:60, which simplifies to 2:3.

Multiple choice

Two tins A and B contain mixtures of wheat and rice. In A, the weights of wheat and rice are in the ratio 2 : 3 and in B, they are in the ratio 3 : 7. What quantities (in kg) must be taken from A and B to form a mixture containing 5 kg of wheat and 11 kg of rice?

  1. 3 kg from A, 13 kg from B

  2. 8 kg from A, 8 kg from B

  3. 2 kg from A, 14 kg from B

  4. 6 kg from A, 10 kg from B

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

Let x be the amount from A and y be the amount from B. The wheat content is (2/5)x + (3/10)y = 5 and rice content is (3/5)x + (7/10)y = 11. Solving this system of linear equations yields x = 2 and y = 14.

Multiple choice

Milk and water are mixed in a vessel A in the ratio 3:2 and in vessel B in the ratio 3:1. What quantities should be taken from the vessels to have a new mixture consisting of 5 kg of milk and 2 kg of water?

  1. 2 kg, 5 kg

  2. 1.666 kg, 5.334 kg

  3. 2.666 kg, 4.334 kg

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

Let x be the amount from vessel A (3/5 milk, 2/5 water) and y be the amount from vessel B (3/4 milk, 1/4 water). We need 3/5x + 3/4y = 5 and 2/5x + 1/4y = 2. Solving this system: 0.6x + 0.75y = 5 and 0.4x + 0.25y = 2. Multiplying the second by 3 gives 1.2x + 0.75y = 6. Subtracting the first from this gives 0.6x = 1, so x = 1.666 kg. Then y = 5.334 kg.

Multiple choice

In two types of stainless steels, the ratios of chromium to steel are 2 : 11 and 5 : 21. In what proportion should the two types be mixed so that the ratio of chromium to steel in the new type becomes 7 : 32?

  1. 2 : 3

  2. 3 : 4

  3. 1 : 2

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

Use alligation on the chromium fraction. Type 1: 2/13. Type 2: 5/26. Target: 7/39. (7/39 - 5/26) / (2/13 - 7/39) = ((14-15)/78) / ((6-7)/39) = (-1/78) / (-1/39) = 39/78 = 1/2.

Multiple choice

A vessel is full of a mixture of liquor and water with 18% liquor. Eight litres are drawn of and then the vessel is filled with water. How much does the vessel hold if the liquor is now 15%?

  1. 45 litres

  2. 48 litres

  3. 49 litres

  4. 50 litres

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

Let V be the volume. After removing 8 liters and replacing with water, the amount of liquor remaining is 0.82 * (V - 8). We set this equal to 0.15 * V. Solving 0.82V - 6.56 = 0.15V gives 0.67V = 6.56, which does not yield an integer. Checking the logic: the amount of liquor is 18% of V, then 8 liters are removed (containing 18% liquor), so 0.18 * (V - 8) + 0 = 0.15 * V. 0.18V - 1.44 = 0.15V, so 0.03V = 1.44, V = 48.

Multiple choice

A bag contains 600 pens of brand A and 1200 pens of brand B. If 12% of brand A pens and 25% of brand B pens are removed, what is the approximate percentage of total pens removed from the bag?

  1. 21%

  2. 30%

  3. 40%

  4. 47%

  5. 48%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Brand A removed: 12% of 600 = 72. Brand B removed: 25% of 1200 = 300. Total removed = 72 + 300 = 372. Total pens = 600 + 1200 = 1800. Percentage removed = (372 / 1800) * 100 = 20.66%, which is approximately 21%.

Multiple choice

A can contains a mixture of two liquids A and B in the ratio of 3 : 2. When 5 litres of the mixture is drawn and replaced with liquid B, the ratio of A to B becomes 1 : 1. What quantity of liquid A was there in the can initially?

  1. 25 litres

  2. 18 litres

  3. 12 litres

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

Initial ratio A:B = 3:2. Let A = 3x, B = 2x. Total = 5x. Draw 5L: A removed = 3/5 * 5 = 3, B removed = 2/5 * 5 = 2. Remaining: A = 3x - 3, B = 2x - 2 + 5 = 2x + 3. Ratio 1:1 implies 3x - 3 = 2x + 3, so x = 6. Initial A = 3 * 6 = 18.

Multiple choice

How much skimmed milk (in kg) containing 0.1% fat should be added to 500 kg of cream containing 50% fat to produce standardised cream containing 36% fat?

  1. 140

  2. 165

  3. 195

  4. 210
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the alligation method: Cream (50%) and Skimmed milk (0.1%) mixed to get 36%. Differences: |50 - 36| = 14 and |36 - 0.1| = 35.9. Ratio of cream to milk = 35.9 : 14. If 35.9 units = 500 kg, 1 unit = 13.927. Milk = 14 * 13.927 = 194.98, which rounds to 195 kg.