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

Vessels A and B contain mixtures of milk and water in the ratio 4 : 5 and 5 : 1 respectively. In what ratio should the quantities of mixture be taken from vessels A and B to form a mixture in which the ratio of milk to water is 5 : 4?

  1. 2 : 5

  2. 4 : 3

  3. 5 : 2

  4. 6 : 3

  5. 8 : 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Use alligation on milk fractions. Vessel A: 4/9. Vessel B: 5/6. Target: 5/9. |5/6 - 5/9| = |15/18 - 10/18| = 5/18. |4/9 - 5/9| = 1/9 = 2/18. Ratio = (5/18) / (2/18) = 5:2.

Multiple choice

In what ratio should tea of first kind, costing Rs. 640 per kg, be mixed with tea of second kind, costing Rs. 500 per kg, so that the mixture gives a profit of 20% when sold at Rs. 648 per kg?

  1. First kind : Second kind = 1 : 2

  2. First kind : Second kind = 2 : 3

  3. First kind : Second kind = 3 : 2

  4. First kind : Second kind = 2 : 5

  5. First kind : Second kind = 4 : 5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Selling price = 648, profit = 20%. Cost price of mixture = 648 / 1.2 = 540. Using alligation: (640 - 540) / (540 - 500) = 100 / 40 = 2.5 = 5/2. The ratio is 2:5.

Multiple choice

The composition of a solution is 5% salt by weight. How many kg of fresh water must be mixed with 120 kg of the solution for the content of salt in the solution to be made 3%?

  1. 60 kg

  2. 70 kg

  3. 80 kg

  4. 90 kg

  5. 100 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The amount of salt remains constant. Initially, salt = 5% of 120 kg = 6 kg. Let x be the amount of water added. New total weight = 120 + x. We want 6 / (120 + x) = 3 / 100. Solving for x: 600 = 360 + 3x, so 3x = 240, x = 80 kg.

Multiple choice

In a mixture, there are 2 parts methane and 5 parts ethane. How much mixture (in litres) should we draw and replace with methane so that the mixture contains methane and ethane in the same amount?

  1. 2.1 litres

  2. 3.2 litres

  3. 4.1 litres

  4. 5.1 litres

  5. 6.1 litres
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the mixture be 2x and 5x. Total is 7x. Replacing a part 'y' of the mixture with methane changes the ratio to 1:1. Solving the resulting equation for y leads to 2.1 liters.

Multiple choice

Two containers X and Y contain chemical and water in the ratios of 4 : 3 and 2 : 3, respectively. Find the ratio in which the two solutions from X and Y should be mixed to obtain a new solution containing half chemical and half water.

  1. X : Y = 7 : 4

  2. X : Y = 7 : 5

  3. X : Y = 5 : 4

  4. X : Y = 7 : 6

  5. X : Y = 6 : 7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the method of alligation: Container X has 4/7 chemical, Container Y has 2/5 chemical, and the mixture needs 1/2 chemical. The differences are |4/7 - 1/2| = 1/14 and |2/5 - 1/2| = 1/10. The ratio is (1/10) : (1/14) = 14 : 10 = 7 : 5.

Multiple choice

A jar contains a mixture of two liquids A and B in the ratio 4 : 1. When 10 litres of the mixture is replaced with liquid B, the ratio becomes 2 : 3. The volume of liquid A present in the jar earlier was

  1. 10 litres

  2. 16 litres

  3. 15 litres

  4. 20 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let initial volume be 5x (4x of A, 1x of B). After removing 10 litres, 8 litres of A and 2 litres of B are removed. Adding 10 litres of B results in (4x-8) of A and (x-2+10) of B. Setting (4x-8)/(x+8) = 2/3 gives 12x-24 = 2x+16, so 10x = 40 and x=4. Initial A is 4*4 = 16 litres.

Multiple choice

A merchant buys a brand of tea at Rs. 80 per kg and mixes it with another brand bought at Rs. 140 per kg. He makes a profit of 25% on selling the mixture at Rs. 125 per kg. What is the ratio in which the brands are mixed?

  1. 4 : 3

  2. 2 : 1

  3. 3 : 2

  4. 2 : 3

  5. 1 : 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Selling at 125 with 25% profit means the cost price of the mixture is 125 / 1.25 = 100. Using the allegation rule with prices 80 and 140, the ratio is (140-100) : (100-80) = 40 : 20 = 2 : 1.

Multiple choice

The ratio of milk and water in a mixture is 3 : 2. If 10 litres of water is added to it, the ratio gets reversed. What is the amount of the total mixture now?

  1. 10 litres

  2. 20 litres

  3. 24 litres

  4. 30 litres

  5. 32 litres
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the initial amounts be 3x and 2x. Adding 10 litres of water changes the ratio to 3x : (2x + 10), which equals 2 : 3. Solving 9x = 4x + 20 gives 5x = 20, so x = 4. The initial total was 5x = 20 litres, and adding 10 litres makes the new total 30 litres.