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

3 containers having capacities in the ratio 5 : 6 : 2 contain mixture of sugar Type A and Type B such that the ratio of A to B in them is 2 : 4, 1 : 3 and 3 : 5 respectively. If all the three containers of sugar are emptied in a single container, what will be the ratio of sugar Type A to sugar Type B in the final mixture?

  1. 85 : 91

  2. 98 : 227

  3. 47 : 109

  4. 391 : 919

  5. 393 : 959
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total parts = 5+6+2 = 13. Container 1: 5 units, A:B = 2:4 (1:2) -> A=5/3, B=10/3. Container 2: 6 units, A:B = 1:3 -> A=6/4=1.5, B=4.5. Container 3: 2 units, A:B = 3:5 -> A=2*(3/8)=0.75, B=1.25. Total A = 5/3 + 1.5 + 0.75 = 1.66 + 2.25 = 3.916. Total B = 10/3 + 4.5 + 1.25 = 3.33 + 5.75 = 9.083. Ratio A:B = 3.916/9.083 = 47/109.

Multiple choice

Bottle A contains 60% milk and the rest is water. Bottle B contains 75% of milk and the rest is water. Some amount of liquid from the first bottle is mixed with twice the same amount of liquid from Bottle B. Find the percentage of milk in the resultant liquid.

  1. 66%

  2. 38%

  3. 71%

  4. 70%

  5. 79%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let amount from A be x, from B be 2x. Milk in A = 0.6x. Milk in B = 0.75 * 2x = 1.5x. Total milk = 2.1x. Total volume = 3x. Percentage = 2.1x / 3x = 0.7 = 70%.

Multiple choice

At a manufacturing unit, there is a container containing a mixture of rose essence and alcohol in the ratio of 5 : 3. If 15 litres of alcohol is added to the container, the ratio of rose essence to alcohol becomes 7 : 5. What was the initial amount of the mixture in the container?

  1. 185 litres

  2. 190 litres

  3. 210 litres

  4. 230 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let rose essence be 5x and alcohol be 3x. Total = 8x. Adding 15L alcohol: 5x / (3x + 15) = 7/5. 25x = 21x + 105, so 4x = 105, x = 26.25. Initial mixture = 8x = 8 * 26.25 = 210.

Multiple choice

Sarah is conducting an experiment in her laboratory with a 15-litre solution that currently contains 45% water. To meet experimental requirements, she needs a solution with 70% water concentration. How many litres of water must Sarah carefully add to achieve this exact concentration?

  1. 6.25 litres

  2. 7.5 litres

  3. 12.5 litres

  4. 14 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial water = 0.45 * 15 = 6.75 litres. Let x be the water added. New total volume = 15 + x. New water = 6.75 + x. We need (6.75 + x) / (15 + x) = 0.70. Solving gives 6.75 + x = 10.5 + 0.7x, so 0.3x = 3.75, x = 12.5.

Multiple choice

Dr. Anderson has a 20-litre solution that currently contains 30% ethanol. To achieve optimal conditions for her research, Dr. Anderson needs to adjust the solution to precisely 50% ethanol concentration. How many litres of pure ethanol should she add to achieve this targeted concentration?

  1. 4

  2. 6

  3. 8

  4. 12

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

Let x be the amount of pure ethanol added. The initial amount of ethanol is 0.30 * 20 = 6 litres. After adding x litres of pure ethanol, the total volume becomes 20 + x, and the new amount of ethanol is 6 + x. Setting the new concentration to 50% gives (6 + x) / (20 + x) = 0.5. Solving this, 6 + x = 10 + 0.5x, so 0.5x = 4, which means x = 8.

Multiple choice

A researcher is working with two types of nutrient solutions, Solution A and Solution B, containing both essential minerals and water. When 3 litres of Solution A and 7 litres of Solution B are mixed, the resulting mixture contains 25% essential minerals. Similarly, when 6 litres of Solution A and 4 litres of Solution B are mixed, the resulting mixture contains 22% essential minerals. In which atio should the researcher mix Solutions A and B to create a new mixture with 23% essential minerals?

  1. 11 : 9

  2. 1 : 9

  3. 9 : 1

  4. 11 : 19
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Tap A can fill a tank in 20 hours; where as Tap B can do so in 60 hours. Pure milk flows out of Tap A and water flows out of Tap B. For how much time should water be allowed to flow out of Tap B such that an 80% concentration of milk is obtained in the tank by the time it is completely full?

  1. 10 hours

  2. 12 hours

  3. 15 hours

  4. 20 hours

  5. 30 hours
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let T be the time for Tap B. Tap A fills 1/20 per hour, Tap B fills 1/60 per hour. Total volume is 1. Milk volume is (1/20) * (T + x) = 0.8, where x is the time A runs alone. Since the tank is full, (1/20)*(T+x) + (1/60)*T = 1. Solving these yields T = 12.

Multiple choice

A pack of cream cheese contains cream and cheese mixtures in the ratio 5 : 3. If 75 ml of cheese mixture is added to the pack, the ratio becomes 5 : 6. What is the quantity (in ml) of cream mixture in the pack?

  1. 125 ml

  2. 120 ml

  3. 140 ml

  4. 65 ml

  5. 90 ml
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the initial quantities of cream and cheese be 5x and 3x respectively. Adding 75 ml of cheese makes the new ratio 5x / (3x + 75) = 5/6, which simplifies to 6x = 3x + 75, so x = 25. The initial quantity of cream is 5x = 5 * 25 = 125 ml.

Multiple choice

A full bucket of paint contains a mixture of 30% blue paint and 70% white paint. A second bucket contains a mixture of 80% blue paint and 20% white paint. The volume of second bucket is 50% more than the first bucket. When both mixtures are combined, find the concentration of blue paint.

  1. 35%

  2. 50%

  3. 60%

  4. 67%

  5. 72%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let volume of first bucket be V. Volume of second is 1.5V. Blue paint in first = 0.3V. Blue paint in second = 0.8 * 1.5V = 1.2V. Total blue = 1.5V. Total volume = 2.5V. Concentration = 1.5V / 2.5V = 0.6 or 60%.

Multiple choice

A manufacturer has two types of fruit juice concentrate. Type A costs Rs. 4.20 per litre, and Type B costs Rs. 5.60 per litre. He wants to mix them to obtain a blend costing exactly Rs. 4.80 per litre. In what ratio should Type A and Type B be mixed?

  1. 1 : 3

  2. 3 : 1

  3. 2 : 1

  4. 4 : 3

  5. 7 : 2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the alligation rule: (Cost of B - Mean Cost) / (Mean Cost - Cost of A) = (5.60 - 4.80) / (4.80 - 4.20) = 0.80 / 0.60 = 8/6 = 4/3.

Multiple choice

Two chemical solutions X and Y are mixed in the ratio 7 : 3, respectively. Solution X contains m% of acid and n% of water, while solution Y contains o% of acid and p% of water. When solution X is combined with solution Y, the final percentage of acid in the total mixture becomes 40% of the total volume. If m - o = 40, find m : o.

  1. 3 : 25

  2. 13 : 3

  3. 20 : 17

  4. 7 : 20

  5. 8 : 23
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let V be total volume. Acid from X = 0.7V * (m/100), Acid from Y = 0.3V * (o/100). Total acid = 0.4V. So, 0.7m + 0.3o = 40. Given m - o = 40, substitute o = m - 40: 0.7m + 0.3(m - 40) = 40 => 0.7m + 0.3m - 12 = 40 => m = 52. Then o = 12. Ratio m:o = 52:12 = 13:3.