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 milkman has 150 ounces of the milk and water mixture, out of which 12% is water. What is the total percentage of milk in the mixture if he adds another 20 ounces of water?

  1. 66.67%

  2. 71.32%

  3. 77.65%

  4. 52.50%

  5. 57.68%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initially, there are 150 ounces of mixture with 12% water, meaning 18 ounces of water and 132 ounces of milk. Adding 20 ounces of water results in 170 total ounces, while the amount of milk remains 132 ounces. The percentage of milk is (132/170) * 100, which is approximately 77.65%.

Multiple choice

A jar contains some quantity of apple juice. Kyla draws 8 ounces of juice from it and then fills the jar with water. She performs this activity three more times. The ratio of the quantity of apple juice now left in the jar to that of water is 16 : 65. How much apple juice did the jar originally hold?

  1. 18 ounces

  2. 22 ounces

  3. 24 ounces

  4. 26 ounces

  5. 30 ounces
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the initial amount of apple juice. After 4 draws of 8 ounces, the fraction of apple juice remaining is (1 - 8/x)^4. Given the ratio of juice to water is 16:65, the fraction of juice remaining is 16/(16+65) = 16/81. Setting (1 - 8/x)^4 = 16/81, we get 1 - 8/x = 2/3, so 8/x = 1/3, which means x = 24.

Multiple choice

A shopkeeper bought 20 kg of rice at Rs. 55 per kg, 25 kg of rice at Rs. 50 per kg, and 35 kg of rice at Rs. 60 per kg. He spent a sum of Rs. 150 on transportation. He mixed all the three types of rice and sold all the stock at Rs. 62.56 per kg. His profit per cent in the entire transaction is:

  1. 8.8

  2. 12.5

  3. 10.5

  4. 9.2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total cost = (20*55) + (25*50) + (35*60) + 150 = 1100 + 1250 + 2100 + 150 = 4600. Total weight = 20 + 25 + 35 = 80 kg. Total revenue = 80 * 62.56 = 5004.8. Profit = 5004.8 - 4600 = 404.8. Profit % = (404.8 / 4600) * 100 = 8.8%.

Multiple choice

In a mixture of alcohol and water, there was 73% water. If the quantity of alcohol in the mixture was 108 litres and 42 litres of water was added to the mixture, then find the ratio of alcohol to water in the mixture.

  1. 167 : 54

  2. 163 : 52

  3. 52 : 163

  4. 54 : 167

  5. 5 : 67
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial mixture: 73% water, 27% alcohol. Alcohol = 108L. 0.27 * Total = 108 => Total = 400L. Water = 400 - 108 = 292L. Add 42L water: New water = 292 + 42 = 334L. Ratio Alcohol:Water = 108 : 334 = 54 : 167.

Multiple choice

Directions : Type in your answer in the input box provided below the question. A dishonest milkman dilutes milk with water and then sells the diluted milk at a price that is 20% more than the price at which he purchased the milk. If he makes a profit of 50% in this manner, how many ml of water does he add to every litre of milk? [quizky-text]

  1. 250

  2. 1

  3. 625

  4. 15625
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let CP of 1000ml milk be 100. SP = 120. Profit = 50%, so SP = 150. The mixture contains 1000ml milk + x ml water. Cost of mixture = 100. SP = 150. Since SP = 1.2 * CP_milk, 150 = 1.2 * (1000 + x) is wrong. Correct approach: Profit = (SP - CP) / CP. 0.5 = (1.2 - (1000/(1000+x))) / (1000/(1000+x)). Solving gives x = 250.

Multiple choice

Directions: Select the correct alternative from the given choices. A mixture of alcohol and water comprises 80% alcohol. First, 20% of the mixture is replaced with• water and then the volume of the resultant mixture is increased• by 20% by adding only alcohol. If the entire process is then repeated once all over again, what is percentage of alcohol in the final mixture?

  1. 63.33%

  2. 72.28%

  3. 61.25%

  4. 81.24%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial: 80% alcohol. Replace 20% with water: 80% of 0.8 = 64% alcohol. Increase volume by 20% with alcohol: (0.64 + 0.2) / 1.2 = 0.84 / 1.2 = 70%. Repeat: 70% of 0.8 = 56%. Increase by 20% with alcohol: (0.56 + 0.2) / 1.2 = 0.76 / 1.2 = 63.33%.