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

Directions: Compare the two quantities in A and B. A container has 80 lts of pure spirit. If y liters of this spirit is replaced with water, the amount of spirit decreases by 20%. Quantity A Quantity B y 16

  1. Quantity A is greater than quantity B.

  2. Quantity B is greater than quantity A.

  3. Both quantities are equal.

  4. The relationship between the quantities cannot be determined.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If 20% of the spirit is removed, 20% of 80 liters is 16 liters. Thus, y = 16. Since Quantity A is 16 and Quantity B is 16, they are equal.

Multiple choice

Three casks of equal volume are filled with a mixture of wine and water. The proportion of wine to water in the three casks is 2 : 3, 3 : 4 and 4 : 5 respectively. The contents of three casks are emptied into a single cask. What is the proportion of wine and water in it?

  1. 401 : 449

  2. 401 : 544

  3. 401 : 344

  4. 445 : 344
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Wine fractions: 2/5, 3/7, 4/9. Water fractions: 3/5, 4/7, 5/9. Total wine = 2/5 + 3/7 + 4/9 = (126 + 135 + 140) / 315 = 401 / 315. Total water = 3/5 + 4/7 + 5/9 = (189 + 180 + 175) / 315 = 544 / 315. Ratio = 401 : 544.

Multiple choice

Two containers A and B have equal quantity of diluted milk. In container A, the concentration of milk is 80% and in container B, it is 60%. If 10% of diluted milk from container A is transferred to B and then 10% of this mixture from B is transferred back to A, what will happen to the concentration of milk in container B?

  1. It increases

  2. It decreases

  3. It doesn`t change

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the initial quantity in each container be 100 units. Container A has 80 units of milk, and B has 60 units. After transferring 10 units from A to B, B now has 110 units of liquid with 60 + 8 = 68 units of milk (concentration 68/110 = 61.8%). When 10% of this mixture (11 units) is transferred back to A, the amount of milk removed from B is 11 * (68/110) = 6.8 units. The remaining milk in B is 68 - 6.8 = 61.2 units in 99 units of liquid, resulting in a concentration of 61.2/99 = 61.8%, which is an increase from the original 60%.

Multiple choice

Barack mixes three varieties of rice, costing Rs. 60, Rs. 10 and Rs. 30 per kg in the ratio 2 : 3 : 5 respectively, in terms of weight, and sells the mixture at Rs. 27 per kg. What % of loss does he suffer?

  1. 10

  2. 11.11

  3. 31.35

  4. 45.67
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total weight = 2+3+5 = 10kg. Total cost = (2*60) + (3*10) + (5*30) = 120 + 30 + 150 = 300. Cost per kg = 300/10 = 30. Selling price = 27. Loss = 30 - 27 = 3. Loss % = (3/30) * 100 = 10%.

Multiple choice

Three containers have their volumes in the ratio 2 : 3 : 5. They are full of mixtures of wine and water. The mixtures contain wine and water in the ratio of (3 : 1), (2 : 1), and (3 : 2), respectively. The contents of all these three containers are poured into a fourth container. Find the amount of wine in the second container, if the wine in the fourth container is equal to 65 Liters.

  1. 10 Liters

  2. 15 Liters

  3. 20 Liters

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

Let volumes be 2x, 3x, 5x. Wine in containers: (3/4)*2x = 1.5x, (2/3)*3x = 2x, (3/5)*5x = 3x. Total wine = 1.5x + 2x + 3x = 6.5x. Given 6.5x = 65, so x = 10. Wine in second container is 2x = 20 Liters.

Multiple choice

In a mixture, the ratio of milk and water is 5 : 3. If water contained is 6 litres initially and 6 litres of milk is now added to this mixture, what will be the new ratio of milk and water?

  1. 6 : 4

  2. 8 : 3

  3. 6 : 5

  4. 26 : 6

  5. 11 : 3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial ratio 5:3 means milk = 5x, water = 3x. Given water = 6, so 3x = 6, x = 2. Milk = 10, water = 6. Adding 6 litres of milk makes milk = 10 + 6 = 16. New ratio is 16:6, which simplifies to 8:3.

Multiple choice

There are three barrels, B1, B2 and B3, filled respectively with 60%, 75% and 80% mixtures of petrol in kerosene. The mixtures in the three barrels are taken in a certain ratio and mixed thoroughly to form a 7 10 mixture of petrol in kerosene. In this mixture, if the quantity of the solution taken from B3 is 2 5 less than the quantity taken from B1, by what percent is the quantity taken from B2 less or more than the quantity taken from B1?

  1. 20% less

  2. 10% less

  3. 10% more

  4. 20% more

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

Let the quantities from B1, B2, and B3 be x, y, and 3x/5 respectively. Equating the final petrol concentration to 70% gives 0.6x + 0.75y + 0.8(3x/5) = 0.7(x + y + 3x/5). Solving gives y = 0.8x, so B2 contributes 20% less than B1.

Multiple choice

The contents in beakers A and B are 80 cm3 of sugar and 80 cm3 of sand, respectively. Now, 20 cm3 of sugar is taken out from A and put into B. After thorough mixing, 20 cm3 of the mixture is taken out from B and put into A. Find the percentage of sand in the mixture in beaker A.

  1. 15%

  2. 20%

  3. 21%

  4. 25%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Beaker A: 80 sugar. Beaker B: 80 sand. Move 20 sugar to B: A has 60 sugar, B has 80 sand + 20 sugar. Mix B: 100 total, 80% sand, 20% sugar. Move 20 of mixture to A: 20 * 0.8 = 16 sand moved to A. A now has 60 sugar + 16 sand + 4 sugar = 64 sugar + 16 sand. Total in A = 80. Sand percentage = 16/80 = 20%.

Multiple choice

Fifty litres of a mixture of milk and water contains 30 percent of water. This mixture is added to eighty litres of another mixture of milk and water that contains 20 percent of water. Then how many litres of water should be added to the resulting mixture to obtain a final mixture that contains 25 percent of water?

  1. 1 L

  2. 2 L

  3. 3 L

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

Mix 1: 50L, 30% water = 15L water. Mix 2: 80L, 20% water = 16L water. Total volume = 130L, total water = 31L. Let x be water added: (31+x)/(130+x) = 0.25. 31+x = 32.5 + 0.25x. 0.75x = 1.5. x = 2.