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 barrel contains mixture of spirit and kerosene in the ratio 8 : 5. When 91 litres of mixture is used from barrel and again refilled with kerosene only, then the ratio becomes 8 : 9. Calculate the quantity of spirit present in the barrel before use.

  1. 238 litres

  2. 280 litres

  3. 300 litres

  4. 340 litres

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

Let initial spirit be 8x and kerosene be 5x. Total = 13x. Removed 91 litres, so removed (8/13)*91 = 56 spirit and (5/13)*91 = 35 kerosene. Remaining: 8x - 56 spirit, 5x - 35 + 91 kerosene. New ratio: (8x - 56) / (5x + 56) = 8/9. 72x - 504 = 40x + 448 => 32x = 952 => x = 29.75. Initial spirit = 8 * 29.75 = 238.

Multiple choice

A test tube contains 80 ml of boric acid. In an experiment, 16 ml of boric acid is removed from test tube and similar amount of glucose solution is poured in it. Again, same amount of mixture of boric acid and glucose solution is taken out of the test tube and replaced by the same amount of glucose solution. Calculate the ratio of the remaining boric acid with quantity of boric acid initially present in the test tube.

  1. 8 : 5

  2. 16 : 25

  3. 8 : 11

  4. 12 : 5

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

Initial acid = 80. After 1st replacement: 80 * (1 - 16/80) = 80 * 0.8 = 64. After 2nd replacement: 64 * 0.8 = 51.2. Ratio of remaining acid to initial = 51.2 / 80 = 512 / 800 = 64 / 100 = 16 / 25.

Multiple choice

A large vessel contained a mixture of 500 ml of strawberry extract and water. 100 ml of this mixture is poured into the other beaker and the same quantity is replaced by water. The percentage of strawberry extract in the vessel is 64%. Find the percentage of strawberry extract initially in the mixture.

  1. 20%

  2. 25%

  3. 60%

  4. 80%

  5. 85%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let initial concentration be x. After replacing 100ml (1/5 of total) with water, concentration becomes x * (1 - 100/500) = 0.8x. We are told 0.8x = 0.64. x = 0.64 / 0.8 = 0.8, which is 80%.

Multiple choice

In a school lab, a student took 20 ml of a solution that contained 20% volume sulphuric acid. To dilute it, he added water to the solution to 3% strength. Find the amount of water added.

  1. 113.33 ml

  2. 115.53 ml

  3. 116.85 ml

  4. 119.12 ml

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

The amount of acid remains constant during dilution. Initially, there is 20 ml * 0.20 = 4 ml of acid. After adding water, the total volume V satisfies 4 / V = 0.03, so V = 4 / 0.03 = 133.33 ml. The amount of water added is 133.33 ml - 20 ml = 113.33 ml.

Multiple choice

Jars A, B, C and D have mixtures of milk and honey in the ratio 2 : 3, 4 : 7, 3 : 7 and 2 : 5, respectively. If all these mixtures are mixed together and the volumes of these jars are in the ratio of 3 : 4 : 5 : 6, then find the ratio of milk to honey in the final mixture.

  1. 4519 : 9341

  2. 9244 : 4658

  3. 4419 : 7341

  4. 2419 : 9341

  5. 5419 : 9341
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Milk/Honey ratios: A=2/5, 3/5; B=4/11, 7/11; C=3/10, 7/10; D=2/7, 5/7. Volumes ratio: 3:4:5:6. Total parts = 3+4+5+6 = 18. Weighted average: Milk = (3*2/5 + 4*4/11 + 5*3/10 + 6*2/7) / 18. Honey = (3*3/5 + 4*7/11 + 5*7/10 + 6*5/7) / 18. Calculating these yields the ratio 4519 : 9341.

Multiple choice

The ratio of alcohol and water is 3 : 2 in a jar. If 5 litres of alcohol is taken out of the jar, then the ratio becomes 4 : 3. How much alcohol is there in the mixture?

  1. 30 litres

  2. 45 litres

  3. 50 litres

  4. 60 litres

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

Let the initial amounts of alcohol and water be 3x and 2x. After removing 5 litres of alcohol, the new ratio is (3x - 5) / 2x = 4 / 3. Solving for x gives 9x - 15 = 8x, so x = 15. The initial amount of alcohol is 3 * 15 = 45 litres.

Multiple choice

In what ratio should a person mix three kinds of metal costing Rs. 60/kg, Rs. 75/kg and Rs. 100 /kg so that the resultant alloy when sold at Rs. 96/kg results in a gain of 20%?

  1. 1 : 2 : 4

  2. 3 : 7 : 6

  3. 1 : 4 : 2

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

Selling price = 96, gain = 20%. Cost price = 96 / 1.2 = 80. Using the mixture rule for three components: (60x + 75y + 100z) / (x+y+z) = 80. 60x + 75y + 100z = 80x + 80y + 80z => 20z = 20x + 5y => 4z = 4x + y. Testing options: 1:4:2 gives 4(2) = 4(1) + 4 => 8 = 8. Correct.

Multiple choice

The Concentration of milk in a container which is having 80 quarts of 80% concentrated milk is reduced by adding X quarts of water. What is the value of X? (1) The concentration changed to 64%. (2) The volume of content in the container is increased by 25%.

  1. Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement 1: 80 * 0.8 = 64. New volume = 64 / 0.64 = 100. Water added = 100 - 80 = 20. Sufficient. Statement 2: Volume increased by 25% = 80 * 1.25 = 100. Water added = 100 - 80 = 20. Sufficient.

Multiple choice

A vessel contains 120 litres of a mixture of milk and water in the ratio 11 : 4, respectively. 45 litres of this mixture is taken out, and then 5 litres of water is added. What is the percentage of water in the resultant mixture?

  1. 31.75%

  2. 31.25%

  3. 35.65%

  4. 42.15%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial: 120L, 11:4 ratio. Milk = 88L, Water = 32L. Remove 45L: Milk removed = 45 * 11/15 = 33L, Water removed = 45 * 4/15 = 12L. Remaining: Milk = 55L, Water = 20L. Add 5L water: Water = 25L, Total = 80L. Percentage water = 25/80 = 31.25%.

Multiple choice

If 20 gallons of water is added to a tub already filled with 120 gallons of water and milk, the concentration of milk in the tub will be 80 percent. What is the initial concentration of milk in the tub?

  1. 88.66 percent

  2. 90 percent

  3. 93.33 percent

  4. 96 percent

  5. 98 percent
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial volume = 120. Let milk = M. After adding 20, total = 140. Milk is 80% of 140 = 112. Initial concentration = 112 / 120 = 0.9333 or 93.33%.

Multiple choice

From 200 gallons of solution having 80 percent milk concentration, 30 gallons is taken out and equal amount of water is added. The new concentration of milk in the mixture is

  1. 60 %

  2. 68 %

  3. 70 %

  4. 172 %

  5. 90 %
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial milk = 200 * 0.8 = 160 gallons. Removing 30 gallons of mixture removes 30 * 0.8 = 24 gallons of milk. Remaining milk = 160 - 24 = 136 gallons. The total volume remains 200 gallons. New concentration = 136/200 = 0.68 or 68%.