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

In a 100 litre mixture containing water and milk in equal proportions, 10 litres of mixture is replaced by 10 litres of water in succession, twice. At the end, what is the ratio of milk to water?

  1. 81 : 119

  2. 9 : 11

  3. 40 : 61

  4. 41 : 59

  5. 11 : 9
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial: 50L milk, 50L water. Replacing 10L of mixture (5L milk, 5L water) with 10L water. After 1st replacement: Milk = 50 - 5 = 45, Water = 50 - 5 + 10 = 55. After 2nd replacement: Milk = 45 - (10/100)*45 = 45 - 4.5 = 40.5. Water = 100 - 40.5 = 59.5. Ratio = 40.5 : 59.5 = 81 : 119.

Multiple choice

There are 2 containers, each containing equal quantities of solution containing milk and water. In the first container, the ratio of water and milk is 2 : 3 and in the second container, the ratio of water to milk is 1 : 4. Now, these two containers are emptied in a tub in the volume ratio 3 : 4. Which of the following is true?

  1. The ratio of water and milk in the resulting mixture is 3 : 4

  2. The ratio of water and milk in the resulting mixture is 2 : 5

  3. The ratio of water and milk in the resulting mixture is 3 : 5

  4. The ratio of water and milk in the resulting mixture is 2 : 3
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Alcohol is mixed with water in the ratio 5 : 2. If the mixture is 7 litres, how many litres of the mixture must be replaced with water to make the ratio of alcohol to water 1 : 1?

  1. 1.8 litres

  2. 2.1 litres

  3. 3.4 litres

  4. 1.6 litres

  5. 2.4 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The initial 7-litre mixture contains 5 litres of alcohol and 2 litres of water. If x litres of the mixture is replaced by water, the remaining alcohol is 5 - (5/7)x and the new water content is 2 - (2/7)x + x. Setting these equal for a 1:1 ratio gives 5 - (5/7)x = 2 + (5/7)x, which solves to x = 2.1 litres.

Multiple choice

36 L of pure water is added to a container containing 160 L of pure alcohol. 98 L of the resultant mixture was taken out and some more quantities of pure alcohol and pure water were added to the container in the ratio 2 : 1. What was the quantity of pure alcohol added to the container, if the resultant ratio of alcohol and water in the container is 4 : 1?

  1. 2 L

  2. 4 L

  3. 6 L

  4. 8 L

  5. 10 L
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial: 160A, 36W. Total 196. Remove 98L (half the mixture). Remaining: 80A, 18W. Add x alcohol and x/2 water. Result: (80+x)/(18+x/2) = 4/1. 80+x = 72 + 2x. x = 8.

Multiple choice

In a chemical factory, a storage tank contains a mixture of alcohol and benzene mixed in the ratio 5 : 7. If 9 litres of the mixture is replaced by 9 litres of benzene, then the ratio of the two liquids becomes 5 : 8. How much alcohol was there in the tank?

  1. 48.75 litres

  2. 51.25 litres

  3. 62.39 litres

  4. 72.82 litres

  5. 92.65 litres
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let alcohol = 5x and benzene = 7x. Total = 12x. Removing 9 litres removes 5/12 * 9 = 3.75 litres of alcohol and 5.25 litres of benzene. Remaining: Alcohol = 5x - 3.75, Benzene = 7x - 5.25 + 9 = 7x + 3.75. Ratio (5x - 3.75) / (7x + 3.75) = 5/8. Solving: 40x - 30 = 35x + 18.75, so 5x = 48.75. Initial alcohol was 5x = 48.75.

Multiple choice

There are 2 vessels filled with a mixture of milk and water. In the first vessel, the water is 2/3 of the milk and in the second vessel, water is just 40% of the milk. In what ratio are these required to be mixed to make a mixture of 24 litres, in which the ratio of water to milk is 1 : 2?

  1. 4 : 3

  2. 5 : 7

  3. 5 : 2

  4. 7 : 5

  5. 3 : 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Vessel 1: Water/Milk = 2/3. Fraction of water = 2/5. Vessel 2: Water/Milk = 40/100 = 2/5. Fraction of water = 2/7. Target: Water/Milk = 1/2. Fraction of water = 1/3. Using alligation: |2/7 - 1/3| : |2/5 - 1/3| = |6/21 - 7/21| : |6/15 - 5/15| = 1/21 : 1/15 = 15:21 = 5:7.

Multiple choice

From a barrel of wine, 4 litres of wine is taken out and it is then filled with water. This process is repeated three more times, and the final mixture in the barrel at the end contains the wine and water in the ratio of 16 : 65. How much wine did the barrel contain initially?

  1. 8 litres

  2. 12 litres

  3. 26 litres

  4. 30 litres

  5. 34 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The ratio of wine to total mixture is 16:81 (since 16:65 is wine:water, total is 16+65=81). The formula for concentration after n replacements is C = C0 * (1 - x/V)^n. Here, (1 - 4/V)^4 = 16/81 = (2/3)^4. Thus, 1 - 4/V = 2/3, so 4/V = 1/3, which means V = 12.

Multiple choice

24 Toffees are bought at 4 per rupee and the same number again for 6 per rupee. Then, they are mixed and sold at 5 per rupee. What is the net profit or loss?

  1. 2% loss

  2. 10% profit

  3. no profit or loss

  4. 4% loss

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

Cost of 24 toffees at 4/rupee is 6 rupees. Cost of another 24 toffees at 6/rupee is 4 rupees. Total cost is 10 rupees for 48 toffees. Selling 48 toffees at 5/rupee yields 48/5 = 9.6 rupees. Loss is 0.4 rupees on 10 rupees, which is 4%.