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 container holds 1,000 cc of oil, and a separate vessel contains 1,000 cc of vinegar. First, 300 cc of oil is taken from the container and added to the vinegar in the vessel, where it is mixed thoroughly. Then, 300 cc of the resulting mixture is transferred back from the vessel to the container. After these two steps, what is the ratio of vinegar in the container to oil in the vessel?

  1. 1 : 2

  2. 2 : 1

  3. 1 : 1

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

Container: 1000 oil. Vessel: 1000 vinegar. Step 1: 300 oil to vessel. Vessel now has 1000 vinegar + 300 oil (total 1300). Step 2: 300 mixture back to container. Mixture is 300/1300 oil and 1000/1300 vinegar. Amount of vinegar returned = 300 * (1000/1300) = 3000/13. Amount of oil remaining in vessel = 300 - 300 * (300/1300) = 300 - 900/13 = 3000/13. Ratio is 1:1.

Multiple choice

A vessel contains 60 liters of pure milk. 12 liters of milk is drawn off and replaced with an equal amount of water. This operation is repeated one more time. What is the remaining quantity of pure milk in the vessel?

  1. 36 liters

  2. 38.4 liters

  3. 40.2 liters

  4. 42 liters

  5. 43.2 liters
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The formula for remaining amount after n replacements is Initial * (1 - replaced/total)^n. Here, 60 * (1 - 12/60)^2 = 60 * (4/5)^2 = 60 * 16/25 = 60 * 0.64 = 38.4 liters.

Multiple choice

. Jar A contains a mixture of milk and water in the ratio 4 : 3, and Jar B contains the same liquids mixed in the ratio 2 : 3. In what structural ratio must liquid quantities be drawn from Jar A and Jar B and mixed together to generate a new solution containing milk and water in the ratio 1 : 1?

  1. 7 : 5

  2. 5 : 7

  3. 4 : 5

  4. 5 : 4

  5. 3 : 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Jar A contains milk and water in fractions 4/7 and 3/7, while jar B contains 2/5 and 3/5. Equating the excess milk from A with the water deficit from B gives x/14 = y/10, so x:y = 7:5.

Multiple choice

A wine distributor wants to mix two wines. Wine A contains 8% alcohol, and Wine B contains 16% alcohol. How many liters of Wine B should be added to 30 liters of Wine A to produce a blend with 12% alcohol?

  1. 20 liters

  2. 25 liters

  3. 30 liters

  4. 35 liters

  5. 40 liters
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the alligation method: Wine A (8%) and Wine B (16%) mixed to get 12%. The ratio of volumes is (16-12) : (12-8) = 4 : 4 = 1 : 1. Since we have 30 liters of Wine A, we need 30 liters of Wine B.

Multiple choice

A vessel contains 6 liters of a solution with 10% alcohol and 90% water. If 3 liters of this solution are replaced with pure alcohol, what percentage of the resulting mixture is alcohol?

  1. 35%

  2. 45%

  3. 55%

  4. 60%

  5. 70%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial: 6 liters, 10% alcohol = 0.6L alcohol, 5.4L water. Replace 3 liters of solution: 3 liters removed contains 0.3L alcohol and 2.7L water. Remaining: 0.3L alcohol, 2.7L water. Add 3 liters pure alcohol: Total alcohol = 0.3 + 3 = 3.3L. Total volume = 6L. Percentage = (3.3 / 6) * 100 = 55%.

Multiple choice

Four grades of oil are 2%, 5%, 8%, and 11% additive by volume. If p liters of the 2% grade, q liters of the 5% grade, r liters of the 8% grade, and t liters of the 11% grade are mixed to form p + q + r + t liters of a mixture that is 6% additive by volume, then what is p in terms of q, r, and t?

  1. − q + 2 r + 5 t 4

  2. − q + 2 r − 5 t 4

  3. q − 2 r − 5 t 6

  4. q − 2 r + 5 t 6

  5. − q − 2 r + 5 t 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

0.02p + 0.05q + 0.08r + 0.11t = 0.06(p + q + r + t). Multiply by 100: 2p + 5q + 8r + 11t = 6p + 6q + 6r + 6t. Rearrange: 4p = -q + 2r + 5t. p = (-q + 2r + 5t) / 4.

Multiple choice

A chef has a 80-liter vat filled with concentrated fruit syrup. He draws out 8 liters of the syrup and replaces it with 8 liters of plain water. This procedure — removing 8 liters of the current mixture and adding 8 liters of water — is repeated multiple times. What is the minimum number of such repetitions needed so that the quantity of syrup remaining in the vat becomes less than the quantity of water?

  1. 4

  2. 5

  3. 7

  4. 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is a mixture problem where the amount of syrup remaining after n replacements is 80 * (1 - 8/80)^n = 80 * (0.9)^n. We want 80 * (0.9)^n < 40, or (0.9)^n < 0.5. For n=6, 0.9^6 = 0.531. For n=7, 0.9^7 = 0.478. Thus 7 repetitions are needed.

Multiple choice

Three containers A, B and C have mixture of pure milk and water. The average of the volume of pure milk in the three containers is 16 litres and average of the volume of the mixture in the three containers is 20 litres. Ratio of water in A, B and C is 2 : 3 : 1. Find the difference between the volume of pure milk in B and C if the sum of volume of mixture in container B and C is 40 litres.

  1. 6 litres

  2. 8 litres

  3. 12 litres

  4. Can't be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Insufficient information is provided to determine the individual volumes of milk in containers B and C. The average milk and mixture volumes don't uniquely identify the distribution across containers.