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 bottle is initially filled with sugar syrup. In each step, two fifth of its content is removed and replaced with water. This process is repeated five times. What is the final ratio of syrup to water in the bottle?

  1. 81 : 544

  2. 81 : 625

  3. 243 : 2882

  4. 243 : 3125

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

If 2/5 is removed, 3/5 of the syrup remains. After 5 steps, the remaining syrup is (3/5)^5 = 243/3125 of the original volume. The water content is 1 - 243/3125 = 2882/3125. The ratio of syrup to water is 243 : 2882.

Multiple choice

A vessel contains 108 litres of milk and water in the ratio of 5:4. If 20 Liters of milk and 36 liter water is added to the mixture then difference between milk and water in mixture ix Y. Find the value of 7Y?

  1. 40

  2. 28

  3. 32

  4. 44
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initially, milk is 108 x 5/9 = 60 litres and water is 48 litres. After adding the stated amounts, milk is 80 litres and water is 84 litres, so their difference is Y = 4 litres. Therefore, 7Y = 28.

Multiple choice

The ratio of milk and water in a container is 2 : 3. When 60 liters of mixture is taken out and replaced with water then the ratio of milk and water becomes 1 : 2. Then find the total capacity of the container.

  1. 360 liters

  2. 220 liters

  3. 440 liters

  4. 350 liters
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let initial milk be 2x and water 3x. Removing 60L removes 24L milk and 36L water. After adding 60L water, milk is 2x-24 and water is 3x-36+60 = 3x+24. Ratio (2x-24)/(3x+24) = 1/2. Solving gives x=72. Total capacity = 5x = 360.

Multiple choice

In a laboratory, two different chemical solutions, solution X and solution Y, are being used in an experiment. Solution X contains a mixture of chemical A and chemical B in the ratio of 3 : 7, while solution Y contains the same chemicals in the ratio of 2 : 5. A scientist needs to mix these two solutions in such a way that the resulting mixture has the ratio of chemical A to chemical B as 5 : 12. If the scientist decides to mix m liters of solution X with n liters of solution Y, then m : n =

  1. 7 : 5

  2. 5 : 7

  3. 10 : 7

  4. 7 : 10
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Solution X has A:B = 3:7 (fraction A = 3/10). Solution Y has A:B = 2:5 (fraction A = 2/7). Mixture has A:B = 5:12 (fraction A = 5/17). Using alligation: |2/7 - 5/17| / |3/10 - 5/17| = |(34-35)/119| / |(51-50)/170| = (1/119) / (1/170) = 170/119 = 10/7.

Multiple choice

Six litres are drawn from a cask full of wine. It is filled with water. Six litres of mixture are again drawn and the cask is again filled with water. The ratio of quantity of wine left in the cask to that of water is 25 : 24. How much of mixture can the cask hold?

  1. 26 litres

  2. 21 litres

  3. 25 litres

  4. 32 litres

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

Let the capacity be V. After two replacements of 6 litres, the wine remaining is V * (1 - 6/V)^2. The ratio of wine to water is 25:24, so wine is 25/49 of the total volume. V * (1 - 6/V)^2 = (25/49) * V. (1 - 6/V)^2 = 25/49. 1 - 6/V = 5/7. 6/V = 2/7. V = 21.