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

From a vessel containing 60 litres of pure wine, 4 litres are drawn out and replaced by water. 4 litres of the mixture is again drawn out and replaced with water. What is the ratio of wine to water in the resultant mixture?

  1. 4 : 3

  2. 17 : 4

  3. 196 : 29

  4. 21 : 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Wine remaining = Initial * (1 - 4/60)^2 = 60 * (56/60)^2 = 60 * (14/15)^2 = 60 * 196/225 = 196/3.75 = 52.266. Water = 60 - 52.266 = 7.733. Ratio = 52.266 : 7.733 = 196 : 29.

Multiple choice

A shopkeeper mixed some sugar costing Rs. 40 per kg with 40 kg of sugar costing Rs. 32 per kg. If he earned a profit of 20% by selling the mixture at Rs. 43.2 per kg, then how much quantity of sugar costing Rs. 40 did he mix?

  1. 35 kg

  2. 37 kg

  3. 40 kg

  4. 45 kg

  5. 47 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the quantity of sugar at Rs 40. Total cost = 40x + 40 * 32 = 40x + 1280. Selling price = 43.2 * (x + 40). Profit is 20 percent, so SP = 1.2 * CP. 43.2(x + 40) = 1.2(40x + 1280). 43.2x + 1728 = 48x + 1536. 192 = 4.8x, so x = 40.

Multiple choice

There is a 30 litre solution of milk and water in which milk forms 60%. How much water must be added to this solution to make it a solution in which the quantity of milk and water is equal?

  1. 6 litres

  2. 5 litres

  3. 7 litres

  4. 10 litres

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

Initial solution has 18L milk and 12L water. To make them equal (50/50), the final amount of water must equal the amount of milk (18L). Since there is already 12L of water, we need to add 18 - 12 = 6L.

Multiple choice

Ritesh deliberately mixed 3 litres of water with 8 litres of milk. Find the amount of mixture that should be replaced by water such that the quantity of milk and water is equal in the final mixture.

  1. 4.2 litres

  2. 3.43 litres

  3. 2.76 litres

  4. 5.54 litres

  5. 4.98 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial: 8 milk, 3 water (Total 11). We want equal parts (5.5 milk, 5.5 water). Replacing x litres of mixture (which is 8/11 milk and 3/11 water) with x litres of water: New milk = 8 - (8/11)x = 5.5. (8/11)x = 2.5. x = 2.5 * 11 / 8 = 3.4375.

Multiple choice

A milk trader has two containers of milk. The first contains 25% water and the rest is milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 14 litres of mixture such that the ratio of water to milk is 3 : 4?

  1. 4 and 10

  2. 6 and 8

  3. 7 and 7

  4. 8 and 6

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

Container 1: 25% water (ratio 1:3). Container 2: 50% water (ratio 1:1). Target: 3:4 water to milk (ratio 3:4). Using alligation on water fraction: 1/4 and 1/2, target 3/7. (1/2 - 3/7) : (3/7 - 1/4) = (1/14) : (5/28) = 2 : 5. Total 7 parts = 14 litres, so 1 part = 2 litres. Amounts are 4 and 10.