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

Keshto stole wine from a butt of sherry which contained 48% of spirit and then replaced what he stole by wine containing only 27% spirit. The butt was then of 34% strength only. How much portion of the butt had Keshto stolen ?

  1. 1/3

  2. 2/3

  3. 1/2

  4. 1/6
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the alligation rule: (48-34) / (34-27) = 14 / 7 = 2. This means 2 parts of the original were replaced by 1 part of the new mixture, so 2/3 of the total was replaced.

Multiple choice

[CAT 1998] There are two containers: the first contains 500 ml of alcohol, while the second contains 500 ml of water. Three cups of alcohol from the first container is taken out and is mixed well in the second container. Then three cups of this mixture is taken out and is mixed in the first container. Let A denote the proportion of water in the first container and B denote the proportion of alcohol in the second container. Then

  1. A > B

  2. A < B

  3. A = B

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the cup size be c. Container 1: 500ml alcohol. Container 2: 500ml water. After moving 3 cups (3c) of alcohol to container 2, container 2 has 500ml water + 3c alcohol. The mixture is 3c/(500+3c) alcohol. Moving 3c of this mixture back to container 1: container 1 now has (500-3c) alcohol + 3c * (3c/(500+3c)) alcohol and 3c * (500/(500+3c)) water. The proportion of water in container 1 is A = (1500c/(500+3c)) / 500 = 3c/(500+3c). The proportion of alcohol in container 2 is B = (3c - 3c * (3c/(500+3c))) / 500 = (1500c+9c^2-9c^2)/(500(500+3c)) = 3c/(500+3c). Thus A = B.

Multiple choice

A container contains V litres solution of milk and water in the ratio 3 : 2. If 10 litres of water is added and the concentration of milk in the resultant solution lies between 50% and 40%, find the range of values of V.

  1. 50 < V < 60

  2. 20 < V < 50

  3. 30 < V < 40

  4. Insufficient data

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

Initial milk is 0.6V, water is 0.4V. After adding 10L water, total volume is V+10. Milk concentration is 0.6V / (V+10). Setting 0.4 < 0.6V/(V+10) < 0.5 leads to 0.4V + 4 < 0.6V < 0.5V + 5. Solving 0.4V + 4 < 0.6V gives V > 20. Solving 0.6V < 0.5V + 5 gives V < 50.

Multiple choice

In the solution of water and sugar, the ratio of sugar to water is 3:5. If 30% of this solution is taken out and 5% of the initial quantity of solution is added as water to the remaining quantity of the mixture than find the new ratio of sugar and water in new solution.

  1. 6:13

  2. 3:7

  3. 7:13

  4. 4:7

  5. 1:2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial ratio 3:5 means 3/8 sugar and 5/8 water. Removing 30% leaves 70% of the mixture. Adding 5% of initial quantity as water changes the proportions. After calculation, the new ratio of sugar to water is 7:13.

Multiple choice

A wholesaler bought walnuts and peanuts with the price of walnuts per kg being thrice that of peanuts per kg. He then sold 8 kg of peanuts at a profit of 10% and 16 kg of walnuts at a profit of 20% to a shopkeeper. However, the shopkeeper lost 5 kg of walnuts and 3 kg of peanuts in transit. He then mixed the remaining nuts and sold the mixture at Rs. 166 per kg, thus making an overall profit of 25%. At what price (in Rs. per kg) did the wholesaler buy the walnuts?

  1. 96

  2. 86

  3. 98

  4. 84
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the price of peanuts be x and walnuts be 3x. Calculate total cost, total quantity after losses, and equate the final selling price to the 25% profit condition. Solving for x gives the price of walnuts as 96.

Multiple choice

Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio

  1. 17 : 25

  2. 19 : 24

  3. 18 : 25

  4. 21 : 25
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let CP of A be a and B be b. SP = 40. Profit 10% means CP = 40/1.1 = 400/11. (3a+2b)/5 = 400/11 => 33a+22b = 2000. Profit 5% means CP = 40/1.05 = 4000/105 = 800/21. (2a+3b)/5 = 800/21 => 42a+63b = 4000. Solving this system gives a/b = 19/24.

Multiple choice

A trader sells 10 litres of a mixture of paints A and B, where the amount of B in the mixture does not exceed that of A. The cost of paint A per litre is Rs. 8 more than that of paint B. If the trader sells the entire mixture for Rs. 264 and makes a profit of 10%, then the highest possible cost of paint B (in Rs. per litre) is

  1. 16

  2. 20

  3. 22

  4. 26
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total SP = 264, Profit = 10%, so Total CP = 264 / 1.1 = 240. Let x be cost of B, then A is x+8. Let q be quantity of B, then 10-q is quantity of A. q <= 10-q, so 2q <= 10, q <= 5. Total CP = q(x) + (10-q)(x+8) = 240. qx + 10x + 80 - qx - 8q = 240. 10x - 8q = 160. x = (160 + 8q) / 10 = 16 + 0.8q. To maximize x, maximize q. Max q = 5. x = 16 + 0.8(5) = 16 + 4 = 20.

Multiple choice

In a milk tank the quantity of milk is 40% more thanwater. If 31 litres of water is added to this mixture, thenfinal ratio of milk and water is 5 : 8. Find the initial quantityof milk.

  1. 35 litres

  2. 45 litres

  3. 30 litres

  4. 40 litres

  5. 48 litres
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the initial quantity of water be w litres, so milk is 1.4w litres. After adding 31 litres of water, 1.4w/(w + 31) = 5/8, which gives w = 25. Therefore, the initial quantity of milk was 1.4 × 25 = 35 litres.

Multiple choice

A mixture of milk and water contains 60% milk. If 20% ofthe mixture is taken out, then the quantity of water in theresultant mixture becomes 48 litres. Find the initial quantityof mixture

  1. 120 litres

  2. 150 litres

  3. 100 litres

  4. 180 litres

  5. 200 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture: 60% milk, 40% water. Removing 20% of the mixture leaves 80% of the original volume. Water remaining = 0.8 * (0.4 * Total) = 48. 0.32 * Total = 48. Total = 48 / 0.32 = 150 litres.

Multiple choice

From a jar of wine containing 32 litres, 4 litres is drawn out, and the jar is filled up with water. If the same proportion of wine is further drawn out two more times, what proportion of wine to water will be there in the resulting mixture?

  1. 245 : 166

  2. 343 : 169

  3. 363 : 173

  4. 323 : 189
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The proportion of wine remaining after n operations is (1 - x/V)^n. Here, V=32, x=4, n=3. Remaining wine = 32 * (1 - 4/32)^3 = 32 * (7/8)^3 = 32 * 343/512 = 343/16. The amount of water is 32 - 343/16 = (512-343)/16 = 169/16. The ratio of wine to water is 343:169.

Multiple choice

If a 50 liters mixture of milk and water is in theratio of 3 : 2. After removal of 10 liters mixture, 12liters milk and 12 liters water is added into themixture. Find the final ratio of water and milk in themixture.

  1. 9 : 7

  2. 7 : 9

  3. 3 : 2

  4. 2 : 3

  5. 1 : 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial: 50L, ratio 3:2 (30L milk, 20L water). Remove 10L mixture (6L milk, 4L water). Remaining: 24L milk, 16L water. Add 12L each: 36L milk, 28L water. Ratio water:milk = 28:36 = 7:9.

Multiple choice

In a mixture of 171 litres, the ratio of the milkand water is 2:1, respectively. If „x‟ litres of water isadded in the mixture, then the ratio of milk to waterbecomes 3:2. Find the value of „x‟.

  1. 19 litres

  2. 28 litres

  3. 32 litres

  4. 24 litres

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

Initial mixture: 171 liters, ratio 2:1 means 114L milk and 57L water. Adding x liters of water makes the ratio 3:2, so 114 / (57 + x) = 3 / 2. Solving 228 = 171 + 3x gives 3x = 57, so x = 19.