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 contains a mixture of milk and water in the ratio of 3 : 7. If 20 litres of the mixture is replaced with water, the ratio of milk to water becomes 1 : 4. What was the initial quantity of the mixture in the container?

  1. 30 litres

  2. 40 litres

  3. 50 litres

  4. 60 litres
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let initial milk = 3x, water = 7x. Total = 10x. Removing 20L of mixture removes 6L milk and 14L water. New milk = 3x - 6, new water = 7x - 14 + 20 = 7x + 6. (3x-6)/(7x+6) = 1/4. 12x - 24 = 7x + 6. 5x = 30, x = 6. Initial total = 10x = 60.

Multiple choice

Container 'A' contains milk and water in the ratio of 4 : 1. Container 'B' has the same mixture in the ratio of 3 : 1. What minimum quantity of mixture in container 'A' should to be added to 10 litres of mixture in container 'B' to get a resultant milk concentration of atleast 78%?

  1. 8 litres

  2. 10 litres

  3. 12 litres

  4. 15 litres

  5. 20 litres
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Container B has 7.5 litres of milk in 10 litres of mixture. If x litres from A are added, the milk amount is 7.5 + 0.8x, and the total volume is 10 + x. Solving 7.5 + 0.8x >= 0.78(10 + x) gives x >= 15 litres.

Multiple choice

A green liquid is mixed with a blue liquid in the proportion 4 : 5 and the mixture is sold at Rs. 20 per litre at a 20% profit. If the green liquid costs Rs. 4 more per litre than the blue liquid, what is the approximate cost of the green liquid per litre?

  1. Rs. 16.33

  2. Rs. 18.88

  3. Rs. 17.66

  4. Rs. 19.22
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Selling price = 20, profit = 20%, so Cost Price = 20 / 1.2 = 16.67. Let green liquid cost x, blue cost x-4. Mixture ratio 4:5. (4x + 5(x-4)) / 9 = 16.67. 9x - 20 = 150. 9x = 170, x = 18.88.

Multiple choice

There are three fruit sellers A, B and C. All of them have a mixture of two types of mangoes. A has (a + 6) kg of mangoes, B has 21 kg of mangoes less than A, while C has (a – 10) kg of mangoes. A, B and C have the two types of mangoes in the ratios 3 : 5, 7 : 8 and 9 : 7, respectively. If A sells 24 kg of mixed mangoes and adds 3 kg of the first type of mangoes, then the new ratio becomes 2 : 3 for him. If C adds x kg of the second type of mangoes to his mixture, then the new ratio of both types becomes 9 : 11 for him. What is the value of (a + x)?

  1. 50

  2. 60

  3. 110

  4. 90

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

A = a+6, B = a+6-21 = a-15, C = a-10. A's ratio 3:5 means 3/8 of (a+6) is type 1. After selling 24kg (ratio 3:5, so 9kg type 1, 15kg type 2) and adding 3kg type 1, new ratio 2:3. (3/8(a+6) - 9 + 3) / (5/8(a+6) - 15) = 2/3. Solving for a: (3/8(a+6) - 6) / (5/8(a+6) - 15) = 2/3 => 9/8(a+6) - 18 = 10/8(a+6) - 30 => 1/8(a+6) = 12 => a+6 = 96 => a = 90. C has 80kg, ratio 9:7 (45kg type 1, 35kg type 2). Adding x kg type 2 gives ratio 9:11. 45 / (35+x) = 9/11 => 5 / (35+x) = 1/11 => 35+x = 55 => x = 20. a+x = 90+20 = 110.

Multiple choice

A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?

  1. 2:5

  2. 4:7

  3. 7:1

  4. 9:1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial: 12L milk, 8L water. Remove 10L (ratio 3:2 means 6L milk, 4L water removed). Remaining: 6L milk, 4L water. Add 10L milk: 16L milk, 4L water. Repeat: Remove 10L (ratio 4:1 means 8L milk, 2L water removed). Remaining: 8L milk, 2L water. Add 10L milk: 18L milk, 2L water. Ratio = 18:2 = 9:1.

Multiple choice

A wine bottle contains 60% alcohol and, the remaining, water. A person takes out some amount of wine from the bottle and replaces it with an equal quantity of another wine containing 30% alcohol. As a result, the bottle now contains 40% alcohol. What fraction of the original wine was taken out from the bottle?

  1. 1 4

  2. 1 3

  3. 2 3

  4. 1 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let V be the volume. Using the formula for replacement: Final concentration = Initial * (1 - x/V)^n + Added * (1 - (1 - x/V)^n). Here, 0.40 = 0.60 * (1 - f) + 0.30 * f, where f is the fraction replaced. 0.40 = 0.60 - 0.60f + 0.30f = 0.60 - 0.30f. 0.30f = 0.20, so f = 2/3.

Multiple choice

Three glasses P, Q and R have capacities in the ratio 1 : 2 : 3. All these glasses are completely filled with mixtures of milk and water. The ratio of milk to water in P is 1 : 2, in Q it is 2 : 3 and in R it is 3 : 1. If the content of all three glasses are put into a bigger container, what will be the ratio of milk to water in the container?

  1. 203 : 117

  2. 203 : 157

  3. 172 : 91

  4. 165 : 88
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total capacity ratio 1:2:3. Total units = 6. P: 1/3 milk, 2/3 water. Q: 2/5 milk, 3/5 water. R: 3/4 milk, 1/4 water. Total milk = 1*(1/3) + 2*(2/5) + 3*(3/4) = 1/3 + 4/5 + 9/4 = (20+48+135)/60 = 203/60. Total water = 1*(2/3) + 2*(3/5) + 3*(1/4) = 2/3 + 6/5 + 3/4 = (40+72+45)/60 = 157/60. Ratio = 203:157.

Multiple choice

A blend of paints requires a proportion of 1 part red paint for every 3 parts of blue paint. However, during the preparation of the mixture, Emily erroneously incorporated only one-third of the required amount of red paint according to the ratio. The total volume of the mixture was 40 liters. What is the quantity of red paint that Emily mistakenly introduced into the mixture, measured in liters?

  1. 4 liters

  2. 6 liters

  3. 8 liters

  4. 10 liters

  5. 12 liters
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Vessels P and Q contain mixtures of fruit juice and soda in the ratios 3 : 7 and 5 : 2, respectively. In what ratio should the quantities of mixture be taken from vessels P and Q to form a mixture in which the ratio of fruit juice to soda is 5 : 3?

  1. 5 : 11

  2. 25 : 91

  3. 91 : 25

  4. 15 : 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using alligation on fruit juice: P has 3/10, Q has 5/7. Target is 5/8. |5/7 - 5/8| = 5/56. |3/10 - 5/8| = |12/40 - 25/40| = 13/40. Ratio = (5/56) : (13/40) = (5/7) : (13/5) = 25 : 91.

Multiple choice

In a chemical laboratory, a scientist is working with two solutions, A and B. Solution A contains 30% of Chemical X, and Solution B contains 50% of Chemical X. The scientist needs to create a mixture with 40% of Chemical X. If the scientist mixes 5 litres of Solution A with 3 litres of Solution B, then how much more of Chemical X (in litres) should be added to achieve this concentration in the mixture?

  1. 1 litre

  2. 1 2 litre

  3. 1 3 litre

  4. 1 4 litre

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

Solution A contributes 5 x 0.30 = 1.5 litres of Chemical X, and Solution B contributes 3 x 0.50 = 1.5 litres. The mixture initially contains 3 litres of X in 8 litres, or 37.5%. If x litres of pure X are added, (3 + x)/(8 + x) = 0.40, giving x = 1/3 litre.

Multiple choice

A milkman has 2 varieties of milk-water solution, solution A has 65% pure milk and solution B has 78% pure milk. He is mixing x mL of solution A with y mL of solution B such that the resultant solution has no less than 70% pure milk and no more than 72% pure milk. If y can take any value between 625mL and 630mL, both inclusive, what is the difference between the minimum and maximum value x can take? It is given that x and y are both integers.

  1. 512

  2. 472

  3. 642

  4. 232

  5. 446
Reveal answer Fill a bubble to check yourself
B Correct answer