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

Several liters of acid were drawn off 54-liter vessel full of acid and an equal amount of water was added. Again, the same volume of the mixture was drawn off and replaced by water. As a result, the vessel contained 24 liters of pure acid. How much of the acid was drawn off initially?

  1. 12 lts

  2. 16lts

  3. 15lts

  4. 18lts

  5. 24lts
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x be the amount drawn off. The concentration of acid after two replacements is 54 * (1 - x/54)^2 = 24. (1 - x/54)^2 = 24/54 = 4/9. 1 - x/54 = 2/3. x/54 = 1/3. x = 18.

Multiple choice

Mr. X mixed 10 kg of variety A rice with 15 kg of variety B rice and sold the mixture at a price 40% more than that of A. He did not get any profit. What is the ratio of the cost price of variety A to that of B per kg?

  1. 2:5

  2. 3:5

  3. 4:5

  4. 5:8

  5. 6:8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let CP of A be x and B be y. Total cost = 10x + 15y. Total weight = 25 kg. Selling price per kg = (10x + 15y) / 25. Selling price = 1.4x. So, (10x + 15y) / 25 = 1.4x. 10x + 15y = 35x. 15y = 25x. x/y = 15/25 = 3/5.

Multiple choice

A Jar contains 30 liters mixture of Milk and Water in the ratio of x:y respectively. When 10 liter of the mixture is taken out and replaced it water, then the ratio becomes 2:3. Then what is the initial quantity of Milk in the Jar?

  1. 12 litres

  2. 15 litres

  3. 18 litres

  4. 20 litres

  5. 16 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial 30L, ratio x:y. After removing 10L, 20L remains. Replacing with 10L water means 20L mixture + 10L water = 30L. Final ratio M:W = 2:3. So Milk = (2/5)*30 = 12L. This 12L was in the 20L remaining mixture. Before removing 10L, the ratio was the same. In 30L, Milk = (12/20)*30 = 18L.

Multiple choice

Ratio of Milk and water in Vessel A is 7:4 and same mixture in the ratio of 5:3, 22 litters mixture from vessel A taken out and poured in vessel B new ratio of milk to water is 27:16. If new quantity of mixture in vessel B is equal to initial quantity of mixture in vessel A, then find quantity of Milk after 8 litters of mixture has been taken out from Vessel A?

  1. 200/29 liters

  2. 546 / 11 liters

  3. 120/13 liters

  4. 220/19 liters

  5. 200/11 liters
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Ajay pays Rs 8.0 per litter of spirit. He adds water and sells the mixture at Rs 9 per litter, thereby making 40 % profit. The proportion of water to spirit received by the customers is?

  1. 45:11

  2. 11:45

  3. 2:45

  4. 45:2

  5. 11:2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A 40% profit means the cost of each litre of mixture is 9/1.4 = 45/7 rupees. Since spirit costs Rs. 8 per litre, the spirit fraction is 45/56 and the water fraction is 11/56, giving water to spirit as 11:45.

Multiple choice

A cistern contains 100 liters of water. 10 liters of water is taken out of it and replaced by the same quantity of soda. This process is repeated one more time. After those 20 liters of the solution is replaced by the same quantity of whiskey. Find the proportion of soda, water, and whiskey in the final mixture?

  1. 19: 71: 25

  2. 38: 72: 50

  3. 19: 81: 25

  4. 38: 81: 50

  5. 29: 71: 25
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial: 100W. Step 1: 90W, 10S. Step 2: 90 * 0.9 = 81W, 10 + 9 = 19S. Step 3: 20L of solution removed. Amount of water removed = 20 * (81/100) = 16.2. Amount of soda removed = 20 * (19/100) = 3.8. Remaining: Water = 81 - 16.2 = 64.8, Soda = 19 - 3.8 = 15.2, Whiskey = 20. Ratio 15.2 : 64.8 : 20 = 152 : 648 : 200 = 19 : 81 : 25.

Multiple choice

A jar contains 'x' litters of Milk, a seller withdraws 25 liters of it and sells it at Rs.20 per liter. He then replaces it water. He repeated the process total three times. Every time while selling he reduces selling price by Rs.2. After this process Milk left in the mixture is only 108 litters so he decided to sell the entire Mixture at Rs. 15 per liter. Then how much profit did he earned if bought Milk at Rs.20 per liter?

  1. Rs. 50

  2. Rs.70

  3. Rs.90

  4. Rs.60

  5. Rs.100
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

How many kilograms of sugar of Rs.5.4 per kg should be mixed with 10 kg of sugar of Rs.4.5 per kg, such that there may be gain of 20% by selling the mixture at Rs.5.94 per kg.

  1. 10 kg

  2. 12 kg

  3. 15 kg

  4. 8 kg

  5. 9 kg
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be the kg of sugar at 5.4. Total cost = 5.4x + 4.5*10. Selling price for 20% gain = 1.2 * (5.4x + 45) / (x + 10) = 5.94. Solving this: 6.48x + 54 = 5.94x + 59.4, which gives 0.54x = 5.4, so x = 10 kg.

Multiple choice

In a 250 liter of a mixture of Milk and Water, Water is X%. The milkman sold 50 litters of the mixture and replaced same quantity with water. If the percent of Milk in final mixture is 64%, then what is the percentage of Milk in the initial mixture?

  1. 20%

  2. 40%

  3. 60%

  4. 80%

  5. 50%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial: 250L, Milk = (100-X)%, Water = X%. Sold 50L, remaining 200L. Replaced 50L with water. Total 250L. Final Milk % = 64%. Amount of milk = 250 * 0.64 = 160L. The 50L removed contained (100-X)% milk. So 250 * (100-X)/100 - 50 * (100-X)/100 = 160. 200 * (100-X)/100 = 160. 2 * (100-X) = 160. 100-X = 80. X = 20. Initial milk = 100-20 = 80%.

Multiple choice

Two vessels A and B contain mixtures of spirit and water. A mixture of 3 parts from A and 2 parts from B is found to contain 29% of spirit and a mixture of 1 part from A and 9 parts from B is found to contain 34 per cent of spirit. Find the percentage of spirit in A and B?

  1. 35, 25

  2. 40, 20

  3. 25, 35

  4. 35,20

  5. 50, 50
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A = x, B = y. (3x + 2y)/5 = 29 => 3x + 2y = 145. (x + 9y)/10 = 34 => x + 9y = 340. Solving this system: x = 340 - 9y. 3(340 - 9y) + 2y = 145 => 1020 - 27y + 2y = 145 => 25y = 875 => y = 35. Then x = 340 - 315 = 25.

Multiple choice

Three bottles contain equal mixtures of spirit and water in the ratio 6 : 1, 5 : 2 and 3 : 1 respectively. If all the solutions are mixed together, the ratio of spirit to water in the final mixture will be?

  1. 64: 65

  2. 65: 64

  3. 19: 65

  4. 65:19

  5. 19: 64
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The ratios are 6:1 (total 7), 5:2 (total 7), 3:1 (total 4). To mix equal volumes, find a common multiple of 7 and 4, which is 28. Multiply ratios: 6:1 becomes 24:4, 5:2 becomes 20:8, 3:1 becomes 21:7. Summing spirit: 24+20+21 = 65. Summing water: 4+8+7 = 19. The ratio is 65:19.