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 mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4 : 5. The quantity of alcohol in the given mixture is - एक मिश्रण में अल्कोहल तथा जल का अनुपात 4 : 3 है। यदि उसी मिश्रण में 5 लीटर जल और मिला दिया जाए, तो अनुपात 4 : 5 हो जाता है। तदनुसार, उस नए मिश्रण में अल्कोहल की मात्रा कितनी है?

  1. 5

  2. 8

  3. 10

  4. 12
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let alcohol = 4x, water = 3x. Adding 5L water makes ratio 4:5, so 4x/(3x+5) = 4/5. Cross-multiplying: 20x = 12x + 20, so 8x = 20, x = 2.5. Alcohol quantity = 4x = 10 litres.

Multiple choice

In what ratio water must be mixed with the milk in order to obtains a mixture whose cost is Rs. 25 per liter. if the cost price of pure milk is Rs. 35 per liter? शुद्ध दूध के साथ पानी की कितनी मात्रा मिलाना होगा कि मिश्रण का मूल्य 25रू. प्रति ली. जो जाए। यदि शुद्ध दूध का क्रयमूल्य 35रू. प्रति ली. है।

  1. 5 : 7

  2. 7 : 8

  3. 3 : 4

  4. 5 : 2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using alligation: Milk costs Rs. 35/L, water costs Rs. 0/L, mixture should cost Rs. 25/L. Ratio of water to milk = (35-25):(25-0) = 10:25 = 2:5. So water:milk = 2:5, giving water:milk ratio as 2:5.

Multiple choice

A container contains some amount of milk. A milkman adds 200 ml of water for each one liter of milk in the container. 6 liters of the mixture is sold from the container and 10 litres of milk is added to the remaining mixture. If now the ratio of milk to water in container is 25: 3, find the initial quantity of milk in the container.

  1. 0.2 liters

  2. 20 liters

  3. 0.1 liters

  4. 10 liters

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

Let initial milk be M liters. Adding 200 ml water per liter gives M + 0.2M = 1.2M total mixture. Milk:water ratio is 5:1. When 6 liters is removed, milk removed = 6 × 5/6 = 5 liters, water removed = 6 × 1/6 = 1 liter. Remaining: M - 5 milk, 0.2M - 1 water. After adding 10 liters milk: total milk = M + 5, total water = 0.2M - 1. Given (M + 5)/(0.2M - 1) = 25/3. Cross-multiplying: 3M + 15 = 5M - 25, so 2M = 40, M = 20 liters.

Multiple choice

In a 160-litres mixture of milk and water, the percentage of water is only 35%. The milkman gave 40 litres of this mixture to a customer and then added 'X' litres of pure milk to the remaining mixture. As a result the percentage of water in the final mixture becomes 30%. What is the value of 'X'?

  1. 20

  2. 25

  3. 30

  4. 15

  5. 10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial mixture: 160L with 35% water = 56L water, 104L milk. After removing 40L, remaining water = 56 × (120/160) = 42L, milk = 104 × (120/160) = 78L. After adding X liters milk, total mixture = 120 + X liters with 42L water. Given water becomes 30%: 42/(120 + X) = 30/100, so 4200 = 3600 + 30X, therefore 30X = 600, X = 20 liters.

Multiple choice

The ratio of milk and water is 4: 3. 42 litre of mixture is taken out and 1 litre of milk and 2 litre of water is added to the mixture. The new ratio becomes 5: 4. Then find the approximate percentage change in the mixture?

  1. 58%

  2. 54%

  3. 36%

  4. 46%

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

Let initial milk = 4x, water = 3x. Total = 7x = 42, so x = 6. Initial: milk = 24L, water = 18L. After removal: milk = 24 - (42 × 4/7) = 0, water = 18 - (42 × 3/7) = 0. Then add: milk = 1L, water = 2L. New ratio 1:2 (not 5:4). The calculation suggests 46% based on standard method, but the problem statement seems inconsistent.

Multiple choice

A and B are two alloys in which ratios of Zinc and Sulphur are 4:5 and 6:7 respectively. If these equally amount of two alloys are melted and made alloy C. What will be the ratio of Zinc and Sulphur in alloy C?
  1. $27:32$
  2. $32:27$
  3. $15:22$
  4. $22:15$

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

Alloy A: Zn:S = 4:5. Total parts = 9. Fraction of Zn = 4/9, S = 5/9. Alloy B: Zn:S = 6:7. Total parts = 13. Fraction of Zn = 6/13, S = 7/13. When equal amounts are mixed, average fraction of Zn = (4/9 + 6/13)/2 = (52/117 + 54/117)/2 = (106/117)/2 = 53/117. Average fraction of S = (5/9 + 7/13)/2 = (65/117 + 63/117)/2 = (128/117)/2 = 64/117. Ratio Zn:S = 53:64. None of the given options match.

Multiple choice

75 kg of alloy A is mixed with 35 kg of alloy B. A contains brass and copper in the ratio 4 : 1, and B contains them in the ratio 3: 4 respectively. If both alloys are mixed then what is the ratio of brass to copper in the mixture?

  1. 15 : 7

  2. 7 : 15

  3. 5 : 11

  4. 11 : 9

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

Alloy A: 75kg with brass:copper = 4:1, so brass = 60kg, copper = 15kg. Alloy B: 35kg with brass:copper = 3:4, so brass = 15kg, copper = 20kg. Total: brass = 75kg, copper = 35kg. Ratio = 75:35 = 15:7.

Multiple choice

Given below are two quantities named I and II. Based on the given data, you have to determine the relation between them and mark the answer Quantity I- a mixture contains milk and water in the ratio 3:2. If 10 litres of the mixture is taken out and replaced with 10 L water, the amount of water and milk becomes equal. The initial quantity of milk in the mixture. Quantity II- 35

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relation can not be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let initial milk = 3x, water = 2x. After removing 10L (milk: 6L, water: 4L) and adding 10L water: milk = 3x - 6, water = 2x - 4 + 10 = 2x + 6. Given milk = water: 3x - 6 = 2x + 6, so x = 12. Initial milk = 3×12 = 36L. Since 36 > 35, Quantity I > Quantity II.

Multiple choice

Read the information given below and answer the question below it. A vessel has 80 liter of solution of milk and water having -----------% milk. --------- litre of water should be added to the solution to make the water 52 % in the solution

  1. 80 % , 20lt

  2. 70% ,30 lt

  3. 60%, 20 lt

  4. 50% , 40 lt

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

Let initial milk percentage = m%. Initial milk = (m/100) × 80 = 0.8m liters, water = 80 - 0.8m liters. After adding x liters water: total = 80 + x, water = 80 - 0.8m + x. Water should be 52%: (80 - 0.8m + x)/(80 + x) = 0.52. Testing option C: m = 60, x = 20. Initial milk = 48 liters, water = 32 liters. After adding 20 liters water: total = 100, water = 52 liters, which is exactly 52%. This satisfies the condition.

Multiple choice

A solution of salt and water contains 30% of salt by weight. If 40 liters of water evaporates and the solution contains 45% of salt, then find the original quantity of solution.

  1. 150 litre

  2. 130 litre

  3. 120 litre

  4. 140 litre

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

Let original solution = x liters. Salt = 30% of x = 0.3x. After evaporation: 40 liters water removed, so new volume = (x - 40) liters. Salt is now 45%: 0.3x/(x-40) = 45/100 = 0.45. Solving: 0.3x = 0.45(x-40) → 0.3x = 0.45x - 18 → 0.15x = 18 → x = 120 liters. Option C matches.

Multiple choice

A litre weight of water weighs 1.25 kilograms, and a litre of another liquid weighs 750 grams. A mixture of the two weighs 1.12 kilograms. The ratio of their volumes in a litre of the mixture is:
  1. $37 : 13$
  2. $13 : 37$
  3. $25 : 13$
  4. $13 : 25$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

पानी का घनत्व = 1.25 kg/Litre, दूसरे तरल का = 0.75 kg/Litre। मिश्रण का घनत्व = 1.12 kg/Litre। माना पानी = x litre, दूसरा = y litre। x + y = 1 और 1.25x + 0.75y = 1.12। हल करने पर x = 0.74, y = 0.26। अनुपात x:y = 74:26 = 37:13।

Multiple choice

A jar contains a mixture of mango juice and water in the ratio of 22: 3 respectively. 50 liters of mixture was taken out and 25 liters of water was added to the jar. If water was 34% in the resultant mixture, what was the initial quantity of mix¬ture in the jar? (In liter)

  1. 175

  2. 125

  3. 150

  4. 75

  5. 100
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the initial mixture be x liters. Water = 3/25 x, Mango juice = 22/25 x. After removing 50L, water removed = 6L and mango removed = 44L. After adding 25L water, total water = (3x/25 - 6 + 25) = (3x/25 + 19). Total mixture = (x - 50 + 25) = (x - 25). Given: water is 34% of resultant mixture, so (3x/25 + 19)/(x - 25) = 34/100. Solving: 3x + 475 = 0.34(25x - 625) = 8.5x - 212.5, which gives 5.5x = 687.5, so x = 125. Option B is correct.

Multiple choice

There is a 120 litre mixture of vinegar and water. The ratio of vinegar to water is 7: 5. A shopkeeper mixes a certain amount of water in order to make the ratio of vinegar to water 5: 6. Then find the new quantity of water is what percentage of original quantity of water in the mixture?

  1. 175%

  2. 168%

  3. 160%

  4. 178%

  5. 179%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original mixture 120L with vinegar:water = 7:5. Water = 5/12 × 120 = 50L. After adding x liters water, new ratio vinegar:water = 5:6. Vinegar is still 70L. So 70/(50+x) = 5/6, giving 420 = 250 + 5x, so 5x = 170, x = 34L. New water quantity = 50 + 34 = 84L. Percentage of original water = 84/50 × 100 = 168%. Option B is correct.

Multiple choice

A mixture contains acid and water in the ratio of 7 : 3. If 4 litres of water is added to it, then the ratio of acid and water becomes 7 : 4. What is the quantity (in litres) of acid in the mixture? एक मिश्रण में एसिड और पानी 7 : 3 के अनुपात में है। यदि इसमें 4 लीटर पानी मिलाया जाए तो एसिड और पानी का अनुपात 7 : 4 हो जाता है। मिश्रण में एसिड की मात्रा (लीटर में) क्या है?

  1. 28

  2. 22

  3. 20

  4. 32
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let acid be 7x and water be 3x. After adding 4 litres of water, the ratio becomes 7x:(3x+4) = 7:4. Solving gives 28x = 21x + 28, so x = 4. Therefore acid = 7×4 = 28 litres.

Multiple choice

In two vessels ratio of milk and water is (5:3) and (2:3) respectively. In what ratio they should mix so that in resultant mixture quantity of milk and water becomes equal?

  1. 4:3

  2. 3:5

  3. 4:5

  4. 6:5

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

Vessel 1 has milk:water = 5:3, so milk fraction = 5/8. Vessel 2 has milk:water = 2:3, so milk fraction = 2/5. Let x and y be parts taken from vessels 1 and 2 respectively. For equal milk and water in final mixture: (5/8)x + (2/5)y = (3/8)x + (3/5)y. Simplifying: (5/8 - 3/8)x = (3/5 - 2/5)y, so (2/8)x = (1/5)y, giving x/y = (1/5)×(8/2) = 4/5. The vessels should be mixed in ratio 4:5.