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

Equal quantities of three mixtures of milk and water are mixed in the ratios 1 : 2, 2 : 3 and 3 : 4. The ratio of water to milk in the mixture is

  1. 193 : 122

  2. 97 : 102

  3. 115 : 201

  4. 147 : 185
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ratios are 1:2, 2:3, 3:4. Sums are 3, 5, 7. To mix equal quantities, multiply by LCM(3,5,7) = 105. Ratios become 35:70, 42:63, 45:60. Total milk = 35+42+45 = 122. Total water = 70+63+60 = 193. Ratio of water to milk = 193:122.

Multiple choice

Deepak has 8 litres of apple wine and 5 litres of grape wine. He accidentally spills some quantity of apple wine and adds an equal quantity of grape wine in it before anyone could see, after which his father mixes the two and finds the ratio of apple wine to grape wine as 7 : 5. Find the quantity of apple wine spilled by Deepak.

  1. 0.532 L

  2. 0.416 L

  3. 0.864 L

  4. 1.256 L

  5. 0.724 L
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the amount spilled. Apple wine remaining = 8 - x. Grape wine = 5 + x. Ratio (8 - x) / (5 + x) = 7/5. 40 - 5x = 35 + 7x. 5 = 12x, so x = 5/12 = 0.4166... L.

Multiple choice

A mixture contains orange juice and apple juice in the ratio 4 : 3, respectively. How much apple juice should be added to the mixture so that the ratio becomes 3 : 4? It is given that the quantity of orange juice present in the mixture is 12 litres.

  1. 6 litres

  2. 7 litres

  3. 8 litres

  4. 9 litres

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

Orange juice = 12L. Ratio 4:3 means apple juice = (12/4)*3 = 9L. Let x be added apple juice. New ratio (12) : (9+x) = 3:4. So 12/ (9+x) = 3/4. 48 = 27 + 3x, 3x = 21, x = 7.

Multiple choice

Kanika was on a diet, so she started drinking a mixture containing lemon water and honey in the ratio of 5 : 3. If 2 litres of honey is added to it, then the ratio of lemon water and honey becomes 7 : 5. Find the quantity of lemon water in the mixture.

  1. 15.5 litres

  2. 17.5 litres

  3. 13.5 litres

  4. 14.5 litres

  5. 16.5 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let lemon water be 5x and honey be 3x. Adding 2 litres of honey makes the ratio 5x / (3x + 2) = 7/5. Solving for x gives 25x = 21x + 14, so 4x = 14 and x = 3.5. The quantity of lemon water is 5 * 3.5 = 17.5 litres.

Multiple choice

Two beakers A and B, both contain two solutions, ethanol and methanol, in the ratio 14 : 6 and 4 : 6, respectively. If the contents of these two beakers are mixed together in a third beaker, such that the new mixture in the third beaker is in the ratio 6 : 4, then find the ratio in which the content of both the beakers A and B must be mixed, respectively.

  1. 1 : 2

  2. 1 : 3

  3. 2 : 1

  4. 3 : 2

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

Beaker A ratio is 14:6 (7:3), Beaker B is 4:6 (2:3). Let the mixture ratio be x:y. Using the allegation method on the ethanol fraction: (7/10)x + (2/5)y = (6/10)(x+y). This simplifies to 0.7x + 0.4y = 0.6x + 0.6y, leading to 0.1x = 0.2y, or x/y = 2/1.

Multiple choice

10 g of ice at 0°C is mixed with 100 g of water at 50°C. What is the resultant temperature of the mixture? (Given: Specific heat of water = 1 cal/gram/°C; Latent heat of ice = 80 cal/gram)

  1. 31.2°C

  2. 32.8°C

  3. 36.7°C

  4. 38.2°C
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Heat lost by water = heat gained by ice to melt + heat gained by melted ice to reach final temp. 100 * 1 * (50 - T) = 10 * 80 + 10 * 1 * (T - 0). 5000 - 100T = 800 + 10T. 4200 = 110T, so T = 38.18 degrees Celsius.

Multiple choice

A 2.0 g mixture of Na2CO3 and NaHCO3 suffered a loss of 0.12 g on heating. The percentage of Na2CO3 in the mixture was

  1. 83.8%

  2. 16.1%

  3. 38.8%

  4. 61.2%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Only NaHCO3 decomposes on heating: 2NaHCO3 -> Na2CO3 + H2O + CO2. The mass loss is due to H2O and CO2. Molar mass of 2NaHCO3 is 168 g/mol, and the loss is 62 g. Loss = 0.12g implies 0.12 * (168/62) = 0.325g of NaHCO3. Na2CO3 = 2.0 - 0.325 = 1.675g. Percentage = (1.675/2.0) * 100 = 83.75%.

Multiple choice

There are three bottles of mixture of syrup and water of ratios 2 : 3, 3 : 4 and 7 : 5. 10 litres of the first and 21 litres of the second bottle are taken. How much quantity from the third bottle is to be taken so that the final mixture from the three bottles will be of ratio 1 : 1?

  1. 25 litres

  2. 20 litres

  3. 35 litres

  4. 30 litres
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x be the quantity taken from the third bottle. Syrup/Water ratios are 2/5, 3/7, 7/12. Total syrup = 10*(2/5) + 21*(3/7) + x*(7/12) = 4 + 9 + 7x/12 = 13 + 7x/12. Total water = 10*(3/5) + 21*(4/7) + x*(5/12) = 6 + 12 + 5x/12 = 18 + 5x/12. Since the final ratio is 1:1, 13 + 7x/12 = 18 + 5x/12. Solving for x: 2x/12 = 5, so x/6 = 5, x = 30.

Multiple choice

Alloy 'A' contains 60% zinc, 25% copper and 15% tin. Alloy 'B' contains 70% zinc, 20% copper and 10% tin. These two alloys are mixed together such that the resultant alloy contains 12% tin. What is the ratio of zinc to copper in the resultant alloy?

  1. 2 : 1

  2. 3 : 1

  3. 4 : 3

  4. 5 : 3

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

Let x and y be the amounts of alloy A and B. Tin: 0.15x + 0.10y = 0.12(x+y). 0.03x = 0.02y, so x/y = 2/3. Zinc: 0.60x + 0.70y = 0.60(2) + 0.70(3) = 1.2 + 2.1 = 3.3. Copper: 0.25x + 0.20y = 0.25(2) + 0.20(3) = 0.5 + 0.6 = 1.1. Ratio of zinc to copper = 3.3 / 1.1 = 3:1.

Multiple choice

The ratios of water and milk in two containers A and B are 4 : 3 and 2 : 3, respectively. To obtain a new mixture in a container C consisting water and milk in the ratio 1 : 1, the liquids in both the containers A and B should be mixed in what ratio?

  1. 7 : 3

  2. 7 : 5

  3. 5 : 3

  4. 5 : 2

  5. 3 : 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the amount from A and y be the amount from B. Water in A = 4/7, Milk in A = 3/7. Water in B = 2/5, Milk in B = 3/5. (4/7x + 2/5y) / (3/7x + 3/5y) = 1/1. 4/7x + 2/5y = 3/7x + 3/5y. 1/7x = 1/5y. x/y = 7/5.

Multiple choice

A milkman is selling milk for Rs. 25 per litre at no profit or loss. Determine the ratio in which he should mix water with milk so that on selling it for Rs. 20 per litre, he can earn a profit of 25%.

  1. Milk : Water = 12 : 5

  2. Milk : Water = 16 : 9

  3. Milk : Water = 13 : 7

  4. Milk : Water = 3 : 2

  5. Milk : Water = 1 : 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Selling price = 20. Profit = 25%. Cost price = 20 / 1.25 = 16. The milkman sells pure milk at 25, but the mixture is effectively costed at 16. Using the allegation rule: (25-16) / (16-0) = 9/16. Ratio of water to milk is 9:16, so Milk:Water = 16:9.

Multiple choice

A solution of 100 litres of mud and water contains 70% water. If the concentration of water is increased to 75%, what is the final quantity of the solution after some more water is added?

  1. 120 litres

  2. 120 millilitres

  3. 20 litres

  4. 20 millilitres

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

Initial water = 70 litres, mud = 30 litres. After adding water, mud remains 30 litres, which is now 25% of the total. 0.25 * Total = 30, so Total = 120 litres.

Multiple choice

A' bought 20 kg of sugar at the rate of Rs. 8.50 per kg and 30 kg of sugar at the rate of Rs. 9.75 per kg. He mixed the two. At what price per kg should he sell the mixture to get 25% profit on the cost price?

  1. Rs. 11.56

  2. Rs. 12.50

  3. Rs. 10.50

  4. Rs. 10.00
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total cost = (20 * 8.50) + (30 * 9.75) = 170 + 292.5 = 462.5. Total weight = 50 kg. Cost per kg = 462.5 / 50 = 9.25. To get 25% profit, selling price = 9.25 * 1.25 = 11.5625.