Practice Quantitative Aptitude questions on Alligation and Mixture, covering the rule of alligation, mixing ingredients at different prices or concentrations, calculating mixture ratios, replacing liquids, and finding the mean price or concentration of a mixture. Takes about 20–25 minutes and is useful for placement tests, TCS NQT, SSC, banking and MBA entrance exams.
Question 1
If 500 gm of salt solution has 30% salt in it, how much salt must be added to make the concentration of salt 50% in the solution?
Explanation
Salt now = 30% of 500 = 150 g. Let x g of salt be added: 150 + x500 + x = 12.
300 + 2x = 500 + x, so x = 200 g.
300 + 2x = 500 + x, so x = 200 g.
Question 2
Chaman has two big cans of wine and water mixture. Chaman mixes the contents of both the cans in a big container. The new mixture has half water and half wine. In what quantity did Chaman mix contents of Can 1 and 2 if Can 2 has wine to water ratio of 2:3 and Can 1 has wine to water ratio 5:3?
Explanation
The wine fraction of Can 1 = 58 and of Can 2 = 25. The mixture has 12 wine.
Let Can 1 and Can 2 contribute x and y. 5x8 + 2y5 = x + y2.
x8 = y10, so x : y = 8 : 10 = 4 : 5.
Let Can 1 and Can 2 contribute x and y. 5x8 + 2y5 = x + y2.
x8 = y10, so x : y = 8 : 10 = 4 : 5.
Question 3
Rohit buys some rice at Rs. 10.40 per kg. He mixes it with some rice having price Rs. 8.8 per kg. The final mixture becomes 15kg in weight and with total worth Rs. 146.40. What is the quantity of rice priced at Rs. 8.8 per kg?
Explanation
Let the rice at Rs. 8.8 per kg be y kg. Then the rice at Rs. 10.40 per kg = 15 - y kg.
10.4(15 - y) + 8.8y = 146.4, so 156 - 1.6y = 146.4 and y = 6 kg.
10.4(15 - y) + 8.8y = 146.4, so 156 - 1.6y = 146.4 and y = 6 kg.
Question 4
A solution of honey and water is 28 litres, with honey and water in ratio 4:3. To this a 21 litre honey-water solution is added that has honey to water ratio as 2:1. Again a 51 litre honey-water solution that has honey to water ratio as 9:8 is added to this. After this 10 litre of the solution is replaced with pure honey. What is ratio of water to honey in the final mixture?
Explanation
The first solution of 28 L (4 : 3) has 16 L honey and 12 L water. The 21 L (2 : 1) has 14 L honey and 7 L water. The 51 L (9 : 8) has 27 L honey and 24 L water.
The total = 100 L with 57 L honey and 43 L water.
Removing 10 L takes out 5.7 L honey and 4.3 L water, leaving 51.3 L honey and 38.7 L water. Adding 10 L pure honey gives 61.3 L honey.
Water : honey = 38.7 : 61.3 = 387 : 613.
The total = 100 L with 57 L honey and 43 L water.
Removing 10 L takes out 5.7 L honey and 4.3 L water, leaving 51.3 L honey and 38.7 L water. Adding 10 L pure honey gives 61.3 L honey.
Water : honey = 38.7 : 61.3 = 387 : 613.
Question 5
A pot contains 40 litres of juice. How much juice will be there in the pot, if 4 litres of juice was removed and was replaced by water and this process was further repeated twice?
Explanation
Each time 4 L out of 40 L is replaced by water, so 910 of the juice remains.
After three times, the juice = 40 × (0.9)³ = 40 × 0.729 = 29.16 litres.
After three times, the juice = 40 × (0.9)³ = 40 × 0.729 = 29.16 litres.
Question 6
How much milk should be added in a milk solution to make milk quantity in it 75%, if 80 L of milk solution has 45% milk in it?
Explanation
The milk in 80 L of the solution = 45% of 80 = 36 L.
Let x litres of milk be added: 36 + x80 + x = 75100, so 36 + x = 60 + 0.75x and 0.25x = 24.
x = 96 litres.
Let x litres of milk be added: 36 + x80 + x = 75100, so 36 + x = 60 + 0.75x and 0.25x = 24.
x = 96 litres.
Question 7
In what proportion must wheat at Rs. 15 per kg. be mixed with wheat at Rs. 18 per kg. So that the mixture will be worth Rs. 17 per kg. ?
Explanation
By the rule of alligation, the ratio of the Rs. 15 wheat to the Rs. 18 wheat = (18 - 17) : (17 - 15) = 1 : 2.
Question 8
A container contains 40 liters of milk. From this container 8 liter of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
Explanation
Each time 8 L out of 40 L is replaced, so the milk left is 3240 of what it was.
After three times, the milk = 40 × (0.8)³ = 40 × 0.512 = 20.48 L.
After three times, the milk = 40 × (0.8)³ = 40 × 0.512 = 20.48 L.
Question 9
A container has 40L milk. 4L milk is taken out and replaced with water, the process done three times. What is the amount of milk now left?
Explanation
When 4 L are replaced out of 40 L each time, the milk left is 3640 = 0.9 of what it was.
After three times, the milk left = 40 × 0.9 × 0.9 × 0.9 = 29.16 L.
After three times, the milk left = 40 × 0.9 × 0.9 × 0.9 = 29.16 L.
Question 10
X mixed sugar of Rs.3.8/kg with sugar of Rs.4.7/kg. If the mixture cost him Rs.4.2/kg, in what ratio did he mix the two types?
Explanation
By the rule of alligation, the ratio of the cheaper to the dearer = (4.7 - 4.2) : (4.2 - 3.8) = 0.5 : 0.4 = 5 : 4.
Question 11
A mixture of 30 liters contains wine and water in the ratio 7: 3. How much water has to be added to it so that the ratio of wine to water may be reversed (in liters)?
Explanation
In 30 litres, wine = 21 litres and water = 9 litres.
To reverse the ratio, wine : water = 3 : 7, so water = 73 × 21 = 49 litres.
Water to be added = 49 - 9 = 40 litres.
To reverse the ratio, wine : water = 3 : 7, so water = 73 × 21 = 49 litres.
Water to be added = 49 - 9 = 40 litres.
Question 12
The number of milliliters of water added to reduce 9 ml. of aftershave lotion, containing 50% alcohol, to a lotion containing 30% alcohol is -
Explanation
The alcohol in 9 ml of lotion = 50% of 9 = 4.5 ml.
For a lotion with 30% alcohol, the total volume = 4.50.30 = 15 ml.
Water to be added = 15 - 9 = 6 ml.
For a lotion with 30% alcohol, the total volume = 4.50.30 = 15 ml.
Water to be added = 15 - 9 = 6 ml.
Question 13
Three bars of gold, weighing 6, 5, 4 grams and of 15, 14, 12 12 carats fineness are mixed together. What is the fineness of the compound?
Explanation
Fineness of the compound = (6 × 15) + (5 × 14) + (4 × 1212)6 + 5 + 4.
= 90 + 70 + 5015 = 21015 = 14 carats.
= 90 + 70 + 5015 = 21015 = 14 carats.
Question 14
The ratio of Copper and Nickel in an alloy should be 4:5. Due to an incorrect process, the resultant alloy has these in the ratio 5:4. What % more of nickel needs to be added so that the required ratio of 4:5 is obtained?
Explanation
With Copper=5 and Nickel=4 (per the 5:4 ratio), Copper stays fixed. Solving 5/(4+x)=45 gives x=2.25, a 56.25% increase over the original 4 units of nickel.
Question 15
A chemist mixed a 60% alcohol solution with a 35% alcohol solution to obtain a 45% alcohol solution. In what ratio (35% solution : 60% solution) were the two solutions mixed?
Explanation
By the rule of alligation, the ratio of the 35% solution to the 60% solution = (60 - 45) : (45 - 35) = 15 : 10 = 3 : 2.
Question 16
A vessel is filled to its capacity with pure milk. Ten litres are withdrawn from it and replaced by water. This procedure is repeated again. The vessel now has 32 litres of milk. Find the capacity of the vessel (in litres).
Explanation
(C-10)2/C = 32 leads to C2-52C+100=0, giving C=50 or C=2. The sensible capacity is 50 litres.
Question 17
A shopkeeper has two varieties of tea, A and B. A costs Rs 60 per kg while B costs Rs 65 per kg. In what ratio must he mix the two varieties of tea so that he can make a profit of 10% by selling the mixture at Rs 68.20?
Explanation
CP of mixture = 68.201.1 = 62. Ratio (A):(B) = (65-62):(62-60) = 3:2.
Question 18
Vessel A contains 150 litres of a mixture of milk and water in the ratio of 3:1. Vessel B contains 200 litres of a mixture in the ratio of 5:2. If the mixtures from both vessels are poured into vessel C, find the ratio of milk to water in the resulting mixture.
Explanation
Vessel A: 112.5 milk, 37.5 water. Vessel B: 200 × 57=142.86 milk, 200 × 27=57.14 water. Total milk=255.36, total water=94.64. Ratio simplifies exactly to 143:53.
Question 19
A milkman adds 1.5 litre of water to a certain amount of milk. He sells the adulterated milk at Rs.28 per litre, while pure milk costs Rs.36 per litre. Find the amount of milk at which he exactly breaks even (neither gains nor loses).
Explanation
Let milk amount = m. Cost of milk = 36m. Revenue from selling (m+1.5) litres at 28 = 28(m+1.5). Setting revenue=cost: 28m+42=36m, giving 8m=42, so m=5.25.
Question 20
Fresh oranges contain 84% water while lemons contain 20% water. How many kg of lemons can be made from 80 kg of fresh oranges (assuming the non-water content is preserved)?
Explanation
80 kg oranges has 16% non-water content = 12.8 kg (invariant). This is 80% of the lemon weight, so lemon weight = 12.80.80 = 16 kg.
Question 21
How many litres of an 8% salt solution should be mixed with a 22% salt solution to obtain 70 litres of a 14% solution?
Explanation
Let x=8% volume. 0.08x+0.22(70-x)=0.14 × 70, giving -0.14x=-5.6, so x=40 litres.
Question 22
A shopkeeper has 2000 kg of sugar, part of which he sells at 10% profit and the rest at 20% profit. He gains 16% on the whole. Find the quantity sold at 20% profit.
Explanation
By alligation, ratio (10% qty):(20% qty) = (20-16):(16-10) = 4:6 = 2:3. Total parts=5. 20%-profit quantity = 35 × 2000 = 1200 kg.
Question 23
A merchant has 1000 kg of sugar, part of which he sells at 10% profit and the rest at 30% profit. He gains 15% on the whole. The quantity sold at 30% profit is:
Explanation
By alligation, ratio (10% qty):(30% qty) = (30-15):(15-10) = 15:5 = 3:1. Total parts=4. 30%-profit quantity = 14 × 1000 = 250 kg.
Question 24
In what ratio must water be mixed with milk to gain 20% on selling the mixture at cost price?
Explanation
CP of mixture = CP of milk/1.2. Ratio water:milk = 0.2:1 = 1:5.
Question 25
In what ratio must tea at Rs. 70 per kg be mixed with tea at Rs. 78 per kg so that the mixture is worth Rs. 74.50 per kg?
Explanation
By alligation, ratio = (78-74.50):(74.50-70) = 3.5:4.5 = 7:9.
