Mixtures and Alligation Competitive Exams
50 questions · Mathematics
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Question 1 of 50
How much pure alcohol must be added to 20 L of a 20% alcohol solution to make it 36% alcohol?
Explanation(4 + x)/(20 + x) = 0.36 gives 4 + x = 7.2 + 0.36x, so 0.64x = 3.2 and x = 5 L.
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Question 2 of 50
How much pure water must be added to 60 L of a 30% solution to reduce it to 20%?
ExplanationSolute = 18 L. For 20%, total = 18 ÷ 0.2 = 90 L. Water to add = 90 − 60 = 30 L.
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Question 3 of 50
A 56 L mixture has milk and water in the ratio 5 : 3. How much water must be added to make the ratio 1 : 1?
ExplanationMilk = 35 L and water = 21 L. For 1 : 1 water must also be 35 L, so add 35 − 21 = 14 L.
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Question 4 of 50
A 30 L mixture contains milk and water in the ratio 4 : 1. How much water must be added to make the ratio 3 : 2?
ExplanationMilk = 24 L and water = 6 L. For 3 : 2 with 24 L milk, water must be 16 L. Water to add = 16 − 6 = 10 L.
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Question 5 of 50
A vessel has 10 L of pure milk. 1 L is removed and replaced with water, and this is done once more. The quantity of pure milk left is:
ExplanationMilk left = 10 × (9/10)² = 8.1 L.
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Question 6 of 50
A 60 L mixture contains milk and water in the ratio 7 : 5. The quantity of water is:
ExplanationTotal parts = 12, so water = (5/12) × 60 = 25 L.
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Question 7 of 50
An alloy of copper and zinc contains them in the ratio 5 : 3. In 24 kg of the alloy, the quantity of zinc is:
ExplanationZinc = (3/8) × 24 = 9 kg.
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Question 8 of 50
A 20 L solution is 40% acid. 4 L of it is removed and replaced with water. The percentage of acid now is:
ExplanationAcid = 8 L. The 4 L removed contains 1.6 L acid. Acid left = 6.4 L in 20 L = 32%.
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Question 9 of 50
A 40 L mixture contains milk and water in the ratio 3 : 2. The quantity of milk is:
ExplanationTotal parts = 5, so milk = (3/5) × 40 = 24 L.
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Question 10 of 50
A milkman buys milk at ₹20/L and mixes water to sell the mixture at ₹20/L. If his gain is 25%, the ratio of water to milk is:
ExplanationCost of the mixture = 20 × 100/125 = ₹16/L. By alligation water : milk = (20 − 16) : (16 − 0) = 1 : 4.
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Question 11 of 50
A 30 L mixture has milk and water in the ratio 2 : 3. If 6 L of water is added, the new ratio of milk to water is:
ExplanationMilk = 12 L and water = 18 L. After adding 6 L water, 12 : 24 = 1 : 2.
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Question 12 of 50
A 45 L mixture has milk and water in the ratio 4 : 5. The quantity of milk is:
ExplanationTotal parts = 9, so milk = (4/9) × 45 = 20 L.
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Question 13 of 50
A trader mixes 26 kg of rice at ₹20/kg with 30 kg of rice at ₹36/kg and sells the mixture at ₹30/kg. His profit percentage is:
ExplanationCost = 520 + 1080 = ₹1600. Selling price = 56 × 30 = ₹1680. Profit = 80/1600 = 5%.
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Question 14 of 50
An alloy of zinc and copper in the ratio 9 : 4 weighs 78 kg. How much copper must be added to make the ratio 3 : 2?
ExplanationZinc = 54 kg and copper = 24 kg. For 3 : 2, copper must be 36 kg. Copper to add = 12 kg.
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Question 15 of 50
A 50 L mixture has milk and water in the ratio 3 : 2. 10 L of the mixture is removed and 10 L of pure milk is added. The new ratio of milk to water is:
ExplanationMilk = 30 L and water = 20 L. The 10 L removed has 6 L milk and 4 L water. Milk = 30 − 6 + 10 = 34 L; water = 16 L. Ratio = 34 : 16 = 17 : 8.
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Question 16 of 50
5 kg of salt is dissolved in 45 kg of water. The percentage of salt in the solution is:
ExplanationSalt percentage = 5/(5 + 45) × 100 = 10%.
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Question 17 of 50
Equal quantities of two varieties costing ₹12/kg and ₹18/kg are mixed and the mixture is sold at ₹18/kg. The gain percentage is:
ExplanationCost of the mixture = (12 + 18)/2 = ₹15/kg. Gain = 3/15 = 20%.
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Question 18 of 50
A vessel has 125 L of pure milk. One-fifth of the liquid is removed and replaced with water, and this is repeated twice more (three times in all). The pure milk left is:
ExplanationMilk left = 125 × (4/5)³ = 125 × 64/125 = 64 L.
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Question 19 of 50
A vessel has 16 L of pure alcohol. 4 L is removed and replaced with water, and this is done once more. The quantity of alcohol left is:
ExplanationAlcohol left = 16 × (12/16)² = 16 × 9/16 = 9 L.
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Question 20 of 50
Two varieties of sugar costing ₹18/kg and ₹24/kg are mixed in the ratio 2 : 1. The cost of the mixture per kg is:
ExplanationMean price = (2 × 18 + 1 × 24)/3 = 60/3 = ₹20.
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Question 21 of 50
A vessel has 50 L of pure milk. 10 L is removed and replaced with water. The same operation is repeated once more. The quantity of pure milk left is:
ExplanationMilk left = 50 × (1 − 10/50)² = 50 × (4/5)² = 32 L.
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Question 22 of 50
A 60 L solution has acid and water in the ratio 2 : 3. How much water must be added to make the ratio of acid to water 1 : 2?
ExplanationAcid = 24 L and water = 36 L. For 1 : 2 water must be 48 L, so add 48 − 36 = 12 L.
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Question 23 of 50
An 80 L mixture has milk and water in the ratio 3 : 1. How much water must be added to make the ratio 3 : 2?
ExplanationMilk = 60 L and water = 20 L. For 3 : 2, water must be 40 L. Water to add = 20 L.
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Question 24 of 50
A 40 L vessel contains milk and water in the ratio 3 : 1. 8 L of the mixture is removed and replaced with water. The quantity of milk now is:
ExplanationMilk = 30 L and water = 10 L. The 8 L removed contains 6 L milk and 2 L water. Milk left = 24 L.
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Question 25 of 50
In what ratio must tea at ₹60/kg be mixed with tea at ₹80/kg to get a mixture worth ₹74/kg? (cheaper : dearer)
ExplanationCheaper : dearer = (80 − 74) : (74 − 60) = 6 : 14 = 3 : 7.
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Question 26 of 50
A 40 L solution contains 25% alcohol. How much water must be added to make it 20% alcohol?
ExplanationAlcohol = 10 L. For 20%, total = 10 ÷ 0.2 = 50 L. Water to add = 50 − 40 = 10 L.
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Question 27 of 50
How many litres must be drawn from a 60 L vessel of pure milk and replaced with water so that the milk and water become equal?
ExplanationMilk must become 30 L: 60 − x = 30, so x = 30 L.
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Question 28 of 50
Two types of tea are mixed in the ratio 2 : 3 to make 15 kg of mixture. The quantity of the first type is:
ExplanationThe first type = (2/5) × 15 = 6 kg.
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Question 29 of 50
20 kg of flour at ₹30/kg is mixed with 30 kg of flour at ₹40/kg. The cost of the mixture per kg is:
ExplanationTotal cost = 600 + 1200 = ₹1800 for 50 kg, so ₹36/kg.
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Question 30 of 50
Milk costing ₹20/L is diluted with water to make a mixture worth ₹16/L. The ratio of milk to water is:
ExplanationWater costs ₹0. By alligation: milk : water = (16 − 0) : (20 − 16) = 16 : 4 = 4 : 1.
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Question 31 of 50
How many kg of sugar must be added to 40 kg of a 10% sugar solution to make it 20% sugar?
ExplanationSugar = 4 kg. (4 + x)/(40 + x) = 0.2 gives 4 + x = 8 + 0.2x, so 0.8x = 4 and x = 5 kg.
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Question 32 of 50
A container holds 40 L of pure milk. 4 L is removed and replaced with water. The quantity of milk now is:
ExplanationMilk left = 40 − 4 = 36 L.
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Question 33 of 50
20 L of pure water is added to 80 L of a 25% acid solution. The percentage of acid in the new solution is:
ExplanationAcid = 20 L in 100 L = 20%.
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Question 34 of 50
In what ratio must milk with 5% fat be mixed with milk with 15% fat to get milk with 8% fat? (5% : 15%)
Explanation(15 − 8) : (8 − 5) = 7 : 3.
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Question 35 of 50
In what ratio should pulses costing ₹15/kg and ₹20/kg be mixed so that selling the mixture at ₹21/kg gives a 20% profit?
ExplanationCost price of the mixture = 21 × 100/120 = ₹17.50. Ratio = (20 − 17.5) : (17.5 − 15) = 2.5 : 2.5 = 1 : 1.
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Question 36 of 50
10 L of 40% sugar solution is mixed with 30 L of 20% sugar solution. The percentage of sugar in the mixture is:
ExplanationSugar = 4 + 6 = 10 L in 40 L, which is 25%.
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Question 37 of 50
A 50 L solution contains 20% acid. The quantity of acid is:
Explanation20% of 50 = 10 L.
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Question 38 of 50
A 40 L solution contains 30% salt. If 10 L of water evaporates, the percentage of salt becomes:
ExplanationSalt = 12 L stays the same. New volume = 30 L, so 12/30 = 40%.
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Question 39 of 50
How many kg of tea at ₹72/kg must be mixed with 20 kg of tea at ₹65/kg to get a mixture worth ₹68/kg?
ExplanationCheaper : dearer = (72 − 68) : (68 − 65) = 4 : 3. With 20 kg of cheaper tea, dearer = 15 kg.
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Question 40 of 50
Equal quantities of milk-water mixtures are taken from two vessels. In the first the ratio of milk to water is 2 : 1 and in the second it is 1 : 2. The ratio of milk to water in the new mixture is:
ExplanationTake 3 L from each. Milk = 2 + 1 = 3 L and water = 1 + 2 = 3 L, so the ratio is 1 : 1.
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Question 41 of 50
20 kg of salt at ₹9/kg is mixed with 30 kg of salt at ₹14/kg. The cost of the mixture per kg is:
ExplanationTotal cost = 180 + 420 = ₹600 for 50 kg, so ₹12/kg.
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Question 42 of 50
A milkman adds 1 L of water to every 4 L of milk and sells the mixture at the price of pure milk. His profit percentage is:
ExplanationFor 4 L milk cost he sells 5 L, so profit = 1/4 = 25%.
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Question 43 of 50
How many kg of rice at ₹45/kg must be mixed with 10 kg of rice at ₹30/kg to get a mixture worth ₹35/kg?
ExplanationCheaper : dearer = (45 − 35) : (35 − 30) = 10 : 5 = 2 : 1. With 10 kg of cheaper rice, dearer = 5 kg.
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Question 44 of 50
10 L of pure milk is mixed with 2.5 L of water. The ratio of milk to water in the mixture is:
Explanation10 : 2.5 = 4 : 1.
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Question 45 of 50
In what ratio must wheat at ₹9.30/kg be mixed with wheat at ₹10.80/kg to get a mixture worth ₹10/kg? (cheaper : dearer)
ExplanationCheaper : dearer = (10.80 − 10) : (10 − 9.30) = 0.80 : 0.70 = 8 : 7.
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Question 46 of 50
From a 60 L vessel of pure milk, 12 L is removed and replaced with water. The ratio of milk to water in the new mixture is:
ExplanationMilk = 48 L and water = 12 L, so the ratio is 4 : 1.
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Question 47 of 50
In what ratio must rice at ₹40/kg be mixed with rice at ₹50/kg to get a mixture worth ₹44/kg? (cheaper : dearer)
ExplanationBy alligation: cheaper : dearer = (50 − 44) : (44 − 40) = 6 : 4 = 3 : 2.
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Question 48 of 50
10 L of milk-water mixture in the ratio 3 : 2 is mixed with 10 L of mixture in the ratio 4 : 1. The ratio of milk to water in the final mixture is:
ExplanationMilk = 6 + 8 = 14 L and water = 4 + 2 = 6 L, so the ratio = 14 : 6 = 7 : 3.
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Question 49 of 50
In what ratio must a 30% solution be mixed with a 50% solution to get a 42% solution? (30% : 50%)
Explanation(50 − 42) : (42 − 30) = 8 : 12 = 2 : 3.
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Question 50 of 50
15 L of a 20% solution is mixed with 25 L of a 40% solution. The percentage in the mixture is:
ExplanationSolute = 3 + 10 = 13 L in 40 L, so 13/40 = 32.5%.
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