PlacementPrepIn what ratio must rice costing Rs. 45/kg be mixed with rice costing Rs. 50/kg so that the mixture costs Rs. 47/kg?
Solution
By alligation: cheaper : dearer = (dearer − mean) : (mean − cheaper) = (50 − 47) : (47 − 45) = 3 : 2.
Answer: (C) 3 : 2
Quantitative Aptitude · Arithmetic
Mixtures and Alligations: placement practice questions
30 moderate questions in the pattern of campus placement tests. Pick an option to check your answer, then open the step-by-step solution.
A 60-litre mixture contains milk and water with 25% water. If 20 litres of water is added, what is the new percentage of water?
Solution
Water = 15 L; after adding, water = 35 L in 80 L.
Water% = 35/80 × 100 = 43.75%.
Answer: (B) 43.75%
A container has 100 litres of milk. 10 litres is taken out and replaced with water. This is done once more. How much milk is left?
Solution
Milk left = 100 × (1 − 10/100)² = 81 litres.
Answer: (C) 81 L
Tea costing Rs. 80/kg and Rs. 100/kg is mixed in the ratio 1 : 3. At what price per kg should the mixture be sold to gain 10%?
Solution
Cost of mixture = (80×1 + 100×3)/4 = 95 per kg.
Selling price = 95 × 110/100 = 104.5.
Answer: (D) Rs. 104.5
Two vessels contain milk and water in the ratios 1 : 3 and 1 : 5. They are mixed in the ratio 3 : 2 by volume. What is the ratio of milk to water in the mixture?
Solution
Milk fraction = 3/5 × 1/4 + 2/5 × 1/6 = 13/60.
Milk : water = 13/60 : 47/60 = 13 : 47.
Answer: (B) 13 : 47
In what ratio must rice costing Rs. 20/kg be mixed with rice costing Rs. 50/kg so that the mixture costs Rs. 28/kg?
Solution
By alligation: cheaper : dearer = (dearer − mean) : (mean − cheaper) = (50 − 28) : (28 − 20) = 22 : 8 = 11 : 4.
Answer: (C) 11 : 4
A 80-litre mixture contains milk and water with 25% water. If 10 litres of water is added, what is the new percentage of water?
Solution
Water = 20 L; after adding, water = 30 L in 90 L.
Water% = 30/90 × 100 = 33 1/3%.
Answer: (A) 33 1/3%
Tea costing Rs. 80/kg and Rs. 100/kg is mixed in the ratio 3 : 1. At what price per kg should the mixture be sold to gain 25%?
Solution
Cost of mixture = (80×3 + 100×1)/4 = 85 per kg.
Selling price = 85 × 125/100 = 106.25.
Answer: (D) Rs. 106.25
Two vessels contain milk and water in the ratios 1 : 4 and 2 : 1. They are mixed in the ratio 2 : 1 by volume. What is the ratio of milk to water in the mixture?
Solution
Milk fraction = 2/3 × 1/5 + 1/3 × 2/3 = 16/45.
Milk : water = 16/45 : 29/45 = 16 : 29.
Answer: (D) 16 : 29
A container has 50 litres of milk. 20 litres is taken out and replaced with water. This is done once more. How much milk is left?
Solution
Milk left = 50 × (1 − 20/50)² = 18 litres.
Answer: (B) 18 L
Two vessels contain milk and water in the ratios 2 : 3 and 1 : 1. Equal quantities are mixed. What is the ratio of milk to water in the mixture?
Solution
Milk fraction = ½ × (2/5 + 1/2) = 0.45.
Milk : water = 0.45 : 0.55 = 9 : 11.
Answer: (A) 9 : 11
In what ratio must rice costing Rs. 20/kg be mixed with rice costing Rs. 60/kg so that the mixture costs Rs. 22/kg?
Solution
By alligation: cheaper : dearer = (dearer − mean) : (mean − cheaper) = (60 − 22) : (22 − 20) = 38 : 2 = 19 : 1.
Answer: (B) 19 : 1
A 40-litre mixture contains milk and water with 20% water. If 40 litres of water is added, what is the new percentage of water?
Solution
Water = 8 L; after adding, water = 48 L in 80 L.
Water% = 48/80 × 100 = 60%.
Answer: (B) 60%
Two vessels contain milk and water in the ratios 5 : 3 and 4 : 3. They are mixed in the ratio 3 : 1 by volume. What is the ratio of milk to water in the mixture?
Solution
Milk fraction = 3/4 × 5/8 + 1/4 × 4/7 = 137/224.
Milk : water = 137/224 : 87/224 = 137 : 87.
Answer: (C) 137 : 87
In what ratio must rice costing Rs. 50/kg be mixed with rice costing Rs. 64/kg so that the mixture costs Rs. 60/kg?
Solution
By alligation: cheaper : dearer = (dearer − mean) : (mean − cheaper) = (64 − 60) : (60 − 50) = 4 : 10 = 2 : 5.
Answer: (A) 2 : 5
A container has 80 litres of milk. 20 litres is taken out and replaced with water. This is done once more. How much milk is left?
Solution
Milk left = 80 × (1 − 20/80)² = 45 litres.
Answer: (B) 45 L
Tea costing Rs. 120/kg and Rs. 150/kg is mixed in the ratio 2 : 1. At what price per kg should the mixture be sold to gain 20%?
Solution
Cost of mixture = (120×2 + 150×1)/3 = 130 per kg.
Selling price = 130 × 120/100 = 156.
Answer: (A) Rs. 156
Two vessels contain milk and water in the ratios 2 : 4 and 1 : 3. They are mixed in the ratio 1 : 2 by volume. What is the ratio of milk to water in the mixture?
Solution
Milk fraction = 1/3 × 2/6 + 2/3 × 1/4 = 5/18.
Milk : water = 5/18 : 13/18 = 5 : 13.
Answer: (C) 5 : 13
In what ratio must rice costing Rs. 25/kg be mixed with rice costing Rs. 50/kg so that the mixture costs Rs. 29/kg?
Solution
By alligation: cheaper : dearer = (dearer − mean) : (mean − cheaper) = (50 − 29) : (29 − 25) = 21 : 4.
Answer: (D) 21 : 4
A 80-litre mixture contains milk and water with 25% water. If 40 litres of water is added, what is the new percentage of water?
Solution
Water = 20 L; after adding, water = 60 L in 120 L.
Water% = 60/120 × 100 = 50%.
Answer: (D) 50%
Tea costing Rs. 90/kg and Rs. 120/kg is mixed in the ratio 2 : 1. At what price per kg should the mixture be sold to gain 20%?
Solution
Cost of mixture = (90×2 + 120×1)/3 = 100 per kg.
Selling price = 100 × 120/100 = 120.
Answer: (A) Rs. 120
Two vessels contain milk and water in the ratios 3 : 4 and 4 : 2. They are mixed in the ratio 3 : 1 by volume. What is the ratio of milk to water in the mixture?
Solution
Milk fraction = 3/4 × 3/7 + 1/4 × 4/6 = 41/84.
Milk : water = 41/84 : 43/84 = 41 : 43.
Answer: (A) 41 : 43
In what ratio must rice costing Rs. 36/kg be mixed with rice costing Rs. 60/kg so that the mixture costs Rs. 55/kg?
Solution
By alligation: cheaper : dearer = (dearer − mean) : (mean − cheaper) = (60 − 55) : (55 − 36) = 5 : 19.
Answer: (B) 5 : 19
A 120-litre mixture contains milk and water with 20% water. If 40 litres of water is added, what is the new percentage of water?
Solution
Water = 24 L; after adding, water = 64 L in 160 L.
Water% = 64/160 × 100 = 40%.
Answer: (B) 40%
Tea costing Rs. 60/kg and Rs. 70/kg is mixed in the ratio 1 : 3. At what price per kg should the mixture be sold to gain 20%?
Solution
Cost of mixture = (60×1 + 70×3)/4 = 67.5 per kg.
Selling price = 67.5 × 120/100 = 81.
Answer: (B) Rs. 81
Two vessels contain milk and water in the ratios 5 : 2 and 1 : 1. They are mixed in the ratio 2 : 1 by volume. What is the ratio of milk to water in the mixture?
Solution
Milk fraction = 2/3 × 5/7 + 1/3 × 1/2 = 9/14.
Milk : water = 9/14 : 5/14 = 9 : 5.
Answer: (D) 9 : 5
In what ratio must rice costing Rs. 30/kg be mixed with rice costing Rs. 50/kg so that the mixture costs Rs. 45/kg?
Solution
By alligation: cheaper : dearer = (dearer − mean) : (mean − cheaper) = (50 − 45) : (45 − 30) = 5 : 15 = 1 : 3.
Answer: (C) 1 : 3
A container has 100 litres of milk. 20 litres is taken out and replaced with water. This is done once more. How much milk is left?
Solution
Milk left = 100 × (1 − 20/100)² = 64 litres.
Answer: (C) 64 L
A 100-litre mixture contains milk and water with 20% water. If 20 litres of water is added, what is the new percentage of water?
Solution
Water = 20 L; after adding, water = 40 L in 120 L.
Water% = 40/120 × 100 = 33 1/3%.
Answer: (C) 33 1/3%
Tea costing Rs. 60/kg and Rs. 70/kg is mixed in the ratio 3 : 1. At what price per kg should the mixture be sold to gain 10%?
Solution
Cost of mixture = (60×3 + 70×1)/4 = 62.5 per kg.
Selling price = 62.5 × 110/100 = 68.75.
Answer: (D) Rs. 68.75
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