Three varieties of rice costing Rs. 40, Rs. 80 and Rs. 30 per kg are mixed in the ratio 1 : 4 : 1. What is the cost of the mixture per kg?
Solution
Cost = (40×1 + 80×4 + 30×1)/6 = 65 per kg.
Answer: (B) Rs. 65
Quantitative Aptitude · Arithmetic
Mixtures and Alligations: MAH CET, NMAT and SNAP practice questions
20 questions in the pattern of MAH MBA CET, NMAT and SNAP. Each question is marked with the exams it suits. Answer it, then open the step-by-step solution.
Exam:
Three varieties of rice costing Rs. 50, Rs. 80 and Rs. 30 per kg are mixed in the ratio 1 : 1 : 5. What is the cost of the mixture per kg?
Solution
Cost = (50×1 + 80×1 + 30×5)/7 = 40 per kg.
Answer: (A) Rs. 40
A milkman mixes water with milk and sells the mixture at the cost price of milk, gaining 25%. In what ratio has he mixed water and milk?
Solution
His gain comes from the free water: water/milk = 25/100 = 1/4.
So water : milk = 1 : 4.
Answer: (B) 1 : 4
In what ratio should a 20% acid solution be mixed with a 50% acid solution to get a 34% solution?
Solution
Alligation: (50 − 34) : (34 − 20) = 16 : 14 = 8 : 7.
Answer: (B) 8 : 7
How many kg of rice at Rs. 30/kg must be mixed with 40 kg of rice at Rs. 25/kg so that the mixture costs Rs. 26/kg?
Solution
Ratio cheaper : dearer = 4 : 1.
Dearer rice = 40 × 1/4 = 10 kg.
Answer: (A) 10 kg
A vessel has 80 litres of milk. 20 litres is taken out and replaced with water. This is done twice in all. How much milk is left?
Solution
Milk left = 80 × (1 − 20/80)^2 = 45 L.
Answer: (A) 45 L
In what ratio must tea at Rs. 48/kg be mixed with tea at Rs. 64/kg so that the mixture costs Rs. 53/kg?
Solution
By alligation: cheaper : dearer = (64 − 53) : (53 − 48) = 11 : 5.
Answer: (B) 11 : 5
A 60-litre solution contains 40% alcohol. How much water must be added to bring the alcohol content down to 10%?
Solution
Alcohol = 24 L, which stays the same.
24 = 10% of (60 + x) ⇒ x = 180 L.
Answer: (B) 180 L
A mixture of 90 litres has milk and water in the ratio 7 : 2. How much water must be added to make the ratio 1 : 6?
Solution
Milk = 70 L, water = 20 L. Milk stays the same.
70 : (20 + x) = 1 : 6 ⇒ x = 400 L.
Answer: (A) 400 L
Milk costs Rs. 50 per litre. A dealer adds water so that water is 25% of the mixture and sells the mixture at Rs. 50 per litre. What is his profit percentage?
Solution
In 100 L of mixture, 75 L is milk costing 3750; he sells 100 L for 5000.
Profit% = 25/75 × 100 = 33 1/3%.
Answer: (B) 33 1/3%
A 40-litre solution contains 50% alcohol. How much water must be added to bring the alcohol content down to 12%?
Solution
Alcohol = 20 L, which stays the same.
20 = 12% of (40 + x) ⇒ x = 126 2/3 L.
Answer: (D) 126 2/3 L
Milk costs Rs. 30 per litre. A dealer adds water so that water is 25% of the mixture and sells the mixture at Rs. 30 per litre. What is his profit percentage?
Solution
In 100 L of mixture, 75 L is milk costing 2250; he sells 100 L for 3000.
Profit% = 25/75 × 100 = 33 1/3%.
Answer: (A) 33 1/3%
Two vessels contain milk and water in the ratios 2 : 5 and 3 : 1. Equal quantities are mixed. What is the ratio of milk to water in the mixture?
Solution
Milk fraction = 2/4 × 2/7 + 2/4 × 3/4 = 29/56.
Milk : water = 29 : 27.
Answer: (D) 29 : 27
A vessel has 80 litres of milk. 20 litres is taken out and replaced with water. This is done three times in all. How much milk is left?
Solution
Milk left = 80 × (1 − 20/80)^3 = 33.75 L.
Answer: (B) 33.75 L
A milkman mixes water with milk and sells the mixture at the cost price of milk, gaining 10%. In what ratio has he mixed water and milk?
Solution
His gain comes from the free water: water/milk = 10/100 = 1/10.
So water : milk = 1 : 10.
Answer: (C) 1 : 10
In what ratio should a 15% acid solution be mixed with a 45% acid solution to get a 37% solution?
Solution
Alligation: (45 − 37) : (37 − 15) = 8 : 22 = 4 : 11.
Answer: (B) 4 : 11
In what ratio must tea at Rs. 25/kg be mixed with tea at Rs. 72/kg so that the mixture costs Rs. 61/kg?
Solution
By alligation: cheaper : dearer = (72 − 61) : (61 − 25) = 11 : 36.
Answer: (D) 11 : 36
Two vessels contain milk and water in the ratios 4 : 5 and 2 : 4. They are mixed in the ratio 2 : 3. What is the ratio of milk to water in the mixture?
Solution
Milk fraction = 2/5 × 4/9 + 3/5 × 2/6 = 17/45.
Milk : water = 17 : 28.
Answer: (B) 17 : 28
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 20%?
Solution
Cost of mixture = (80×3 + 100×1)/4 = 85.
SP = 85 × 120/100 = 102.
Answer: (C) Rs. 102
How many kg of rice at Rs. 50/kg must be mixed with 264 kg of rice at Rs. 20/kg so that the mixture costs Rs. 28/kg?
Solution
Ratio cheaper : dearer = 22 : 8.
Dearer rice = 264 × 8/22 = 96 kg.
Answer: (C) 96 kg
These are original practice questions written by Target Campus in the pattern and difficulty of MAH MBA CET, NMAT, SNAP and other MBA entrance tests. They are not previous-year papers.
Preparing for MAH CET, NMAT, SNAP or CAT? Courses, live classes and mocks by Dr. Kiran Derle at Target Campus.
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