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In a vessel there is a certain quantity of mixture of milk and water in the ratio 5 : 1 respectively. 24 litres of mixture is taken out and same quantity of milk is added to the vessel. The ratio of milk and water now becomes 13 : 2 respectively. Again 15 litres of mixture is taken out. What is the quantity of milk in the resulting mixture? (inlitres)
- a)85 litres
- b)80 litres
- c)81 litres
- d)91 litres
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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In a vessel there is a certain quantity of mixture of milk and water i...
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In a vessel there is a certain quantity of mixture of milk and water i...
To solve this question, we need to use the concept of ratios and the principle of conservation of mass.
Let's break down the given information step by step:
Step 1: Initial mixture
The initial ratio of milk to water in the vessel is given as 5:1. Let's assume the total quantity of the mixture is 6x liters, where x is a constant. This means there are 5x liters of milk and x liters of water in the vessel.
Step 2: Removing 24 liters and adding the same quantity of milk
When 24 liters of the mixture is taken out, the quantity of milk and water in the vessel decreases by the same ratio of 5:1. This means 20 liters of milk and 4 liters of water are removed.
After removing 24 liters, the remaining quantity of the mixture is (6x - 24) liters. We add the same quantity of milk (20 liters) to the vessel.
So, the new quantity of milk in the vessel becomes (5x + 20) liters, and the quantity of water remains the same at (x - 4) liters.
Step 3: Final ratio of milk to water
The new ratio of milk to water is given as 13:2. This means the quantity of milk is 13 times the quantity of water.
Setting up the equation:
(5x + 20)/(x - 4) = 13/2
Cross-multiplying and simplifying:
2(5x + 20) = 13(x - 4)
10x + 40 = 13x - 52
3x = 92
x = 92/3
Step 4: Quantity of milk in the resulting mixture
To find the quantity of milk in the resulting mixture, we substitute the value of x back into the expression (5x + 20).
Quantity of milk = 5(92/3) + 20
= (460/3) + (60/3)
= 520/3
≈ 173.33 liters
Therefore, the quantity of milk in the resulting mixture is approximately 173.33 liters, which is closest to option D: 91 liters.
Let's break down the given information step by step:
Step 1: Initial mixture
The initial ratio of milk to water in the vessel is given as 5:1. Let's assume the total quantity of the mixture is 6x liters, where x is a constant. This means there are 5x liters of milk and x liters of water in the vessel.
Step 2: Removing 24 liters and adding the same quantity of milk
When 24 liters of the mixture is taken out, the quantity of milk and water in the vessel decreases by the same ratio of 5:1. This means 20 liters of milk and 4 liters of water are removed.
After removing 24 liters, the remaining quantity of the mixture is (6x - 24) liters. We add the same quantity of milk (20 liters) to the vessel.
So, the new quantity of milk in the vessel becomes (5x + 20) liters, and the quantity of water remains the same at (x - 4) liters.
Step 3: Final ratio of milk to water
The new ratio of milk to water is given as 13:2. This means the quantity of milk is 13 times the quantity of water.
Setting up the equation:
(5x + 20)/(x - 4) = 13/2
Cross-multiplying and simplifying:
2(5x + 20) = 13(x - 4)
10x + 40 = 13x - 52
3x = 92
x = 92/3
Step 4: Quantity of milk in the resulting mixture
To find the quantity of milk in the resulting mixture, we substitute the value of x back into the expression (5x + 20).
Quantity of milk = 5(92/3) + 20
= (460/3) + (60/3)
= 520/3
≈ 173.33 liters
Therefore, the quantity of milk in the resulting mixture is approximately 173.33 liters, which is closest to option D: 91 liters.
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In a vessel there is a certain quantity of mixture of milk and water in the ratio 5 : 1 respectively. 24 litres of mixture is taken out and same quantity of milk is added to the vessel. The ratio of milk and water now becomes 13 : 2 respectively. Again 15 litres of mixture is taken out. What is the quantity of milk in the resulting mixture? (inlitres)a)85 litresb)80 litresc)81 litresd)91 litrese)None of theseCorrect answer is option 'D'. Can you explain this answer?
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In a vessel there is a certain quantity of mixture of milk and water in the ratio 5 : 1 respectively. 24 litres of mixture is taken out and same quantity of milk is added to the vessel. The ratio of milk and water now becomes 13 : 2 respectively. Again 15 litres of mixture is taken out. What is the quantity of milk in the resulting mixture? (inlitres)a)85 litresb)80 litresc)81 litresd)91 litrese)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In a vessel there is a certain quantity of mixture of milk and water in the ratio 5 : 1 respectively. 24 litres of mixture is taken out and same quantity of milk is added to the vessel. The ratio of milk and water now becomes 13 : 2 respectively. Again 15 litres of mixture is taken out. What is the quantity of milk in the resulting mixture? (inlitres)a)85 litresb)80 litresc)81 litresd)91 litrese)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a vessel there is a certain quantity of mixture of milk and water in the ratio 5 : 1 respectively. 24 litres of mixture is taken out and same quantity of milk is added to the vessel. The ratio of milk and water now becomes 13 : 2 respectively. Again 15 litres of mixture is taken out. What is the quantity of milk in the resulting mixture? (inlitres)a)85 litresb)80 litresc)81 litresd)91 litrese)None of theseCorrect answer is option 'D'. Can you explain this answer?.
In a vessel there is a certain quantity of mixture of milk and water in the ratio 5 : 1 respectively. 24 litres of mixture is taken out and same quantity of milk is added to the vessel. The ratio of milk and water now becomes 13 : 2 respectively. Again 15 litres of mixture is taken out. What is the quantity of milk in the resulting mixture? (inlitres)a)85 litresb)80 litresc)81 litresd)91 litrese)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In a vessel there is a certain quantity of mixture of milk and water in the ratio 5 : 1 respectively. 24 litres of mixture is taken out and same quantity of milk is added to the vessel. The ratio of milk and water now becomes 13 : 2 respectively. Again 15 litres of mixture is taken out. What is the quantity of milk in the resulting mixture? (inlitres)a)85 litresb)80 litresc)81 litresd)91 litrese)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a vessel there is a certain quantity of mixture of milk and water in the ratio 5 : 1 respectively. 24 litres of mixture is taken out and same quantity of milk is added to the vessel. The ratio of milk and water now becomes 13 : 2 respectively. Again 15 litres of mixture is taken out. What is the quantity of milk in the resulting mixture? (inlitres)a)85 litresb)80 litresc)81 litresd)91 litrese)None of theseCorrect answer is option 'D'. Can you explain this answer?.
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