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Two petrol tanks P1 and P2 contain equal quantities of a mixture of pure petrol and some cheaper fuel. The concentration of petrol is same in both P1 and P2. If 8 litres of mixture in P1 is replaced with pure petrol then the concentration of petrol in P1 becomes twice of what it was initially. If 16 litres of solution from P2 is replaced with pure petrol, then what is the ratio of final concentration of petrol in P2 to the initial concentration of petrol in P2?
- a)4 : 1
- b)5 : 2
- c)3 : 1
- d)3 : 3
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two petrol tanks P1 and P2 contain equal quantities of a mixture of pu...
Let’s first consider solution P1:
The concentration of petrol in P1 becomes twice of what it was initially.
Quantity of petrol initially present in P1 = Net increase of petrol = (8 litres of pure petrol) - (petrol lost in 8 litres of solution in P1)
Now, 16 litres replacement in P2 can be considered as the replacement of two 8 litres volumes of the solution.
This will lead to a net increase of two times the initial quantity of petrol. Therefore, this will triple the concentration of petrol in P2.
Hence, option 3.
The concentration of petrol in P1 becomes twice of what it was initially.
Quantity of petrol initially present in P1 = Net increase of petrol = (8 litres of pure petrol) - (petrol lost in 8 litres of solution in P1)
Now, 16 litres replacement in P2 can be considered as the replacement of two 8 litres volumes of the solution.
This will lead to a net increase of two times the initial quantity of petrol. Therefore, this will triple the concentration of petrol in P2.
Hence, option 3.
Alternatively,
Let the amount of petrol in both the tanks be x. Let the amount of cheaper fuel in both the tanks be y. The concentration of petrol in both tanks initially is x/(x + y)
Let there be m litres of petrol in the 8 litres of mixture that are drawn from P1.
As 8 litres of petrol is added to the mixture, the new amount o f petrol in the mixture is x - m + 8
The concentration of petrol in this new mixture is (x - m + 8)/(x + y) But, this is equal to 2x/(x + y) x + 8 - m = 2x
m = 8 - x
When 16 litres of mixture are withdrawn from P2, 2m litres of petrol are drawn. These are replaced by 16 litres of petrol.
New amount of petrol in P2 = x - 2m +16 = x - 16 + 2x + 16 = 3x
New concentration of petrol in P2 = 3x/(x + y)
Ratio of final concentration of petrol in P2 to initial concentration of petrol in P2 is 3 : 1 Hence, option 3.
Let there be m litres of petrol in the 8 litres of mixture that are drawn from P1.
As 8 litres of petrol is added to the mixture, the new amount o f petrol in the mixture is x - m + 8
The concentration of petrol in this new mixture is (x - m + 8)/(x + y) But, this is equal to 2x/(x + y) x + 8 - m = 2x
m = 8 - x
When 16 litres of mixture are withdrawn from P2, 2m litres of petrol are drawn. These are replaced by 16 litres of petrol.
New amount of petrol in P2 = x - 2m +16 = x - 16 + 2x + 16 = 3x
New concentration of petrol in P2 = 3x/(x + y)
Ratio of final concentration of petrol in P2 to initial concentration of petrol in P2 is 3 : 1 Hence, option 3.
Most Upvoted Answer
Two petrol tanks P1 and P2 contain equal quantities of a mixture of pu...
Initial Concentration of Petrol in P1 and P2:
Let's assume that initially, both tanks P1 and P2 contain x litres of the mixture of pure petrol and cheaper fuel. Since the concentration of petrol is the same in both tanks, the quantity of petrol in both tanks is the same at the beginning.
Concentration of Petrol in P1 after Replacement:
If 8 litres of the mixture in P1 is replaced with pure petrol, the quantity of petrol in P1 remains the same, but the total quantity of the mixture decreases by 8 litres. Therefore, the concentration of petrol in P1 becomes twice what it was initially.
Let's calculate the concentration of petrol in P1 initially and after replacement.
Initial Concentration of Petrol in P1:
The initial concentration of petrol in P1 is given by (x liters of petrol)/(x liters of mixture) = 1.
Concentration of Petrol in P1 after Replacement:
After replacing 8 liters of the mixture with pure petrol, the total quantity of the mixture in P1 becomes (x - 8) liters. Since the concentration of petrol becomes twice, the concentration of petrol in P1 after replacement is given by (x liters of petrol)/((x - 8) liters of mixture) = 2.
From the above equations, we can write:
(x)/(x - 8) = 2
Solving this equation, we get:
x = 16
Therefore, the initial quantity of the mixture in P1 and P2 is 16 liters.
Concentration of Petrol in P2 after Replacement:
If 16 liters of the solution from P2 is replaced with pure petrol, the quantity of petrol in P2 remains the same, but the total quantity of the solution decreases by 16 liters. Let's calculate the concentration of petrol in P2 after replacement.
Initial Concentration of Petrol in P2:
Since the concentration of petrol is the same in both P1 and P2, the initial concentration of petrol in P2 is also 1.
Concentration of Petrol in P2 after Replacement:
After replacing 16 liters of the solution with pure petrol, the total quantity of the solution in P2 becomes (16 - 16) = 0 liters. Therefore, the concentration of petrol in P2 after replacement is given by (x liters of petrol)/(0 liters of mixture) = Undefined.
Ratio of Final Concentration of Petrol in P2 to Initial Concentration of Petrol in P2:
As the concentration of petrol in P2 after replacement is undefined, we cannot calculate the ratio of the final concentration of petrol in P2 to the initial concentration of petrol in P2. Therefore, the answer is not determinable.
Hence, the correct option is (d) Not Determinable.
Let's assume that initially, both tanks P1 and P2 contain x litres of the mixture of pure petrol and cheaper fuel. Since the concentration of petrol is the same in both tanks, the quantity of petrol in both tanks is the same at the beginning.
Concentration of Petrol in P1 after Replacement:
If 8 litres of the mixture in P1 is replaced with pure petrol, the quantity of petrol in P1 remains the same, but the total quantity of the mixture decreases by 8 litres. Therefore, the concentration of petrol in P1 becomes twice what it was initially.
Let's calculate the concentration of petrol in P1 initially and after replacement.
Initial Concentration of Petrol in P1:
The initial concentration of petrol in P1 is given by (x liters of petrol)/(x liters of mixture) = 1.
Concentration of Petrol in P1 after Replacement:
After replacing 8 liters of the mixture with pure petrol, the total quantity of the mixture in P1 becomes (x - 8) liters. Since the concentration of petrol becomes twice, the concentration of petrol in P1 after replacement is given by (x liters of petrol)/((x - 8) liters of mixture) = 2.
From the above equations, we can write:
(x)/(x - 8) = 2
Solving this equation, we get:
x = 16
Therefore, the initial quantity of the mixture in P1 and P2 is 16 liters.
Concentration of Petrol in P2 after Replacement:
If 16 liters of the solution from P2 is replaced with pure petrol, the quantity of petrol in P2 remains the same, but the total quantity of the solution decreases by 16 liters. Let's calculate the concentration of petrol in P2 after replacement.
Initial Concentration of Petrol in P2:
Since the concentration of petrol is the same in both P1 and P2, the initial concentration of petrol in P2 is also 1.
Concentration of Petrol in P2 after Replacement:
After replacing 16 liters of the solution with pure petrol, the total quantity of the solution in P2 becomes (16 - 16) = 0 liters. Therefore, the concentration of petrol in P2 after replacement is given by (x liters of petrol)/(0 liters of mixture) = Undefined.
Ratio of Final Concentration of Petrol in P2 to Initial Concentration of Petrol in P2:
As the concentration of petrol in P2 after replacement is undefined, we cannot calculate the ratio of the final concentration of petrol in P2 to the initial concentration of petrol in P2. Therefore, the answer is not determinable.
Hence, the correct option is (d) Not Determinable.
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Two petrol tanks P1 and P2 contain equal quantities of a mixture of pure petrol and some cheaper fuel. The concentration of petrol is same in both P1 and P2. If 8 litres of mixture in P1 is replaced with pure petrol then the concentration of petrol in P1 becomes twice of what it was initially. If 16 litres of solution from P2 is replaced with pure petrol, then what is the ratio of final concentration of petrol in P2 to the initial concentration of petrol in P2?a)4 : 1b)5 : 2c)3 : 1d)3 : 3Correct answer is option 'C'. Can you explain this answer?
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Two petrol tanks P1 and P2 contain equal quantities of a mixture of pure petrol and some cheaper fuel. The concentration of petrol is same in both P1 and P2. If 8 litres of mixture in P1 is replaced with pure petrol then the concentration of petrol in P1 becomes twice of what it was initially. If 16 litres of solution from P2 is replaced with pure petrol, then what is the ratio of final concentration of petrol in P2 to the initial concentration of petrol in P2?a)4 : 1b)5 : 2c)3 : 1d)3 : 3Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two petrol tanks P1 and P2 contain equal quantities of a mixture of pure petrol and some cheaper fuel. The concentration of petrol is same in both P1 and P2. If 8 litres of mixture in P1 is replaced with pure petrol then the concentration of petrol in P1 becomes twice of what it was initially. If 16 litres of solution from P2 is replaced with pure petrol, then what is the ratio of final concentration of petrol in P2 to the initial concentration of petrol in P2?a)4 : 1b)5 : 2c)3 : 1d)3 : 3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two petrol tanks P1 and P2 contain equal quantities of a mixture of pure petrol and some cheaper fuel. The concentration of petrol is same in both P1 and P2. If 8 litres of mixture in P1 is replaced with pure petrol then the concentration of petrol in P1 becomes twice of what it was initially. If 16 litres of solution from P2 is replaced with pure petrol, then what is the ratio of final concentration of petrol in P2 to the initial concentration of petrol in P2?a)4 : 1b)5 : 2c)3 : 1d)3 : 3Correct answer is option 'C'. Can you explain this answer?.
Two petrol tanks P1 and P2 contain equal quantities of a mixture of pure petrol and some cheaper fuel. The concentration of petrol is same in both P1 and P2. If 8 litres of mixture in P1 is replaced with pure petrol then the concentration of petrol in P1 becomes twice of what it was initially. If 16 litres of solution from P2 is replaced with pure petrol, then what is the ratio of final concentration of petrol in P2 to the initial concentration of petrol in P2?a)4 : 1b)5 : 2c)3 : 1d)3 : 3Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two petrol tanks P1 and P2 contain equal quantities of a mixture of pure petrol and some cheaper fuel. The concentration of petrol is same in both P1 and P2. If 8 litres of mixture in P1 is replaced with pure petrol then the concentration of petrol in P1 becomes twice of what it was initially. If 16 litres of solution from P2 is replaced with pure petrol, then what is the ratio of final concentration of petrol in P2 to the initial concentration of petrol in P2?a)4 : 1b)5 : 2c)3 : 1d)3 : 3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two petrol tanks P1 and P2 contain equal quantities of a mixture of pure petrol and some cheaper fuel. The concentration of petrol is same in both P1 and P2. If 8 litres of mixture in P1 is replaced with pure petrol then the concentration of petrol in P1 becomes twice of what it was initially. If 16 litres of solution from P2 is replaced with pure petrol, then what is the ratio of final concentration of petrol in P2 to the initial concentration of petrol in P2?a)4 : 1b)5 : 2c)3 : 1d)3 : 3Correct answer is option 'C'. Can you explain this answer?.
Solutions for Two petrol tanks P1 and P2 contain equal quantities of a mixture of pure petrol and some cheaper fuel. The concentration of petrol is same in both P1 and P2. If 8 litres of mixture in P1 is replaced with pure petrol then the concentration of petrol in P1 becomes twice of what it was initially. If 16 litres of solution from P2 is replaced with pure petrol, then what is the ratio of final concentration of petrol in P2 to the initial concentration of petrol in P2?a)4 : 1b)5 : 2c)3 : 1d)3 : 3Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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