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Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
- a)19 : 5
- b)16 : 5
- c)14 : 5
- d)16 : 7
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. I...
Quantity of alcohol in vessel P = 62.5 / 100 * 2 = 5 / 4 litres
Quantity of alcohol in vessel Q = 87.5 / 100 * 4 = 7 / 2 litres
Quantity of alcohol in the mixture formed = 5 / 4 + 7 / 2 = 19 / 4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5.
Quantity of alcohol in vessel Q = 87.5 / 100 * 4 = 7 / 2 litres
Quantity of alcohol in the mixture formed = 5 / 4 + 7 / 2 = 19 / 4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5.
Most Upvoted Answer
Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. I...
To find the ratio of alcohol and water in the resulting mixture, we need to calculate the amount of alcohol and water in each vessel and then combine them.
Let's assume that the amount of alcohol in vessel P is A liters and the amount of water in vessel P is W liters. Similarly, let's assume that the amount of alcohol in vessel Q is B liters and the amount of water in vessel Q is X liters.
The total amount of liquid in vessel P is 2 liters (since we are taking 2 liters from vessel P) and the total amount of liquid in vessel Q is 4 liters (since we are taking 4 liters from vessel Q).
We know that the percentage of alcohol in vessel P is 62.5%. Therefore, we can write the equation: A/(A+W) = 62.5/100. Simplifying this equation gives us: A = 0.625(A+W).
Similarly, the percentage of alcohol in vessel Q is 87.5%. Therefore, we can write the equation: B/(B+X) = 87.5/100. Simplifying this equation gives us: B = 0.875(B+X).
Now, when we mix 2 liters from vessel P and 4 liters from vessel Q, the total amount of liquid in the resulting mixture is 2+4=6 liters.
Let's calculate the amount of alcohol in the resulting mixture. From vessel P, we are taking 2 liters, which contains 0.625A liters of alcohol. From vessel Q, we are taking 4 liters, which contains 0.875B liters of alcohol. Therefore, the total amount of alcohol in the resulting mixture is 0.625A + 0.875B.
Similarly, let's calculate the amount of water in the resulting mixture. From vessel P, we are taking 2 liters, which contains W liters of water. From vessel Q, we are taking 4 liters, which contains X liters of water. Therefore, the total amount of water in the resulting mixture is W + X.
Now, we can calculate the ratio of alcohol to water in the resulting mixture by dividing the total amount of alcohol by the total amount of water. Therefore, the ratio is (0.625A + 0.875B) / (W + X).
We can substitute the values of A and B from the equations we derived earlier. A = 0.625(A+W) and B = 0.875(B+X).
After substituting the values, we get the equation: (0.625(0.625(A+W)) + 0.875(0.875(B+X))) / (W + X).
Simplifying this equation gives us: (0.625^2A + 0.625^2W + 0.875^2B + 0.875^2X) / (W + X).
Since we are looking for the ratio, we can simplify this equation further. Dividing the numerator and denominator by (0.625^2) gives us: (A + (0.625/0.875)^2W + B + (0.875/0.625)^2X) / (W + X).
Simplifying this equation gives us: (A + (0.625/0.875)^2W + B + (0.875/0.625)^
Let's assume that the amount of alcohol in vessel P is A liters and the amount of water in vessel P is W liters. Similarly, let's assume that the amount of alcohol in vessel Q is B liters and the amount of water in vessel Q is X liters.
The total amount of liquid in vessel P is 2 liters (since we are taking 2 liters from vessel P) and the total amount of liquid in vessel Q is 4 liters (since we are taking 4 liters from vessel Q).
We know that the percentage of alcohol in vessel P is 62.5%. Therefore, we can write the equation: A/(A+W) = 62.5/100. Simplifying this equation gives us: A = 0.625(A+W).
Similarly, the percentage of alcohol in vessel Q is 87.5%. Therefore, we can write the equation: B/(B+X) = 87.5/100. Simplifying this equation gives us: B = 0.875(B+X).
Now, when we mix 2 liters from vessel P and 4 liters from vessel Q, the total amount of liquid in the resulting mixture is 2+4=6 liters.
Let's calculate the amount of alcohol in the resulting mixture. From vessel P, we are taking 2 liters, which contains 0.625A liters of alcohol. From vessel Q, we are taking 4 liters, which contains 0.875B liters of alcohol. Therefore, the total amount of alcohol in the resulting mixture is 0.625A + 0.875B.
Similarly, let's calculate the amount of water in the resulting mixture. From vessel P, we are taking 2 liters, which contains W liters of water. From vessel Q, we are taking 4 liters, which contains X liters of water. Therefore, the total amount of water in the resulting mixture is W + X.
Now, we can calculate the ratio of alcohol to water in the resulting mixture by dividing the total amount of alcohol by the total amount of water. Therefore, the ratio is (0.625A + 0.875B) / (W + X).
We can substitute the values of A and B from the equations we derived earlier. A = 0.625(A+W) and B = 0.875(B+X).
After substituting the values, we get the equation: (0.625(0.625(A+W)) + 0.875(0.875(B+X))) / (W + X).
Simplifying this equation gives us: (0.625^2A + 0.625^2W + 0.875^2B + 0.875^2X) / (W + X).
Since we are looking for the ratio, we can simplify this equation further. Dividing the numerator and denominator by (0.625^2) gives us: (A + (0.625/0.875)^2W + B + (0.875/0.625)^2X) / (W + X).
Simplifying this equation gives us: (A + (0.625/0.875)^2W + B + (0.875/0.625)^
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Community Answer
Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. I...
Quantity of alcohol in vessel P = 62.5 / 100 * 2 = 5 / 4 litres
Quantity of alcohol in vessel Q = 87.5 / 100 * 4 = 7 / 2 litres
Quantity of alcohol in the mixture formed = 5 / 4 + 7 / 2 = 19 / 4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5.
Quantity of alcohol in vessel Q = 87.5 / 100 * 4 = 7 / 2 litres
Quantity of alcohol in the mixture formed = 5 / 4 + 7 / 2 = 19 / 4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5.
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Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?a)19 : 5b)16 : 5c)14 : 5d)16 : 7Correct answer is option 'A'. Can you explain this answer?
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Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?a)19 : 5b)16 : 5c)14 : 5d)16 : 7Correct answer is option 'A'. 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 vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?a)19 : 5b)16 : 5c)14 : 5d)16 : 7Correct answer is option 'A'. 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 vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?a)19 : 5b)16 : 5c)14 : 5d)16 : 7Correct answer is option 'A'. Can you explain this answer?.
Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?a)19 : 5b)16 : 5c)14 : 5d)16 : 7Correct answer is option 'A'. 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 vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?a)19 : 5b)16 : 5c)14 : 5d)16 : 7Correct answer is option 'A'. 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 vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?a)19 : 5b)16 : 5c)14 : 5d)16 : 7Correct answer is option 'A'. Can you explain this answer?.
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