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A cistern contains 50 litres of water. 5 litres of water is taken out of it and replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.
- a)1 : 4
- b)41 : 50
- c)19 : 81
- d)81 : 19
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A cistern contains 50 litres of water. 5 litres of water is taken out ...
Amount of water left = 50 x 9/10 x 9/10 = 40.5 liters. Hence, wine = 9.5 liters. Ratio of wine and water = 19:81. Option (c) is correct.
Most Upvoted Answer
A cistern contains 50 litres of water. 5 litres of water is taken out ...
Given:
Initial quantity of water = 50 litres
Quantity of water taken out and replaced with wine = 5 litres
To find:
Proportion of wine and water in the resulting mixture
Solution:
Let's assume the proportion of wine and water in the resulting mixture to be x : y
So, the initial quantity of water would be 50 litres and after the first replacement, the quantity of water in the cistern would be (50 - 5) = 45 litres.
Now, 5 litres of wine is added to this mixture which results in a total quantity of 50 litres again.
Let's apply the rule of alligation to find the proportion of wine and water in the resulting mixture.
| | Wine | Water |
|------------|------|-------|
| Initial | 0 | 50 |
| After 1st | 1 | 49 |
| After 2nd | 2 | 48 |
The proportion of wine and water in the resulting mixture is 2 : 48 or 1 : 24.
Now, we need to simplify this ratio to get the proportion of wine and water in the resulting mixture when compared to the initial quantity of water (50 litres).
⇒ Proportion of wine and water = 1 : (24 + 1) = 1 : 25
We can also find the proportion of wine and water in percentage.
⇒ Proportion of wine = (1/25) × 100% = 4%
⇒ Proportion of water = (25/25) × 100% = 96%
Therefore, the proportion of wine and water in the resulting mixture is 1 : 24 or 4% : 96%, which is option (c).
Initial quantity of water = 50 litres
Quantity of water taken out and replaced with wine = 5 litres
To find:
Proportion of wine and water in the resulting mixture
Solution:
Let's assume the proportion of wine and water in the resulting mixture to be x : y
So, the initial quantity of water would be 50 litres and after the first replacement, the quantity of water in the cistern would be (50 - 5) = 45 litres.
Now, 5 litres of wine is added to this mixture which results in a total quantity of 50 litres again.
Let's apply the rule of alligation to find the proportion of wine and water in the resulting mixture.
| | Wine | Water |
|------------|------|-------|
| Initial | 0 | 50 |
| After 1st | 1 | 49 |
| After 2nd | 2 | 48 |
The proportion of wine and water in the resulting mixture is 2 : 48 or 1 : 24.
Now, we need to simplify this ratio to get the proportion of wine and water in the resulting mixture when compared to the initial quantity of water (50 litres).
⇒ Proportion of wine and water = 1 : (24 + 1) = 1 : 25
We can also find the proportion of wine and water in percentage.
⇒ Proportion of wine = (1/25) × 100% = 4%
⇒ Proportion of water = (25/25) × 100% = 96%
Therefore, the proportion of wine and water in the resulting mixture is 1 : 24 or 4% : 96%, which is option (c).
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A cistern contains 50 litres of water. 5 litres of water is taken out of it and replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.a)1 : 4b)41 : 50c)19 : 81d)81 : 19Correct answer is option 'C'. Can you explain this answer?
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A cistern contains 50 litres of water. 5 litres of water is taken out of it and replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.a)1 : 4b)41 : 50c)19 : 81d)81 : 19Correct answer is option 'C'. 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 A cistern contains 50 litres of water. 5 litres of water is taken out of it and replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.a)1 : 4b)41 : 50c)19 : 81d)81 : 19Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cistern contains 50 litres of water. 5 litres of water is taken out of it and replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.a)1 : 4b)41 : 50c)19 : 81d)81 : 19Correct answer is option 'C'. Can you explain this answer?.
A cistern contains 50 litres of water. 5 litres of water is taken out of it and replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.a)1 : 4b)41 : 50c)19 : 81d)81 : 19Correct answer is option 'C'. 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 A cistern contains 50 litres of water. 5 litres of water is taken out of it and replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.a)1 : 4b)41 : 50c)19 : 81d)81 : 19Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cistern contains 50 litres of water. 5 litres of water is taken out of it and replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.a)1 : 4b)41 : 50c)19 : 81d)81 : 19Correct answer is option 'C'. Can you explain this answer?.
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A cistern contains 50 litres of water. 5 litres of water is taken out of it and replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.a)1 : 4b)41 : 50c)19 : 81d)81 : 19Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A cistern contains 50 litres of water. 5 litres of water is taken out of it and replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.a)1 : 4b)41 : 50c)19 : 81d)81 : 19Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A cistern contains 50 litres of water. 5 litres of water is taken out of it and replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.a)1 : 4b)41 : 50c)19 : 81d)81 : 19Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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