Question: A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
[A].
[A].
| 1 |
| 3 |
[B].
| 1 |
| 4 |
[C].
| 1 |
| 5 |
[D].
| 1 |
| 7 |
Answer: Option C
Explanation:
Suppose the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water.
| Quantity of water in new mixture = | 3 – | 3x | + x | litres | ||
| 8 |
| Quantity of syrup in new mixture = | 5 – | 5x | litres | ||
| 8 |
| 3 – | 3x | + x | = | 5 – | 5x | |||||
| 8 | 8 |
5x + 24 = 40 – 5x
10x = 16
| x = | 8 | . |
| 5 |
| So, part of the mixture replaced = | 8 | x | 1 | = | 1 | . | ||
| 5 | 8 | 5 |