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 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. 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