Abhishek Gokhale

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?

Dear Ghufran, First let us assume the variable which we have to find (say X) which represents the quantity of mixture to be drawn off and replaced with water. Now when we draw X amount of mixture it will contain 3 parts of water and 5 parts of syrup (total 8 parts) and also it is replaced by water so, Parts of water in new mixture = 3 - 3 X/8 + X Parts of syrup in new mixture = 5 - 5X/8 Now we require that the mixture should be half water and half syrup i.e 4 parts of syrup and 4 parts of water so we equate any of the above equations with 4 for eg 3 - 3X/8 +X = 4 which on solving will give X=8/5 Also you can equate the equations to get the answer since we require equal ( half each) parts of syrup and water 3 - 3X/8 + X = 5 -5X/8 Which on solving will also give the same answer X =8/5 Hence 8/5th of the mixture should be drawn off and replaced by water to get half syrup and half water.