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?

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/8+ x)litres Quantity of syrup in new mixture = (5 -5x/8)litres therefore, (3 -3x/8+ x) = (5 -5x/8) 5x + 24 = 40 - 5x 10x = 16 x = 8/5 So, part of the mixture replaced = (8/5 x1/8)=1/5 . read less

Its so simple dude, 5 parts syrup nd 3 parts water, totally 8 parts , for our convenience let the total quantity of mixture be 8 litres. So from this 8 liters some amt is taken and replaced with water, let that be x liters. Even in that x liters that we take from 8 liters have 5 parts syrup nd 3 parts water so please find below eqn 3- 3x/8 + x= 5-5x/8 24- 3x+8x= 40-5x 10x=16 X=1.6 lits read less

Solution: Let the amount of water be 3x and that of syrup be 5x. => The quantity of liquid = 8x. Since we are not changing the quantity of syrup, it remain as 5x. In order to get the mixture half water and half syrup we need to have their ratio as 1:1. Adding"2x" water make quantities of both ingredients equal. However, this make total quantity to 10x but the mixture will be half syrup and half water. read less

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. read less

One fifth......it is like if l lts of content is assumed, 3l/8 will b water and 5l/8 will be syrup. Now if a lts of content is removed and a lts of water is added , then water content in new mixture will be 3(l-a)/8+a which must b equal to syrup in new mixture, 5(l-a)/8. Equating them, you'd get a=l/5. That means 1/5th of original content needs to b removed and replaced with water read less