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Class 12 Tuition > Learn Class XI-XII Tuition (PUC) > A vessel is filled with liquid, 3 parts of which are...
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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?

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Physics Maths proficient Software developer in perl and shell

Suppose 80 liters of liquid we have 30 l water and 50 l syrup.we take out 'x' units of liquid from the vessel. So we draw 3x/8 units of water and 5x/8 units of syrup from the vessel. Remaining quantities of water and syrup left are now 30-(3x/8) and 50-(5x/8) units respectively. We now add 'x' units...
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Suppose 80 liters of liquid we have 30 l water and 50 l syrup.we take out 'x' units of liquid from the vessel. So we draw 3x/8 units of water and 5x/8 units of syrup from the vessel. Remaining quantities of water and syrup left are now 30-(3x/8) and 50-(5x/8) units respectively. We now add 'x' units of water. Now quantities of water and syrup are 30-(3x/8)+x and 50-(5x/8) respectively. As there must be equal quantities of water and syrup now, we have 30-(3x/8)+x = 50-(5x/8) Solve to get x=16 units which means you need to draw 20% or 1/5th of the liquid from the vessel. read less
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Maths, Physics & Chemistry, IIT Kanpur & IIT Bombay graduate

Answer: 1/5th of the vessel volume. Let's assume the capacity of vessel be (3+5=) 8 ltrs. Now, the basic principle of all such questions is that when you remove any amount of the mixture, it removes both the liquids in the same ratio as the mixture itself. So, let's suppose we take x ltrs out of the...
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Answer: 1/5th of the vessel volume. Let's assume the capacity of vessel be (3+5=) 8 ltrs. Now, the basic principle of all such questions is that when you remove any amount of the mixture, it removes both the liquids in the same ratio as the mixture itself. So, let's suppose we take x ltrs out of the vessel. This means 5x/8 amount of syrup and 3x/8 amount of water gets removed. which means the remaining mixture has (3-(3x/8)) ltrs of water & (5-(5x/8)) syrup. Now when we add x ltrs of water to this mixture, the amount of water and syrup becomes equal. Thus, (x+3-(3x/8)) = (5-(5x/8)) => x=1.6 ltrs. Since we assumed that vessel is 8 ltrs. in volume=> 1.6/8 = 1/5th of the mixture in the vessel needs to be replaced with water. Hope it helps. :) read less
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Let x litres of this liquid be replaced with water Let x litres of this liquid be replaced with water. Quantity of syrup in new mixture = (5 -5x/8)litres 3- 3x/8 + x= 5-5x/8 24- 3x+8x= 40-5x 10x=16 X=1.6 lits
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Tutor,Mentor,Consultant and Professional drives through result oriented approach.

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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,...
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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
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Aptitude analyser

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...
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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
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Teacher - Mathematics and Physics (Grades 9 through 12)

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...
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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
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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...
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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
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Experienced Math teacher for 9-12 math

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....
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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
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