A vessel is filled with liquid, 3 parts of which are water and 5 parts

Question

A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. What part of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

A. 1/5

B. 2/7

B. 7/11

C. 6/7

E. 7/8

Kinshook · Accepted Answer

Given: A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. 
Asked: What part of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

Before:  
Water = 3/8
Syrup = 5/8

Let x part of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup

After: 
Water = 3/8(1-x) + x
Syrup = 5/8(1-x) 
Since mixture becomes half water and half syrup
3/8(1-x) + x = 5/8(1-x)
2/8(1-x) = x
(1-x) = 4x
x = 1/5

IMO A

danbrown9445 · Answer

Let there be 1L of liquid.
Hence Syrup is  \frac{5}{8}  L.

Let x part drawn off.
x part will contain 5/8*x quantity of syrup.
So syrup left is:

\frac{5}{8} - \frac{5}{8}*x = \frac{{5-5x}}{8}

This equals to 1/2 of the liquid.

\frac{{5-5x}}{8}=\frac{1}{2}

-5x = -1

x=1/5

CrackverbalGMAT · Answer

\frac{Final}{Initial} = (1 - \frac{b}{a})^n

Final = The Final Quantity of that component who's   concentration is being reduced  .

Initial = The Initial Quantity of that component who's   concentration is being reduced  .

b = Amount of liquid replaced

a = Final Volume in the container   after the replacement   of quantity b.

n = number of times the operation is done

here the concentration of syrup is being reduced.

Initial quantity = 5/8 Final quantity = 1/2 (Since the final ratio is 1 : 1)

Therefore  \frac{\frac{1}{2}}{\frac{5}{8}} = 1 - \frac{b}{a}

\frac{4}{5} = 1 - \frac{b}{a}

\frac{b}{a} = 1 - \frac{4}{5} = \frac{1}{5}

Option A

Arun Kumar

Mona2019 · Answer

Let the solution be 8 litres.
So, 5 litres is syrup, 3 litre is water.
For the solution to have equal quantity of syrup and water, it needs to have 4 litre syrup and 4 litre water.
4 litre syrup means (8/5)*4 litre solution.
Which is 6.4litres of solution.
So the remaining 1.6 litres has to be removed and same quantity of water has to be added.
So the ratio/part of solution to be removed is 1.6/8 = 0.2 = 1/5

Posted from my mobile device

stne · Answer

Let the total quantity be  16 , let  x   be withdrawn , now we have left with  16-x

So syrup before adding water   =\frac{5}{8}* (16-x)

Syrup after adding water = \frac{1}{2} *16 =8

After we add water back, again we have total quantity  16  , but the  VOLUME  or  QUANTITY  of syrup remains unchanged.

NOTE : we are adding ONLY water, hence QUANTITY of syrup in the soln. before and after water addition remains unaltered.

so syrup before water addition = syrup after water addition

\frac{5}{8}* (16-x) = 8

x= \frac{16}{5}  , this is  \frac{1}{5}   of the total initial soln.

\frac{16}{5} * \frac{1}{16}= \frac{1}{5}

Ans-A

Hope it's clear.

SwethaReddyL · Answer

Bunuel  /  CrackverbalGMAT  - just a quick question on the formal used here
a = Final Volume in the container   after the replacement   of quantity b.
FQ/IQ =  , isn't the c here not the total capacity? 
this is how i approached but didn't get the answer,

since half and half the final quantity should be 4 and 4
acc to formula,
4/5 =  
4/5 = 8-x/8
32 = 40-5x
5x = 8
x = 8/5 is what i got
a little help please - the mistake is taking c as 8 i think but i wanna know the gap in my logic
thanks in advance,
swetha

Bunuel · Answer

A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. What part of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

A. 1/5
B. 2/7
B. 7/11
C. 6/7
E. 7/8

Let the total mixture be 1.

Initial water = 3/8
Initial syrup = 5/8

Suppose fraction x of the mixture is drawn off and replaced with water.

After drawing off x, the syrup left is:

5/8 * (1 - x)

For the final mixture to be half syrup:

5/8 * (1 - x) = 1/2

5(1 - x) = 4

1 - x = 4/5

x = 1/5

Answer: A.

In the formula,

\frac{FQ}{IQ}=1-\frac{b}{a}

b  is the amount of mixture drawn off and replaced.

a  is the total quantity of the mixture in the vessel after replacement. Since the vessel remains full, this is also the total capacity of the vessel.

So using 8 as the total quantity is fine.

Your equation gives:

\frac{4}{5}=1-\frac{x}{8}

so  x=\frac{8}{5} . But this  x  is the  amount  drawn off, not the fraction of the whole mixture drawn off.

Since the whole mixture is 8 parts, the fraction drawn off is:

\frac{8/5}{8}=\frac{1}{5}

kevincan · Answer

A shortcut is to realize that when you draw off and replace, the total volume doesn’t change 
Suppose you start with 8 equal parts of liquid , 5 of them syrup. You want to end up with 4 parts , so get rid of 1 of the 5 syrup parts

1/5 is the answer

A vessel is filled with liquid, 3 parts of which are water and 5 parts

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A vessel is filled with liquid, 3 parts of which are water and 5 parts

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