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

Question

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
E. 1/9

chetan2u · Accepted Answer

Adding two more ways..

(I) Straight answer would be the fraction that is removed of total will fraction of syrup that is removed, so 3:5 becomes 4:4, so change in syrup is (5-4) in 5 units so  \frac{5-4}{5} =1/5

Other ways to think of is..

(II) Let total be 80 so water : syrup = 30:50
This becomes 40:40 after transfer
So 10 of syrup moves from syrup to water, but it is a combination of syrup and water that is removed...
So if in 50, we remove 10, 
therefore in total (50+30=80), we remove  \frac{10*80}{50} =16

So as a fraction, 16 out of 80 is 16/80=1/5

(III) Ratio  = 3:5 = 3y:5y 
say we take out x units this will contain  \frac{3x}{3+5}  water and  \frac{5x}{3+5}  syrup..
Overall effect on water =  \frac{x-3x}{8}=\frac{5x}{8} 
So new ratio =  3y+\frac{5x}{8}:5y-\frac{5x}{8}=1:1.........(3y+\frac{5x}{8})/(\frac{5y-5x}{8})=\frac{1}{1} ......
 3y+\frac{5x}{8}=\frac{5y-5x}{8}...........2y=\frac{5x}{4}.....y=\frac{5x}{8}. ..

Initial =  3y+5y=8y=8*\frac{5x}{8}=5x 
So x is  \frac{x}{5x}  of 5x....or 1/5

C

sumit411 · Answer

Answer is C 1535478082737.jpg Thank you = Kudos

shard87 · Answer

sumit411

1) Why did you take initial concentation 5/8
2) how could the final volume be 8

Nice approach but I guess I am missing some concept on my side.

sumit411 · Answer

1) Initial concentration is 5 volumes of syrup in 8 units of total solution. Now this is the basic definition of concentration

Eg what you mean by 10% alcohol solution?
10 units of alcohol in 100 units of solution

2) 3+5=8
So I used 8 units as total volume.

https://gmatclub.com/forum/weighted-ave ... l#p1586082

Check out removal/replacement in mixture topic.

targetbusiness · Answer

VeritasKarishma  and  Bunuel  May I request you to solve this with an easy approach.
I tried to understand the explanations given in the thread, but couldn't.

chetan2u · Answer

Hi..

Straight answer would be the fraction that is removed of total will fraction of syrup that is removed, so 3:5 becomes 4:4, so change in syrup is (5-4) in 5 units so  \frac{5-4}{5} =1/5

Other way....

Let total be 80 so water : syrup = 30:50
This becomes 40:40
So 10 of syrup moves from syrup to water, but it is a combination of syrup and water that is removed...
So if in 50, we remove 10, 
therefore in total (50+30=80), we remove  \frac{10*80}{50} =16

So as a fraction 16 out of 80 is 16/80=1/5

KarishmaB · Answer

You can just use the weighted avg formula here:

w1/w2 = (A2 - Aavg) / (Aavg - A1) 
The concentration of water in original solution is A1 = 3/8, the concentration of water in second solution is 1 (it is pure water). The concentration of water in final solution is A2 = 1/2

w1/w2 = (1 - 1/2) / (1/2 - 3/8) = 4/1

The original solution must be 4 parts and the water added (by removing some solution) must be 1 part. So 1/5 of the solution must have been replaced with water.

Answer (C)

eega · Answer

Given mixture contains 3 parts water and 5 parts syrup
let r be the percent of water added replacing syrup

final mixture contains 1/2 syrup and 1/2 water
hence 1/2 syrup = (100-r)*5/8 + r*0

solving r = 1/5  (Option C)

hr1212 · Answer

Let initial solution of mixture be T, and x solution of this mixture is replaced with water.

Equate quantity of water before and after,

Quantity of water in mixture T after x part is removed + x liter of water added = Half quantity of water in the final solution T

(T-x)*3/8 + x = T/2
3T/8 - 3x/8 + x = T/2
5x/8 = T/8
x = T/5

Hence, x liter of water added is 1/5 of the original solution.

IMO: C

vinquant100 · Answer

USE ALLIGATIONS AND U R SORTED. https://gmatclub.com/forum/download/file.php?id=84150 .. GMAT-Club-Forum-n4zmp1jp.png

Kinshook · Answer

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?

Let the liquid be 1 liter in volume.

Water = 3/8 liters
Syrup = 5/8 liters

Let x liter of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup
Water = 3/8 - 3x/8 + x liters
Syrup = 5/8 - 5x/8 liters

3/8 - 3x/8 + x = 5/8 - 5x/8
10x/8 = 2/8
x = 1/5

IMO C

PSKhore · Answer

Shouldn't water be 3/8 - 3x/8 + 5x/8???

PSKhore · Answer

why is the new ratio 1???

Bunuel · Answer

No, it should not be 3/8 - 3x/8 + 5x/8.

When x liters of the mixture are removed, 3x/8 of that is water. So you subtract 3x/8 from the original 3/8 water. Then, you add back x liters of pure water.

So the total water becomes: 3/8 - 3x/8 + x.

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