One cup of sugar water was poured out of 300 g of 8% sugar water and t

Question

One cup of sugar water was poured out of 300 g of 8% sugar water and then the same amount of pure water was poured into the solution. After that 2% sugar water was added, resulting in 400 g of 6% sugar water. What weight of sugar water was initially poured out?

A. 20 g 
B. 25 g 
C. 30 g 
D. 35 g 
E. 40 g

GMATGuruNY · Answer

Resulting amount of sugar = 6% of 400 grams = 24 grams.

Since the added sugar water increases the total volume from 300 grams to 400 grams, the amount of added sugar water = 400-300 = 100 grams
Since the added sugar water is 2% sugar, the weight of the added sugar = 2% of 100 = 2 grams.
Implication:
Before the 2% sugar water is added, the amount of sugar in the container = 24-2 = 22 grams.

Original amount of sugar in the container = 8% of 300 grams = 24 grams.
Since the removal process decreases the original amount of sugar from 24 grams to 22 grams, the amount of sugar removed = 24-22 = 2 grams.
Since the original solution is 8% sugar, these 2 grams must constitute 8% of the removed sugar water:
 2 = \frac{8}{100}x 
 x = \frac{100}{8} = 25 
 B

nick1816 · Answer

x..........2
......6.....
3...........1

x= 6+(4/3)= 22/3

the percentage of sugar after replacement=22/3%

V_R= V_I(1-\frac{x}{300)} 
 \frac{22}{3}*300=8*300(1-\frac{x}{300})

(1-\frac{x}{300})= \frac{11}{12} 
 \frac{x}{300}= \frac{1}{12} 
x=25

MathRevolution · Answer

=>
Suppose  x  is the weight of sugar water poured out.

Then  (\frac{8}{100})(300-x) + (\frac{2}{100})(400-300) = (\frac{6}{100})(400)  or  8(300-x) + 200 = 2400.

So,  8x = 200  and  x = 25.

Therefore, B is the answer.
Answer: B

Archit3110 · Answer

GMATGuruNY 
please see highlighted part

GMATGuruNY · Answer

I've corrected the typo. Thanks for calling it to my attention.

Kinshook · Answer

Given: One cup of sugar water was poured out of 300 g of 8% sugar water and then the same amount of pure water was poured into the solution. After that 2% sugar water was added, resulting in 400 g of 6% sugar water.

Asked: What weight of sugar water was initially poured out?

Let the weight of sugar water that was initially poured out be x gms

One cup of sugar water was poured out of 300 g of 8% sugar water and then the same amount of pure water was poured into the solution.
Sugar = 8%*(300-x)

After that 2% sugar water was added, resulting in 400 g of 6% sugar water.
Sugar = 8%*(300-x) + 2%*(400-300) = 8%(300-x) + 2 gm
Sugar = 6%*400 = 24 
8%(300-x) + 2 = 24
x = 300 - 22/8% = 25 gm

IMO B

luisdicampo · Answer

Deconstructing the Question

Initial solution:  300 g at 8% . 
Let  x  be the amount poured out. 
Pure water is added (0% sugar). 
Then 2% solution is added. 
Final mixture:  400 g at 6% .

Step-by-step

Initial sugar:

0.08 	imes 300 = 24

Sugar removed:

0.08x

Sugar remaining:

24 - 0.08x

After adding pure water, sugar unchanged.

Amount of 2% solution added:

400 - 300 = 100

Sugar added:

0.02 	imes 100 = 2

Final sugar:

26 - 0.08x

Final mixture has:

0.06 	imes 400 = 24

Equation:

26 - 0.08x = 24

0.08x = 2

x = \frac{2}{0.08}

x = 25

Answer: 25 g

One cup of sugar water was poured out of 300 g of 8% sugar water and t

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One cup of sugar water was poured out of 300 g of 8% sugar water and t

Prep Toolkit

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