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Bunuel
A saline solution is 2% salt by weight, with the rest being water. After more water is added, the salt concentration decreases to 1% by weight. What is the ratio of the final weight of water to the initial weight of water in the solution?

A. 1:2
B. 50:49
C. 2:1
D. 99:49
E. 100:49


 


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will do this with allegation method where we are mixing water with
1. water with 98% solution
2.water with 100% pure water
3. resulting in 99% water in final solution

using the allegation formula we got

99-98/ 100-99 = 1: 1
so intial water is =0.98 units
pure water is = 1 unit
final water is 1.98 unit



ratio of final water/ initial water = 1.98/0.98 = 99/49
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There is 98% water in original solution and we are mixing it with 100% solution to make it 99% percent water. By Weighted average method or we find that we are mixing both solution in 1:1 ratio.

Now lets assume that there is initially 100(98 gram water + 2 gram salt) gram solution and we added another another 100 gram water which mean now mixture is 198 gram water and 2 gram salt.

Hence final water to initial water ratio is 198:98 or 99:1. Option D
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Assume initially there are 2 g of salt and 90 g of water. Let's say x = total new water added in grams. We have:

2/ (100+x) = 1/100
x = 100

So the ratio of the final weight of water to the initial weight of water in the solution = (100 + 98)/98 = 99/49

Answer: D
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Let initial weight of solution be 100kg

Initial weight of salt = 2% of 100 = 2kg
Initial weight of water = 98kg

Let's say 100kgs of water was added. Final weight becomes 200
Final % of salt becomes = 2/200 = 1%
Final weight of water = 99% of 200 = 198

Final weight of water / Initial weight of water = 198/98 = 99/49

Therefore option D is correct.
Bunuel
A saline solution is 2% salt by weight, with the rest being water. After more water is added, the salt concentration decreases to 1% by weight. What is the ratio of the final weight of water to the initial weight of water in the solution?

A. 1:2
B. 50:49
C. 2:1
D. 99:49
E. 100:49


 


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let total be 100
salt is 2 so weight of salt in water ; 2/100 and part of salt in water is 2/98

water is increased by 1% ; water weight is now 1/99 and salt conc will become 1/100

final weight of water to initial weight
2/98 *y= 1/99 *x
1/49* y = 1/99 * x
x/y = 99/49

option D
Bunuel
A saline solution is 2% salt by weight, with the rest being water. After more water is added, the salt concentration decreases to 1% by weight. What is the ratio of the final weight of water to the initial weight of water in the solution?

A. 1:2
B. 50:49
C. 2:1
D. 99:49
E. 100:49


 


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30 seconds solution:

It says 2% salt that means If solution is 100, then wt of salt=2 and rest is water = 98.
If more water is added, the salt % is 1.
So to make salt 1%, 2 will be 1% of 200. So we will add 100 amt of water.

Hence, initial weight of water =98
final weight of water =100+98 => 198

Ratio: 198/98 => 99/49

Option D) 99/49
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Solution 1
Salt : 2x
Water: 98x
Solution 2
Salt: 1y
Water: 99y
1y=2x since only water has been added
So 99y = 99*2
Ratio of final weight of water to the initial weight of water
99*2/98
99/49
Hence, D.
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Bunuel
A saline solution is 2% salt by weight, with the rest being water. After more water is added, the salt concentration decreases to 1% by weight. What is the ratio of the final weight of water to the initial weight of water in the solution?

A. 1:2
B. 50:49
C. 2:1
D. 99:49
E. 100:49


 


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SOLUTION:

Based on given information for a 100g solution the weight of salt is 2g and the weight of water is 98g i.e. the ratio of weight of salt to weight of water is 2/98 or 1/49.

Further, when more water, say x grams is added the concentration of salt decreases to 1%. Therefore, the new ratio of weight of salt to weight of water becomes 1/99.

The quantity of salt in both cases remains the same. The ratio of weight of water is 99/49 i.e approx. 2:1. Hence, Option C.

2/(98+x) = 1/99

=> x+98 = 198
=> x=100

Ratio of weights of water is (x+98)/98 i.e. 198/98 (~2:1)

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Concentration at the beginning is 2%, so we can say that we hace 2 of salt and 98 of water
After adding some water salt concentration drop to 1%, so now we have 2 of salt in a solution of 200, so water is 198
We're asked for the rate among water volume at the end water volume at the beginning = 198/98 = 99/49
Answer is (D)
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Final salt water is getting decreased by 1 percent, 49:98 = 1:2
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S%/W% for solution 1 and solution 2:-
2/98 and 1/99

Assume solution 1's weight is 100g.

c1v2=c2v2
2*100=1*x
x=200

weight is water in solution 2:-

99/100*200= 198g

Ratio of the final weight of water to the initial weight of water in the solution?

198/98= 99/49= 99:49 (D)


Bunuel
A saline solution is 2% salt by weight, with the rest being water. After more water is added, the salt concentration decreases to 1% by weight. What is the ratio of the final weight of water to the initial weight of water in the solution?

A. 1:2
B. 50:49
C. 2:1
D. 99:49
E. 100:49


 


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for the GMAT Club Olympics Competition

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Given:

The solution's initial concentration is 2%.

Which means the amount of salt / total amount should be equal to 2 / 100


SaltWaterTotal Solution
2g98g100g


Now, we are given that some amount of water is added, and the solution's concentration reduces to 1%. Let that added amount of water be x.

SaltWaterTotal Solution
2g(98+x) g(100 + x) g


We can determine the value of x by equating

1/ 100 = 2 / (100 + x)

X = 102 g

Ratio of added amount of water to original water is

98 + 102 : 98

Which is 100 : 49

Correct answer : Option (D)
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let initial saline solution as 100 lit,
so, salt 2%=2/100
water would be 98%=98/100
let x lit. water is added to 2% salt solutn.,
then it reduced to 1% alt solution means now water is 99%=99/100
and volume of final solution would become (100+x)lit
so, 98+x/100+x=99/100
x= 100
final water / initial water=98+x/98=98+100/98=99/49

Bunuel
A saline solution is 2% salt by weight, with the rest being water. After more water is added, the salt concentration decreases to 1% by weight. What is the ratio of the final weight of water to the initial weight of water in the solution?

A. 1:2
B. 50:49
C. 2:1
D. 99:49
E. 100:49


 


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Bunuel
A saline solution is 2% salt by weight, with the rest being water. After more water is added, the salt concentration decreases to 1% by weight. What is the ratio of the final weight of water to the initial weight of water in the solution?

A. 1:2
B. 50:49
C. 2:1
D. 99:49
E. 100:49


 


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In 100 grams of water 2 grams of salt is present. Hence, water = 98 grams

When the saline solution is diluted, the amount of salt remains the same.

2/x * 100 = 1

x = 200

In this, 2 grams is the weight of the salt, and 198 grams is the weight of the water.

Ratio = 198/98 = 99/49

Option D
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I'm looking for a fraction with (final water weight) / (initial water weight). Because I'm adding more water, I can immediately eliminate A. I find it easiest to assume the quantity is 100.

Initial salt: 2g
Initial water: 98g

Once we add water (x) to the 100g, with the 2g of salt staying the same and now being only 1% of the micture, this translates to the equation:
2/(100+x) = 1/100
x= 100

Thus, final water weight is 98+100 = 198 -> 198/98 = 99/49

Answer: D)
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IMO should be D

Lets assume that water was 98 ml and salt was 2 ml initially. Let 'x' be the water added to the solution after which the salt concentration decreases to 1/100

Thus,

[2][/100+x]=[1][/100]

x=100

Final Water / Initial Water = 198/98 = 99/49
Bunuel
A saline solution is 2% salt by weight, with the rest being water. After more water is added, the salt concentration decreases to 1% by weight. What is the ratio of the final weight of water to the initial weight of water in the solution?

A. 1:2
B. 50:49
C. 2:1
D. 99:49
E. 100:49


 


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Strategy
Focus on Water component and use algebra
Variables: Initial Salt = "Si"; Initial Water = "Wi"; Water added = "x"; Final Water = "Wf"
Rephrase Question: What is Wf:Wi?

1. Set initial total to 100 units
  • Wi = (100) - (Si) = (100) - (2) = 98
2. Determine final totals
  1. (Wi + x)/(100 + x) = 99/100
  • 9800 + (100x) = 9900 + (99x)
  • x = 100 units
2. Wf = Wi + x = (98) + (100) = 198 units
3. Determine Ratio
  • (Wf) : (Wi) = (198) : (98) = 99:49

Answer: D
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