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Math Expert V
Joined: 02 Sep 2009
Posts: 59628
A 48 gallon solution of salt and water is 10% salt. How many gallons  [#permalink]

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15 00:00

Difficulty:   15% (low)

Question Stats: 82% (02:04) correct 18% (02:28) wrong based on 311 sessions

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A 48 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?

A. 8
B. 12
C. 13
D. 14
E. 16

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Posts: 1870
Re: A 48 gallon solution of salt and water is 10% salt. How many gallons  [#permalink]

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1
4
Bunuel wrote:
A 48 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?

A. 8
B. 12
C. 13
D. 14
E. 16

Amount of salt = 4.8
Assume x gallons of water are added.

4.8 / 48 + x = 8/100
480 = 8x + 384
8x = 96
x = 12

Correct Option: B
##### General Discussion
Senior Manager  S
Joined: 21 Mar 2016
Posts: 494
Re: A 48 gallon solution of salt and water is 10% salt. How many gallons  [#permalink]

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1
1
Amount of salt = 10% of 48 = 4.8 gallons

this 4.8 gallons will be 8% of new mixture
therefore,
resulting mixture = 4.8/0.08 = 60 gallons

gallons to be added = 60-48 = 12 gallons,, option B
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Re: A 48 gallon solution of salt and water is 10% salt. How many gallons  [#permalink]

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1
N1*V1=N2*V2

10*48 = 8*V2

V2=60 --> 60-48 = 12
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Re: A 48 gallon solution of salt and water is 10% salt. How many gallons  [#permalink]

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let x=gallons of water to be added
.9(48)+x=.92(48+x)
x=12 gallons
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Re: A 48 gallon solution of salt and water is 10% salt. How many gallons  [#permalink]

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Bunuel wrote:
A 48 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?

A. 8
B. 12
C. 13
D. 14
E. 16

Attachment: Capture.PNG [ 2.49 KiB | Viewed 5143 times ]

Now we get 8% = 4.8

So, 100% = 4.8/8*100

Hence , 100% = 60

We know 48 + x = 60

So, X = 12

Hence answer must be (B) 12
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Retired Moderator G
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A 48 gallon solution of salt and water is 10% salt. How many gallons  [#permalink]

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1
Bunuel wrote:
A 48 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?

A. 8
B. 12
C. 13
D. 14
E. 16

Let the quantity of water to be added be X liters.

Quantity of Salt in the gallon = 10/100 ( 48) = 4.8 liters.

=> 4.8 = 0.08 ( 48 + X ) ( Here the quantity remains same but the concentration gets diluted, since we add X liters of water.
=> 48 = 8/10 ( 48 + X )
=> 480 = 384 + 8X
=> 96 = 8X
=> X =12. ---> Choice B.
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Re: A 48 gallon solution of salt and water is 10% salt. How many gallons  [#permalink]

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Backsolve. I started with B because it was easy.
48+12=60.
8% of 60=4.8

Senior SC Moderator V
Joined: 22 May 2016
Posts: 3736
A 48 gallon solution of salt and water is 10% salt. How many gallons  [#permalink]

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Bunuel wrote:
A 48 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?

A. 8
B. 12
C. 13
D. 14
E. 16

Let x = amount of water to be added.

Water is 0% salt. It is added in on LHS to track on the idea that two quantities are being mixed (the 10% solution and water)**

(.10)(48) + 0x = (.08)(48 + x)

4.8 + 0x = 3.84 + .08x

.96 = .08x ---> 96 = 8x

x = 12

**Method
Let 48 gallon solution = A
Let water to be added = B

A + B = Total volume of resultant solution

(A's Concentration)(A's Volume) + (B's Concentration)(B's Volume) = (Desired Concentration)(Total Volume of resultant solution)
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Re: A 48 gallon solution of salt and water is 10% salt. How many gallons  [#permalink]

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snorkeler wrote:
N1*V1=N2*V2

10*48 = 8*V2

V2=60 --> 60-48 = 12

can we use this formula in the below question

https://gmatclub.com/forum/how-many-lit ... ml#p903692
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Re: A 48 gallon solution of salt and water is 10% salt. How many gallons  [#permalink]

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Bunuel wrote:
A 48 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?

A. 8
B. 12
C. 13
D. 14
E. 16

Currently we have 0.1 x 48 = 4.8 gallons of salt. We can let the amount of water added = y; thus:

4.8/(48 + y) = 8/100

4.8(100) = 8(48 + y)

480 = 384 + 8y

96 = 8y

12 = y

Alternate Solution:

We have 48 gallons of a 10% solution. We will add x gallons of water (0% solution), which will yield (48 + x) gallons of an 8% solution. Putting this into an equation, we have:

48(0.10) + x(0.0) = (48 + x)(0.08)

4.8 = 0 = 3.84 + 0.08x

0.96 = 0.08x

96 = 8x

x = 12

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Re: A 48 gallon solution of salt and water is 10% salt. How many gallons  [#permalink]

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_________________ Re: A 48 gallon solution of salt and water is 10% salt. How many gallons   [#permalink] 15 Apr 2019, 01:01
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