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Math Expert V
Joined: 02 Sep 2009
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How many liters of a 40% iodine solution need to be mixed with 35 lite  [#permalink]

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How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 35% iodine solution?

A. 35
B. 49
C. 100
D. 105
E. 140

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Joined: 12 Sep 2015
Posts: 3778
Re: How many liters of a 40% iodine solution need to be mixed with 35 lite  [#permalink]

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Bunuel wrote:
How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 35% iodine solution?

A. 35
B. 49
C. 100
D. 105
E. 140

One approach is to sketch the solutions with their components separated. 20% of 35 liters = 7 liters, so the original solution contains 7 liters of iodine.

To this solution, we'll add x liters of the solution that's 40% iodine. 40% of x liters = 0.4x liters. So, we're adding 0.4x liters of iodine.

When we combine the two solutions, it's easy to see how the resulting mixture looks, since we need only add the volumes of iodine in each solution. As you can see, our resulting mixture has a TOTAL volume of 35 + x liters.
We can also see that the resulting mixture contains 7 + 0.4x liters of iodine.
Since the resulting mixture must by 35% (aka 35/100) iodine, we can write the following equation:
(7 + 0.4x)/(35 + x liters) = 35/100
First simplify 35/100 to get: (7 + 0.4x)/(35 + x liters) = 7/20
Cross multiply to get: 20(7 + 0.4x) = 7(35 + x liters)
Expand: 140 + 8x = 245 + 7x
Solve: x = 105

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Math Expert V
Joined: 02 Aug 2009
Posts: 7742
Re: How many liters of a 40% iodine solution need to be mixed with 35 lite  [#permalink]

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Bunuel wrote:
How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 35% iodine solution?

A. 35
B. 49
C. 100
D. 105
E. 140

These Qs are best done with weighted Average method....

Two solutions - x of 40% and 35 of 20% results in a solution of 35% solution..

SO ratio = $$\frac{QTY- of- 40}{Qty- of- 20%} =\frac{35-20}{40-35} = \frac{15}{5}.....$$
so $$\frac{x}{35} = \frac{15}{5} = 3..................x = 35*3 = 105$$

D
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SVP  B
Joined: 06 Nov 2014
Posts: 1877
Re: How many liters of a 40% iodine solution need to be mixed with 35 lite  [#permalink]

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Bunuel wrote:
How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 35% iodine solution?

A. 35
B. 49
C. 100
D. 105
E. 140

Solution 1:
Assume the iodine solution to be mixed = x lts.
Iodine = 0.4x lts, Water = 0.6x lts.

Solution 2: 35 liters of a 20% iodine solution
Iodine = 7 lts, Water = 28 lts.

Total iodine = 0.4x + 7
Total water = 0.6x + 28

The resultant is a 35% idoine solution.
Hence (0.4x + 7) / (x + 35) = 35/100
40x + 700 = 35x + 1225
5x = 525
x = 105 lts

Correct Option: D
Board of Directors D
Joined: 01 Sep 2010
Posts: 3360
Re: How many liters of a 40% iodine solution need to be mixed with 35 lite  [#permalink]

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2
A more straight approach

$$0.4X + 0.2 Y = 0.35X + 0.35 Y$$

$$0.05X = 0.15Y$$ AND our $$Y = 35$$

$$0.05X = 5.25$$

$$X = \frac{5.25}{0.05} = 105$$

D is the one
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GMAT 1: 660 Q49 V31 GPA: 3.98
Re: How many liters of a 40% iodine solution need to be mixed with 35 lite  [#permalink]

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Bunuel wrote:
How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 35% iodine solution?

A. 35
B. 49
C. 100
D. 105
E. 140

60% water solution mixed with 80% water solution to get 65% water solution.

Solution will be mixed in the ratio::-

x/35= 80-65/65-60
x/35= 15/5
x= 3*35= 105

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Intern  B
Joined: 12 Aug 2013
Posts: 46
Re: How many liters of a 40% iodine solution need to be mixed with 35 lite  [#permalink]

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D it will be

weighted avg concept :-

20 --------------------35-------------------40

qyantity of 20%/quantity of 40% = 40- 35/35-20

35/x = 5/15
x = 105
Director  S
Joined: 21 Mar 2016
Posts: 518
Re: How many liters of a 40% iodine solution need to be mixed with 35 lite  [#permalink]

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Bunuel wrote:
How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 35% iodine solution?

A. 35
B. 49
C. 100
D. 105
E. 140

60% water solution mixed with 80% water solution to get 65% water solution.

Solution will be mixed in the ratio::-

x/35= 80-65/65-60
x/35= 15/5
x= 3*35= 105

Hi, Divyadisha ,, may i knw how did u get that formula
Director  S
Joined: 21 Mar 2016
Posts: 518
Re: How many liters of a 40% iodine solution need to be mixed with 35 lite  [#permalink]

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chetan2u wrote:
Bunuel wrote:
How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 35% iodine solution?

A. 35
B. 49
C. 100
D. 105
E. 140

These Qs are best done with weighted Average method....

Two solutions - x of 40% and 35 of 20% results in a solution of 35% solution..

SO ratio = $$\frac{QTY- of- 40}{Qty- of- 20%} =\frac{35-20}{40-35} = \frac{15}{5}.....$$
so $$\frac{x}{35} = \frac{15}{5} = 3..................x = 35*3 = 105$$

D

hi chetan2u can u plz explain tat formula,
Manager  B
Joined: 16 Mar 2016
Posts: 126
Location: France
GMAT 1: 660 Q47 V33 GPA: 3.25
Re: How many liters of a 40% iodine solution need to be mixed with 35 lite  [#permalink]

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If x is the number of liter of the 40% iodine solution, we have :
0.4 *x + 0.2 * 35 = 0.35 ( 35 + x)
0.4 *x + 0.2 * 35 = 0.35 * 35 + 0.35 * x
0.05 * x = 35 (0.35 - 0.2)
0.05 * x = 35 * 0.15
x = 35 * 3 = 105
VP  P
Joined: 07 Dec 2014
Posts: 1199
Re: How many liters of a 40% iodine solution need to be mixed with 35 lite  [#permalink]

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let x=liters of 40% iodine solution needed
.4x+(.2)(35)=.35(x+35)
x=105 liters
Board of Directors P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4501
Location: India
GPA: 3.5
Re: How many liters of a 40% iodine solution need to be mixed with 35 lite  [#permalink]

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Bunuel wrote:
How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 35% iodine solution?

A. 35
B. 49
C. 100
D. 105
E. 140

Attachment: Capture.PNG [ 4.45 KiB | Viewed 4906 times ]

35% ----> 7 + 0.4x
100%---->$$\frac{(7 + 0.4x)}{35} *100$$ = $$\frac{(7 + 0.4x)}{7}*20$$

Or, $$\frac{(140 + 8x)}{7}$$ = 35 + x

Or, 140 + 8x = 245 + 7x

Or, x = 245 - 140

Or, x = 105

Hence answer will be (D) 105
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CEO  V
Joined: 12 Sep 2015
Posts: 3778
Re: How many liters of a 40% iodine solution need to be mixed with 35 lite  [#permalink]

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Top Contributor
Bunuel wrote:
How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 35% iodine solution?

A. 35
B. 49
C. 100
D. 105
E. 140

Another approach is to use Weighted Averages:

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

In this case, we have:
35% iodine = (proportion of 20% solution)(20% iodine ) + (proportion of 40% solution)(40% iodine)

To determine the proportions, let's let x = the volume of 40% solution needed
We already know we have 35 liters of 20% solution
This means the TOTAL volume = 35 + x
So, the proportion of 20% solution 35/(35 + x)
And the proportion of 40% solution x/(35 + x)

Plug these values into formula to get: 35 = [35/(35 + x)](20) + [x/(35 + x)](40)
Multiply both sides by (35 + x) to get: 35(35 + x) = (35)(20) + (x)(40)
Expand: 1225 + 35x = 700 + 40x
Subtract 700 from both sides: 525 + 35x = 40x
Subtract 35x from both sides: 525 = 5x
Solve: x = 105

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Director  V
Joined: 27 May 2012
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How many liters of a 40% iodine solution need to be mixed with 35 lite  [#permalink]

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1
Bunuel wrote:
How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 35% iodine solution?

A. 35
B. 49
C. 100
D. 105
E. 140

Dear Moderator,
Please change tag from " work/rate" to "mixture Problems ". Thank you.
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- Stne
Math Expert V
Joined: 02 Sep 2009
Posts: 55618
Re: How many liters of a 40% iodine solution need to be mixed with 35 lite  [#permalink]

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stne wrote:
Bunuel wrote:
How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 35% iodine solution?

A. 35
B. 49
C. 100
D. 105
E. 140

Dear Moderator,
Please change tag from " work/rate" to "mixture Problems ". Thank you.

_________________
Done. Thank you.
_________________ Re: How many liters of a 40% iodine solution need to be mixed with 35 lite   [#permalink] 15 Sep 2018, 05:31
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