How many liters of a 40% iodine solution need to be mixed with 35 lite

Question

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

BrentGMATPrepNow · Accepted Answer

One approach is to sketch the solutions with their components  separated .

Let's start with the 35 liters of 20% iodine solution:
 https://i1168.photobucket.com/albums/r500/GMATPrepNow/iod1_zpsf0bsrp7b.png 
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. 
 https://i1168.photobucket.com/albums/r500/GMATPrepNow/iod2_zpsrfwax55u.png 
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. 
 https://i1168.photobucket.com/albums/r500/GMATPrepNow/iod3_zpsb5mru95s.png

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

Answer: D

RELATED VIDEO
 https://www.youtube.com/watch?v=7Or9gzROsjQ

OptimusPrepJanielle · Answer

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

chetan2u · Answer

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

Carcass · Answer

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

Divyadisha · Answer

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

D is the answer

ravisinghal · Answer

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

Alex75PAris · Answer

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

gracie · Answer

let x=liters of 40% iodine solution needed
.4x+(.2)(35)=.35(x+35)
x=105 liters

Abhishek009 · Answer

Capture.PNG 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

BrentGMATPrepNow · Answer

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 =  (20) +  (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

Answer: D

RELATED VIDEO
 https://www.youtube.com/watch?v=B7J6lr_qBG4

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How many liters of a 40% iodine solution need to be mixed with 35 lite

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