When solving mixture questions, I often find it useful to sketch the solutions with the ingredients SEPARATED.

We have 3 grams of solution R, which is comprised of 8% liquid A
So, 8% of the 3 grams will be liquid A
8% of 3 = (0.08)(3) = 0.24
So, solution R consists of 0.24 grams of liquid A



We'll now ADD 7 grams of solution S, which is comprised of 18% liquid A
18% of 7 = (0.18)(7) = 1.26
So, solution S consists of 1.26 grams of liquid A



Liquid A accounts for what percent of the weight of the resulting solution?
When we combine the solutions BY PARTS, we get the following:


So, liquid A makes up 1.5 grams of the 10 grams in the resulting solution.
1.5/10 = 15/100 = 15%

Answer: C

Cheers,
Brent

RELATED VIDEO

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Solution

Here we are mixing two solutions R and S. the percentages of A in the two solutions are 8% and 18% respectively. So the resultant mixture will also contain liquid A. and it will also depend on the weights of R and S

We can write that %A in mixture = \(\frac{(3 * 8% + 7 *18%)}{(3 +7)}\) the result is almost equal to 15%. Hence 15% is the right answer.
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I chose Answer C, but it was considered wrong!

Why does it shows "E" as the correct answer,whereas,it should be "C". Answer is incorrect.

Fixed. Thanks for pointing that out.

Hope you find this forum informative and useful.


Regards,
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Thanks
.......Junayed

Another approach is to use the Weighted Averages formula:

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

The weight of the resulting solution is 10 grams (3 grams + 7 grams = 10 grams)

Solution R makes up 3/10 of the resulting solution.
Solution R is comprised of 8% liquid A

Solution S makes up 7/10 of the resulting solution.
Solution S is comprised of 18% liquid A

Apply the formula to get:
% liquid A in final solution = (3/10)(8) + (7/10)(18)
= 24/10 + 126/10
= 150/10
= 15%

Answer: C

Cheers,
Brent

RELATED VIDEO FROM MY COURSE

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Sandy, regarding: 3∗8/(3+7)

Shouldn't it be (3*0.8 + 0.18*7)/3+7

which would give (0.24 + 1.26)/10

= 1.5/10

= 0.15

= 15%

=(portion) * (percent) of A + (portion) * (percent) of B
= 3/(3+7) * .08 + 7/(3+7) * 0.18
= .024 + .126
= .15 = 15%


Other Method:

R(3)-----------------S(7)
8%----------x--------18%
x-8------------------18-x

18-x/x-8 = 3/7
x=15
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